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https://github.com/magic3007/cv-typst | https://raw.githubusercontent.com/magic3007/cv-typst/master/doc/skills.typ | typst | *Programming Languages and Softwares*: C/C++, Python, Golang, Rust, CUDA, Pytorch \
*Tech Skills*: Placement and Routing Algorithm Designs in VLSI CAD, High Performance Computing, GPU Acceleration using CUDA, Deep Learning Systems |
|
https://github.com/jgm/typst-hs | https://raw.githubusercontent.com/jgm/typst-hs/main/test/typ/text/edge-02.typ | typst | Other | // Error: 24-26 expected "ascender", "cap-height", "x-height", "baseline", "descender", or length
#set text(bottom-edge: "")
|
https://github.com/polarkac/MTG-Stories | https://raw.githubusercontent.com/polarkac/MTG-Stories/master/stories/048_Dominaria%20United.typ | typst | #import "@local/mtgset:0.1.0": conf
#show: doc => conf("Dominaria United", doc)
#include "./048 - Dominaria United/001_Episode 1: Echoes In The Dark.typ"
#include "./048 - Dominaria United/002_Episode 2: Sand in the Hourglass.typ"
#include "./048 - Dominaria United/003_Episode 3: The Locked Tower.typ"
#include "./048 - Dominaria United/004_Homecoming.typ"
#include "./048 - Dominaria United/005_Episode 4: A Brutal Blow.typ"
#include "./048 - Dominaria United/006_The Education of Ulf.typ"
#include "./048 - Dominaria United/007_Death and Salvation.typ"
#include "./048 - Dominaria United/008_Faith in Birds.typ"
#include "./048 - Dominaria United/009_Shards of Nightmares.typ"
#include "./048 - Dominaria United/010_Episode 5: A Whisper in the Wind.typ"
|
|
https://github.com/jneug/typst-mantys | https://raw.githubusercontent.com/jneug/typst-mantys/main/src/api.typ | typst | MIT License |
#import "@preview/t4t:0.3.2": is, alias
#import "./mty.typ"
#import "./mty.typ": idx, make-index, module, package, lineref
#import "./theme.typ"
/// === Describing arguments and values <describing-arguments>
/// Highlight an argument name.
/// #shortex(`#meta[variable]`)
///
/// - name (string, content): Name of the argument.
/// -> content
#let meta( name ) = mty.rawc(theme.colors.argument, {sym.angle.l + name + sym.angle.r})
//#let meta = mty.rawc.with(theme.colors.argument)
/// Shows #arg[value] as content.
/// - #shortex(`#value("string")`)
/// - #shortex(`#value([string])`)
/// - #shortex(`#value(true)`)
/// - #shortex(`#value(1.0)`)
/// - #shortex(`#value(3em)`)
/// - #shortex(`#value(50%)`)
/// - #shortex(`#value(left)`)
/// - #shortex(`#value((a: 1, b: 2))`)
///
/// - value (any): Value to show.
/// -> content
#let value( value ) = {
if is.str(value) and value.contains("=>") {
return mty.rawc(theme.colors.value, value)
} else if mty.is-choices(value) or mty.is-func(value) or mty.is-lambda(value) {
return value
} else {
return mty.rawc(theme.colors.value, repr(value))
}
}
#let _v = value
/// Highlights the default value of a set of #cmd[choices].
/// - #shortex(`#default("default-value")`)
/// - #shortex(`#default(true)`)
/// - #shortex(`#choices(1, 2, 3, 4, default: 3)`)
///
/// - value (any): The value to highlight.
/// -> content
#let default( value ) = mty.add-mark(<default>, underline(_v(value), offset:0.2em, stroke:1pt+theme.colors.value))
#let _d = default
/// Create a link to the reference documentation at #link("https://typst.app/docs/reference/").
/// #example[```
/// See the #doc("meta/locate") function.
/// ```]
///
/// - target (string): Path to the subpage of `https://typst.app/docs/reference/`.
/// The `lowercase` command for example is located in the category `text` and
/// has #arg(target: "text/lowercase").
/// - name (string): Optional name for the link. With #value(auto), the #arg[target]
/// is split on `/` and the last part is used.
/// - anchor (string): An optional HTML page anchor to append to the link.
/// - fnote (boolean): Show the reference link in a footnote.
/// -> content
#let doc( target, name:none, anchor:none, fnote:false ) = {
if name == none {
name = target.split("/").last()
}
let url = "https://typst.app/docs/reference/" + target
if mty.is.not-empty(anchor) {
url += "#" + anchor
}
link(url, mty.rawi(name))
if fnote {
footnote(link(url))
}
}
/// Adds a custom type to link to a type definition in the manual.
///
/// - name (string): Name for the new type.
/// - target (str, label, location, dictionary): Target to link the type to. Can be anything the #doc("link") function accepts.
/// - color (color): A color for the type.
#let add-type( name, target:none, color:theme.colors.dtypes.type) = {
state("@mty-custom-types").update(types => {
let t = types
if not mty.is.dict(types) {
t = (:)
}
t.insert(name, (name: name, target: target, color: color))
t
})
}
/// Shows a highlightd data type with a link to the reference page.
///
/// #arg[t] may be any value to pass to #doc("foundations/type") to get the type or a #dtype("string") with the name of a datatype. To show the `string` type, use #raw(lang:"typ", `#dtype("string")`.text). To force the parsing of the values type, set #arg(parse-type: true).
/// - #shortex(`#dtype("int")`)
/// - #shortex(`#dtype(1)`)
/// - #shortex(`#dtype(1deg)`)
/// - #shortex(`#dtype(true)`)
/// - #shortex(`#dtype(())`)
/// - #shortex(`#dtype(red)`)
/// Custom types can be added with @@add-type.
///
/// - type (any): Either a value to take the type from or a string with the dataype name.
/// - fnote (boolean): If #value(true), the reference lin kis shown in a footnote.
/// - parse-type (boolean): If #arg[t] should always be passed to #doc("foundations/type").
/// -> content
#let dtype( type, fnote:false, parse-type:false ) = {
if mty.not-is-func(type) and mty.not-is-lambda(type) {
if parse-type or alias.type(type) != "string" {
type = str(alias.type(type))
}
}
// some type mappings
if is.str(type) {
type = (
"integer": "int", "boolean": "bool", "dict": "dictionary", "arr": "array", "string": "str"
).at(type, default:type)
}
context {
let custom-types = state("@mty-custom-types", ()).final()
let color = auto
let d = none
if mty.is-func(type) {
d = doc("foundations/function", fnote:fnote)
type = "function"
} else if mty.is-lambda(type) or type.contains("=>") {
d = doc("foundations/function", name:type, fnote:fnote)
type = "function"
} else if type == "any" {
d = doc("foundations", name:"any", fnote:fnote)
} else if type.ends-with("alignment") {
d = doc("layout/alignment", name:type, fnote:fnote)
} else if type == "location" {
d = doc("introspection/" + type, fnote:fnote)
} else if type in ("angle", "direction", "fraction", "length", "ratio", "relative") {
d = doc("layout/" + type, fnote:fnote)
} else if type in ("array", "bool", "bytes", "content", "datetime", "dictionary", "duration", "float", "function", "int", "label", "plugin", "regex", "selector", "str", "type", "version") {
d = doc("foundations/" + type, fnote:fnote)
} else if type in ("color", "stroke") {
d = doc("visualize/" + type, fnote:fnote)
} else {
if type in custom-types {
if not mty.is-none(custom-types.at(type).target) {
d = link(custom-types.at(type).target, mty.rawi(type))
} else {
d = mty.rawi(type)
}
if not mty.is-none(custom-types.at(type).color) {
color = custom-types.at(type).color
}
} else {
d = mty.rawi(type)
}
}
if mty.is-auto(color) {
color = theme.colors.dtypes.at(type, default: theme.colors.dtypes.type)
}
box(fill: color, radius:2pt, inset: (x: 4pt, y:0pt), outset:(y:2pt), d)
}
}
/// Shows a list of datatypes.
/// - #shortex(`#dtypes(false, "integer", (:))`)
/// - ..types (any): List of values to get the type for or strings with datatype names.
/// -> content
#let dtypes( ..types, sep: box(inset:(left:1pt,right:1pt), sym.bar.v)) = {
types.pos().map(dtype.with(fnote:false)).join(sep)
}
/// Shows an argument, either positional or named. The argument name is highlighted with #cmd-[meta] and the value with #cmd-[value].
///
/// - #shortex(`#arg[name]`)
/// - #shortex(`#arg("name")`)
/// - #shortex(`#arg(name: "value")`)
/// - #shortex(`#arg("name", 5.2)`)
///
/// - ..args (any): Either an argument name (#dtype("string")) or a (`name`: `value`) pair either as a named argument or as exactly two positional arguments.
/// -> content
#let arg(..args) = {
let a = none
if args.pos().len() == 1 {
a = meta(mty.get.text(args.pos().first()))
} else if args.named() != (:) {
a = {
meta(args.named().keys().first())
mty.rawi(sym.colon + " ")
_v(args.named().values().first())
}
} else if args.pos().len() == 2 {
a = {
meta(args.pos().first())
mty.rawi(sym.colon + " ")
_v(args.pos().at(1))
}
} else {
panic("Wrong argument count. Got " + repr(args.pos()))
return
}
mty.add-mark(<arg>, a)
}
/// Shows a body argument.
/// #ibox(width:100%)[
/// Body arguments are positional arguments that can be given
/// as a separat content block at the end of a command.
/// ]
/// - #shortex(`#barg[body]`)
///
/// - name (string): Name of the argument.
/// -> content
#let barg( name ) = {
let b = {
mty.rawi(sym.bracket.l)
meta(mty.get.text(name))
mty.rawi(sym.bracket.r)
}
mty.mark-body(b)
}
/// Shows an argument sink.
/// - #shortex(`#sarg[args]`)
///
/// - name (string): Name of the argument.
/// -> content
#let sarg( name ) = {
let s = ".." +meta( mty.get.text(name))
mty.mark-sink(s)
}
/// Creates a list of arguments from a set of positional and/or named arguments.
///
/// #dtype("string")s and named arguments are passed to #cmd-[arg], while #dtype("content")
/// is passed to #cmd-[barg].
/// The result is to be unpacked as arguments to #cmd-[cmd].
/// #example[```
/// #cmd( "conditional-show", ..args(hide: false, [body]) )
/// ```]
/// - ..args (any): Either an argument name (#dtype("string")) or a (`name`: `value`) pair either as a named argument or as exactly two positional arguments.
/// -> array
#let args( ..args ) = {
let arguments = args.pos().filter(mty.is.str).map(arg)
arguments += args.pos().filter(mty.is.content).map(barg)
arguments += args.named().pairs().map(v => arg(v.at(0), v.at(1)))
arguments
}
/// Shows a list of choices possible for an argument.
///
/// If #arg[default] is set to something else than #value("__none__"), the value
/// is highlighted as the default choice. If #arg[default] is already given in
/// #arg[values], the value is highlighted at its current position. Otherwise
/// #arg[default] is added as the first choice in the list.
/// - #shortex(`#choices(left, right, center)`)
/// - #shortex(`#choices(left, right, center, default:center)`)
/// - #shortex(`#choices(left, right, default:center)`)
/// - #shortex(`#arg(align: choices(left, right, default:center))`)
/// -> content
#let choices( default: "__none__", ..values ) = {
let list = values.pos().map(_v)
if default != "__none__" {
if default in values.pos() {
let pos = values.pos().position(v => v == default)
list.at(pos) = _d(default)
} else {
list.insert(0, _d(default))
}
}
mty.add-mark(<arg-choices>, list.join(box(inset:(left:1pt,right:1pt), sym.bar.v)))
}
#let content( name ) = {
mty.mark-lambda( "" + name )
}
/// Shows a Typst reserved symbol argument.
/// - #shortex(`#symbol("dot")`)
/// - #shortex(`#symbol("angle.l", module:"sym")`)
/// - #shortex(`#arg(format: symbol("angle.l", module:"sym"))`)
/// -> content
#let symbol( name, module: none ) = {
let full-name = if mty.is.not-none(module) {
mty.module(module) + `.` + mty.rawc(theme.colors.command, name)
} else {
mty.rawc(theme.colors.command, name)
}
mty.mark-lambda(full-name)
}
/// Create a function argument.
/// Function arguments may be used as an argument value with #cmd-[arg].
/// - #shortex(`#func("func")`)
/// - #shortex(`#func("clamp", module:"calc")`)
/// - #shortex(`#arg(format: func("upper"))`)
#let func( name, module: none ) = {
if type(name) == "function" {
name = repr(name)
}
let full-name = if mty.is.not-none(module) {
mty.module(module) + `.` + mty.rawc(theme.colors.command, name)
} else {
mty.rawc(theme.colors.command, name)
}
mty.mark-func(emph(mty.rawi(sym.hash) + full-name))
}
/// Create a lambda function argument.
/// Lambda arguments may be used as an argument value with #cmd-[arg].
/// To show a lambda function with an argument sink, prefix the type with two dots.
/// - #shortex(`#lambda("integer", "boolean", ret:"string")`)
/// - #shortex(`#lambda("..any", ret:"boolean")`)
/// - #shortex(`#arg(format: lambda("string", ret:"content"))`)
/// -> content
#let lambda( ..args, ret:none ) = {
args = args.pos().map(v => {
if v.starts-with("..") {
".." + dtype(v.slice(2))
} else {
dtype(v)
}
})
if mty.is.arr(ret) and ret.len() > 0 {
ret = sym.paren.l + ret.map(dtype).join(",") + if ret.len() == 1 {","} + sym.paren.r
} else if mty.is.dict(ret) and ret.len() > 0 {
ret = sym.paren.l + ret.pairs().map(pair => {sym.quote + pair.first() + sym.quote + sym.colon + dtype(pair.last())}).join(",") + sym.paren.r
} else {
ret = dtype(ret)
}
mty.mark-lambda(sym.paren.l + args.join(",") + sym.paren.r + " => " + ret )
}
/// === Describing commands <describing-commands>
/// Renders the command #arg[name] with arguments and adds an entry with
/// #arg(kind:"command") to the index.
///
/// #arg[args] is a collection of positional arguments created with #cmd[arg],
/// #cmd[barg] and #cmd[sarg].
///
/// All positional arguments will be rendered first, then named arguments
/// and all body arguments will be added after the closing paranthesis.
///
/// - #shortex(`#cmd("cmd", arg[name], sarg[args], barg[body])`)
/// - #shortex(`#cmd("cmd", ..args("name", [body]), sarg[args])`)
///
/// - name (string): Name of the command.
/// - module (string): Name of a module, the command belongs to.
/// - ret (any): Returned type.
/// - index (boolean): Whether to add an index entry.
/// - unpack (boolean): If #value(true), the arguments are shown in separate lines.
/// - ..args (any): Arguments for the command, created with the argument commands above or @@args.
/// -> content
#let cmd(name, module:none, ret:none, index:true, unpack:false, ..args) = {
if index {
mty.idx(kind:"cmd", hide:true)[#mty.rawi(sym.hash)#mty.rawc(theme.colors.command, name)]
}
mty.rawi(sym.hash)
if mty.is.not-none(module) {
mty.module(module) + `.`
} else {
// raw("", lang:"cmd-module")
mty.place-marker("cmd-module")
}
mty.rawc(theme.colors.command, name)
let fargs = args.pos().filter(mty.not-is-body)
let bargs = args.pos().filter(mty.is-body)
if unpack == true or (unpack == auto and fargs.len() >= 5) {
mty.rawi(sym.paren.l) + [\ #h(1em)]
fargs.join([`,`\ #h(1em)])
[\ ] + mty.rawi(sym.paren.r)
} else {
mty.rawi(sym.paren.l)
fargs.join(`, `)
mty.rawi(sym.paren.r)
}
bargs.join()
if ret != none {
ret = (ret,).flatten()
box(inset:(x:2pt), sym.arrow.r)//mty.rawi("->"))
dtypes(..ret)
}
}
/// Same as @@cmd, but does not create an index entry.
#let cmd- = cmd.with(index:false)
/// Shows the option #arg[name] and adds an entry with #arg(kind:"option")
/// to the index.
/// - #shortex(`#opt[examples-scope]`)
///
/// - name (string, content): Name of the option.
/// - index (boolean): Whether to create an index entry.
/// - clr (color): A color
/// -> content
#let opt(name, index:true, clr:blue) = {
if index {
mty.idx(kind:"option")[#mty.rawc(theme.colors.option, name)]
} else {
mty.rawc(theme.colors.option, name)
}
}
/// Same as @@opt, but does not create an index entry.
#let opt- = opt.with(index:false)
/// Shows the variable #arg[name] and adds an entry to the index.
/// - #shortex(`#var[colors]`)
/// -> content
#let var( name ) = {
mty.rawi(sym.hash)
mty.rawc(theme.colors.command, name)
}
/// Same as @@var, but does not create an index entry.
#let var- = var
/// Creates a label for the command with name #arg[name].
///
/// - name (string): Name of the command.
/// - module (string): Optional module name.
/// -> label
#let cmd-label( name, module: "" ) = label(module + name + "()")
/// Creates a label for the variable with name #arg[name].
///
/// - name (string): Name of the variable.
/// - module (string): Optional module name.
/// -> label
#let var-label( name, module: "" ) = label(module + name)
#let __s_mty_command = state("@mty-command", none)
/// Displays information of a command by formatting the name, description and arguments.
/// See this command description for an example.
///
/// - name (string): Name of the command.
/// - label (string): Custom label for the command. Defaults to #value(auto).
/// - ..args (content): List of arguments created with the argument functions like @@arg.
/// - body (content): Description for the command.
/// -> content
#let command(name, label:auto, ..args, body) = [
#__s_mty_command.update(name)
#block(
below: 0.65em,
above: 1.3em,
text(weight:600)[#cmd(name, unpack:auto, ..args)<cmd>]
)
#block(inset:(left:1em), spacing: 0pt, breakable:true, body)#cmd-label(mty.def.if-auto(name, label))
#__s_mty_command.update(none)
// #v(.65em, weak:true)
]
/// Displays information for a variable defintion.
/// #example[```
/// #variable("primary", types:("color",), value:green)[
/// Primary color.
/// ]
/// ```]
///
/// - name (string): Name of the variable.
/// - types (array): Array of types to be passed to @@dtypes.
/// - value (any): Default value.
/// - body (content): Description of the variable.
/// -> content
#let variable( name, types:none, value:none, label:auto, body ) = [
#set terms(hanging-indent: 0pt)
#set par(first-line-indent:0.65pt, hanging-indent: 0pt)
/ #var(name)#{if value != none {" " + sym.colon + " " + _v(value)}}#{if types != none {h(1fr) + dtypes(..types)}}<var>: #block(inset:(left:2em), body)#var-label(mty.def.if-auto(name, label))
]
/// Displays information for a command argument.
/// See the argument list below for an example.
///
/// - name (string): Name of the argument.
/// - is-sink (boolean): If this is a sink argument.
/// - types (array): Array of types to be passed to @@dtypes.
/// - choices (array): Optional array of valid values for this argument.
/// - default (any): Optional default value for this argument.
/// - body (content): Description of the argument.
/// -> content
#let argument(
name,
is-sink: false,
types: none,
choices: none,
default: "__none__",
body
) = {
types = (types,).flatten()
v(.65em)
block(
above: .65em,
stroke:.75pt + theme.colors.muted,
inset: (top:10pt, left: -1em + 8pt, rest:8pt),
outset: (left: 1em),
radius: 2pt, {
place(top+left, dy: -15.5pt, dx: 5.75pt,
box(inset:2pt, fill:white,
text(size:.75em, font:theme.fonts.sans, theme.colors.muted, "Argument")
)
)
if is-sink {
sarg(name)
} else if default != "__none__" {
arg(..mty.get.dict(name, default))
} else {
arg(name)
}
h(1fr)
if mty.is.not-none(types) { dtypes(..types) } else if default != "__none__" { dtype(default) }
block(width:100%, below: .65em, inset:(x:.75em), body)
})
}
/// A wrapper around @@command calls that belong to an internal module.
/// The module name is displayed as a prefix to the command name.
/// #example[```
/// #module-commands("mty")[
/// #command("rawi")[
/// Shows #arg[code] as inline #doc("text/raw") text (with #arg(block: false)).
/// ]
/// ]
/// ```]
///
/// - module (string): Name of the module.
/// - body (content): Content with @@command calls.
/// -> content
#let module-commands(module, body) = [
// #let add-module = (c) => {
// mty.marginnote[
// #mty.module(module)
// #sym.quote.angle.r.double
// ]
// c
// }
// #show <cmd>: add-module
// #show <var>: add-module
// #show raw.where(lang:"cmd-module"): (it) => mty.module(module) + mty.rawi(sym.dot.basic)
#show <cmd>: (it) => {
show mty.marker("cmd-module"): (it) => {
mty.module(module) + mty.rawi(sym.dot.basic)
}
it
}
#body
]
/// Creates a selector for a command label.
///
/// - name (string): Name of the command.
/// -> selector
#let cmd-selector(name) = selector(<cmd>).before(cmd-label(name))
/// Creates a reference to a command label.
///
/// - name (string): Name of the command.
/// - module (string): Optional module name.
/// - format (function): Function of #lambda("string", "location", ret:"content") to format the reference. The first argument is the name of the command (the same as #arg[name]) and the second is the location of the referenced label.
/// -> content
#let cmdref(name, module: none, format: (name, loc) => [command #cmd(name) on #link(loc)[page #loc.page()]]) = if module != none {
// TODO use module in reference
} else {
link(cmd-label(name), cmd-(name))
}
// locate(loc => {
// let res = query(cmd-selector(name), loc)
// if res == () {
// panic("No label <" + str(cmd-label(name)) + "> found.")
// } else {
// let e = res.last()
// format(name, e.location())
// }
// })
/// Creats a relative reference showing the text "above" or "below".
/// - #shortex(`#relref(cmd-label("meta"))`)
/// - #shortex(`#relref(cmd-label("shortex"))`)
///
/// - label (label): The label to reference.
/// -> content
#let relref( label ) = locate(loc => {
let q = query(selector(label).before(loc), loc)
if q != () {
return link(q.last().location(), "above")
} else {
q = query(selector(label).after(loc), loc)
}
if q != () {
return link(q.first().location(), "below")
} else {
panic("No label " + str(label) + " found.")
}
})
#let update-examples-scope( imports ) = {
state("@mty-imports-scope").update(imports)
}
// #let example(..args) = state("@mty-example-imports").display(
// (imports) => mty.code-example(scope: imports, ..args)
// )
#let example(scope:(:), ..args) = if scope == none {
mty.code-example(scope: (:), ..args)
} else {
state("@mty-imports-scope").display(
(imports) => mty.code-example(scope: imports + scope, ..args)
)
}
#let side-by-side = example.with(side-by-side:true)
#let shortex( code, sep: sym.arrow.r, mode:"markup", scope:(:) ) = state("@mty-imports-scope").display(
(imports) => [#raw(code.text, lang:"typ") #sep #eval(code.text, mode:"markup", scope:imports + scope)]
)
#let sourcecode( title: none, file: none, ..args, code ) = {
let header = ()
if mty.is.not-none(title) {
header.push(text(fill:white, title))
}
if mty.is.not-none(file) {
header.push(h(1fr))
header.push(text(fill:white, emoji.folder) + " ")
header.push(text(fill:white, emph(file)))
}
mty.sourcecode(
frame: mty.frame.with(title: if header == () { "" } else { header.join() }),
..args,
code,
)
}
#let codesnippet = mty.sourcecode.with(frame: mty.frame, numbering: none)
#let ibox = mty.alert.with(color:theme.colors.info)
#let wbox = mty.alert.with(color:theme.colors.warning)
#let ebox = mty.alert.with(color:theme.colors.error)
#let sbox = mty.alert.with(color:theme.colors.success)
#let version( since:(), until:() ) = {
if is.not-empty(since) or is.not-empty(until) {
mty.marginnote(gutter: 1em, dy: 0pt, {
set text(size:.8em)
if is.not-empty(since) { [_since_ #text(theme.colors.secondary, mty.ver(..since))] }
if is.not-empty(since) and is.not-empty(until) { linebreak() }
if is.not-empty(until) { [until #text(theme.colors.secondary, mty.ver(..until))] }
})
}
}
#let __all__ = (
arg: arg,
args: args,
argument: argument,
add-type: add-type,
barg: barg,
choices: choices,
cmd-: cmd-,
cmd-label: cmd-label,
cmd-selector: cmd-selector,
cmd: cmd,
cmdref: cmdref,
codesnippet: codesnippet,
command: command,
content: content,
doc: doc,
dtype: dtype,
dtypes: dtypes,
default: default,
ebox: ebox,
// example: example,
func: func,
ibox: ibox,
idx: idx,
lambda: lambda,
lineref: lineref,
make-index: make-index,
meta: meta,
module-commands: module-commands,
module: module,
opt-: opt-,
opt: opt,
package: package,
relref: relref,
sarg: sarg,
sbox: sbox,
shortex: shortex,
side-by-side: side-by-side,
sourcecode: sourcecode,
symbol: symbol,
update-examples-scope: update-examples-scope,
value: value,
var-: var-,
var: var,
variable: variable,
version: version,
wbox: wbox,
)
|
https://github.com/RanolP/resume | https://raw.githubusercontent.com/RanolP/resume/main/modules/solved-ac.typ | typst | #import "components.typ": icon
#import "./util.typ": format-thousand
#let solve-tier-colors = (
Unrated: color.rgb("#2d2d2d"),
Bronze5: color.rgb("#9d4900"),
Bronze4: color.rgb("#a54f00"),
Bronze3: color.rgb("#ad5600"),
Bronze2: color.rgb("#b55d0a"),
Bronze1: color.rgb("#c67739"),
Silver5: color.rgb("#38546e"),
Silver4: color.rgb("#3d5a74"),
Silver3: color.rgb("#435f7a"),
Silver2: color.rgb("#496580"),
Silver1: color.rgb("#4e6a86"),
Gold5: color.rgb("#d28500"),
Gold4: color.rgb("#df8f00"),
Gold3: color.rgb("#ec9a00"),
Gold2: color.rgb("#f9a518"),
Gold1: color.rgb("#ffb028"),
Platinum5: color.rgb("#00c78b"),
Platinum4: color.rgb("#00d497"),
Platinum3: color.rgb("#27e2a4"),
Platinum2: color.rgb("#3ef0b1"),
Platinum1: color.rgb("#51fdbd"),
Diamond5: color.rgb("#009ee5"),
Diamond4: color.rgb("#00a9f0"),
Diamond3: color.rgb("#00b4fc"),
Diamond2: color.rgb("#2bbfff"),
Diamond1: color.rgb("#41caff"),
Ruby5: color.rgb("#e0004c"),
Ruby4: color.rgb("#ea0053"),
Ruby3: color.rgb("#f5005a"),
Ruby2: color.rgb("#ff0062"),
Ruby1: color.rgb("#ff3071"),
Master: color.rgb("#b491ff"),
)
#let solved-ac-tier-map = (
"Unrated",
..("Bronze", "Silver", "Gold", "Platinum", "Diamond", "Ruby").map(tier => range(5, 0, step: -1).map(num => (
tier + str(num)
))).fold((), (acc, curr) => (..acc, ..curr)),
"Master",
)
#let solved-ac-profile(handle) = {
[#metadata(handle) <solved-ac-user>]
let user-db = json("../assets/.automatic/solved/user.json")
if user-db.at(handle, default: none) != none {
let user = user-db.at(handle)
let tier-color = solve-tier-colors.at(solved-ac-tier-map.at(user.solveTier))
[
#icon(
"solved-ac/arena-tier-" + str(user.arenaTier),
height: 0.7em,
width: auto,
bottom: 0em,
) /
#icon(
"solved-ac/solve-tier-" + str(user.solveTier),
width: auto,
bottom: -1em / 4,
)
#text(
fill: tier-color,
weight: 700,
)[
#handle#super[\##{
user.rank
}, top #{ calc.round(user.topPercent, digits: 2) }%]
]
#text(
fill: tier-color.darken(40%),
size: 0.75em,
)[(#format-thousand(user.solvedCount) solve)]
]
} else {
text(fill: color.rgb("#ff0000"))[\#NO_SOLVED_USER_DATA\#]
}
}
#let solved-ac-profile-short(handle) = {
[#metadata(handle) <solved-ac-user>]
let user-db = json("../assets/.automatic/solved/user.json")
if user-db.at(handle, default: none) != none {
let user = user-db.at(handle)
let tier-color = solve-tier-colors.at(solved-ac-tier-map.at(user.solveTier))
[
#handle#super[
#set text(size: 1.5em)
#icon(
"solved-ac/solve-tier-" + str(user.solveTier),
width: auto,
bottom: -1em / 4,
) $and$
#icon(
"solved-ac/arena-tier-" + str(user.arenaTier),
height: 0.7em,
width: auto,
bottom: 0em,
)
]
]
} else {
text(fill: color.rgb("#ff0000"))[\#NO_SOLVED_USER_DATA\#]
}
}
|
|
https://github.com/choglost/LessElegantNote | https://raw.githubusercontent.com/choglost/LessElegantNote/main/layouts/mainmatter.typ | typst | MIT License | #import "@preview/i-figured:0.2.4"
#import "@preview/codly:0.2.1": *
#import "../utils/style.typ": 字号, 字体
#import "../utils/custom-numbering.typ": custom-numbering
#import "../utils/custom-heading.typ": heading-display, active-heading, current-heading
#import "../utils/indent.typ": fake-par
#import "../utils/unpairs.typ": unpairs
#let mainmatter(
// documentclass 传入参数
twoside: false,
info :(:),
// 其他参数
theme-color: rgb("3C71BF"),// 主题色，包括标题、strong类型强调的颜色
// 正文相关
text-font: 字体.宋体,
text-size: 字号.五号,
par-leading: 0.7em,// 行距
par-spacing: 0.7em,// 段间距
// 特殊类型文本
strong-font: 字体.黑体,
// 标题相关
heading-font: (字体.黑体, 字体.黑体, 字体.黑体, 字体.黑体),// 标题字体
heading-size: (字号.三号, 字号.四号, 字号.五号, 字号.五号),
heading-weight: ("regular", "regular", "regular", ),
heading-above: (2em, 1.5em, 1em, 0.7em),
heading-below: (2em, 1.5em, 1em, 0.7em), // 标题下方
heading-pagebreak: (true, false), // 标题换页
heading-align: (center, auto), // 标题居中
heading-fill: (black,), // 标题颜色
// 页眉相关
header-render: auto,
display-header: false,
skip-on-first-level: true,
stroke-width: 0.5pt,
reset-footnote: false,
..args,
it,
) = {
// 默认参数
info = (
numbering-style: "literature",
) + info
// 处理 heading- 开头的其他参数
heading-fill = (theme-color,)
let heading-text-args-lists = args.named().pairs().filter(pair => pair.at(0).starts-with("heading-")).map(pair => (
pair.at(0).slice("heading-".len()),
pair.at(1),
))
// 辅助函数
let array-at(arr, pos) = {
arr.at(calc.min(pos, arr.len()) - 1)
}
// 文本和段落样式
set text(font: text-font, size: text-size)
set par(leading: par-leading, justify: true, first-line-indent: 2em)
show par: set block(spacing: par-spacing)
// 特殊类型文本
// 代码块
show: codly-init.with()
codly(display-name: false)
// set block(width: 60%)
show raw: it => {
set text(font: 字体.等宽)
it
}
show emph: it => {
set text(weight: "bold")
// show: show-cn-fakebold // 伪加粗
it
}
show strong: it => {
set text(font: strong-font, theme-color)
it
}
// 设置脚注
show footnote.entry: set text(font: 字体.宋体, size: 字号.五号)
// 设置 equation 的编号和假段落首行缩进
show math.equation.where(block: true): i-figured.show-equation
// 设置 figure 的编号，表格表头置顶 + 不用冒号用空格分割 + 样式
show heading: i-figured.reset-counters
show figure: i-figured.show-figure
show figure.where(kind: table): set figure.caption(position: top)
set figure.caption(separator: " ")
show figure.caption: set text(font: 字体.宋体, size: 字号.小五)
// 处理标题
// 设置标题的 numbering
set heading(numbering: custom-numbering.with(style: info.numbering-style))
// counter(heading).update(0)
show heading: it => {
// 设置字体字号
set text(
font: array-at(heading-font, it.level),
size: array-at(heading-size, it.level),
weight: array-at(heading-weight, it.level),
fill: array-at(heading-fill, it.level),
..unpairs(heading-text-args-lists.map(pair => (pair.at(0), array-at(pair.at(1), it.level)))),
)
set block(above: array-at(heading-above, it.level), below: array-at(heading-below, it.level))
it
fake-par //加入假段落模拟首行缩进
}
// 标题居中与自动换页
show heading: it => {
if (array-at(heading-pagebreak, it.level)) {
// 如果打上了 no-auto-pagebreak 标签，则不自动换页
if ("label" not in it.fields() or str(it.label) != "no-auto-pagebreak") {
pagebreak(weak: true)
}
}
if (array-at(heading-align, it.level) != auto) {
set align(array-at(heading-align, it.level))
it
} else {
it
}
}
// 处理列表
// 无序列表 list
set list(indent: 1.3em, body-indent: 0.4em) //marker: ("•","·")
show list: it => {
set block(above: 0.7em, below: 0.7em)
it
fake-par
}
// 有序列表 enum
set enum(indent: 0.8em, body-indent: 0.4em, numbering: "1.")
show enum: it => {
set block(above: 0.7em, below: 0.7em)
it
fake-par
}
// 术语列表 terms
set terms(indent: 0em, hanging-indent: 2.65em)
show terms: it => {
set block(above: 0.7em, below: 0.7em)
it
fake-par
}
// 表格
set table(align: center + horizon)
// 处理页眉
set page(..(
if display-header {
(
header: {
// 重置 footnote 计数器
if reset-footnote {
counter(footnote).update(0)
}
locate(loc => {
// 5.1 获取当前页面的一级标题
let cur-heading = current-heading(level: 1, loc)
// 5.2 如果当前页面没有一级标题，则渲染页眉
if not skip-on-first-level or cur-heading == none {
if header-render == auto {
// 一级标题和二级标题
let first-level-heading = if not twoside or calc.rem(loc.page(), 2) == 0 {
heading-display(active-heading(level: 1, loc))
} else {
""
}
let second-level-heading = if not twoside or calc.rem(loc.page(), 2) == 2 {
heading-display(active-heading(level: 2, prev: false, loc))
} else {
""
}
set text(font: 字体.楷体, size: 字号.五号)
stack(
first-level-heading + h(1fr) + second-level-heading,
v(0.25em),
if first-level-heading != "" or second-level-heading != "" {
line(length: 100%, stroke: stroke-width + black)
},
)
} else {
header-render(loc)
}
v(0em) // header-vspace
}
})
},
)
} else {
(
header: {
// 重置 footnote 计数器
if reset-footnote {
counter(footnote).update(0)
}
},
)
}
))
// 处理页脚的页码
set page(footer: [
#align(center)[
#text(counter(page).display("1"))
]
])
counter(page).update(1)
it
} |
https://github.com/jgm/typst-hs | https://raw.githubusercontent.com/jgm/typst-hs/main/test/typ/visualize/path-03.typ | typst | Other | // Error: 7-31 point array must contain exactly two entries
#path(((0%, 0%), (0%, 0%, 0%)))
|
https://github.com/fenjalien/metro | https://raw.githubusercontent.com/fenjalien/metro/main/src/impl/angle.typ | typst | Apache License 2.0 | #import "/src/utils.typ": content-to-string, combine-dict
#import "/src/defs/units.typ": rad, arcminute, arcsecond
#import "num/num.typ"
#let default-options = (
angle-mode: "input",
angle-symbol-degree: sym.degree,
angle-symbol-minute: arcminute,
angle-symbol-second: arcsecond,
angle-separator: none,
number-angle-product: none
)
// The following is used for complex numbers
#let is-angle(ang) = {
let typ = type(ang)
return typ == angle or (typ == str and ang.ends-with(regex("deg|rad"))) or (typ == content and repr(ang.func()) == "sequence" and ang.children.last() in (math.deg, rad))
}
#let to-number(ang) = {
let typ = type(ang)
return if typ == angle {
ang
} else if typ == str {
float(ang.slice(0, ang.len() - 3)) * if ang.ends-with("deg") { 1deg } else { 1rad }
} else {
let children = ang.children
let mult = if children.pop() == math.deg { 1deg } else { 1rad }
float(content-to-string(children.join())) * mult
}
}
// Note the options should hold num options
#let parse(options, ang) = {
let typ = type(ang)
return num.parse(
options,
to-number(ang) / if options.at("complex-angle-unit", default: "degrees") == "degrees" { 1deg } else { 1rad }
)
}
// The following is used for the `ang` function
#let get-options(options) = combine-dict(options, default-options + num.default-options, only-update: true)
#let ang(ang, options) = {
options = get-options(options)
let input-mode = if ang.len() > 1 { "arc" } else { "decimal" }
if options.angle-mode != "input" and input-mode != options.angle-mode {
let to-float = num.to-float.with(options)
ang = if input-mode == "arc" {
(to-float(ang.first()) + to-float(ang.at(1)) / 60 + if ang.len() > 2 { to-float(ang.at(2)) / 3600},)
} else {
let a = to-float(ang.first())
(calc.trunc(a),)
a = calc.fract(a) * 60
(calc.trunc(a),)
a = calc.fract(a) * 60
(calc.round(a),)
}
}
let symbols = (
options.angle-symbol-degree,
options.angle-symbol-minute,
options.angle-symbol-second
)
return math.equation({
ang.zip(symbols).map(
((a, s)) => num.num(a, options) + options.number-angle-product + s
).join(options.angle-separator)
})
} |
https://github.com/alerque/polytype | https://raw.githubusercontent.com/alerque/polytype/master/data/page-geometry/typst.typ | typst | #set page(
paper: "a7",
margin: 1cm,
)
#set par(
first-line-indent: 1cm,
justify: true,
)
// Note the manual glue node here is a hack around first
// paragraph in block not respecting first-line-indent:
// https://github.com/typst/typst/issues/311
#h(1cm)An A7 page with 1cm margins and 1cm paragraph indentation.
|
|
https://github.com/Myriad-Dreamin/typst.ts | https://raw.githubusercontent.com/Myriad-Dreamin/typst.ts/main/crates/reflexo-world/README.md | markdown | Apache License 2.0 | # reflexo-world
Typst's World implementation for reflexo.
See [Typst.ts](https://github.com/Myriad-Dreamin/typst.ts)
|
https://github.com/msakuta/typst-test | https://raw.githubusercontent.com/msakuta/typst-test/master/higher-order-automatic-differentiation.typ | typst | #set page(
numbering: "1",
)
#set math.equation(numbering: "(1)")
#set heading(numbering: "1.")
#show link: underline
#align(center, text(17pt)[
*Higher-order automatic differentiation*
])
#outline()
= Overview
Sometimes we want to have more than 1 order differentiation. An example is quadratic programming. However, it is very hard to find literature that can handle more than 1 order differentiation.
= Manual calculation of higher order chain rules
It is possible to calculate higher order chain rules by hand, if the order is finite, but it is notoriously error prone. For example, we already use the chain rule of product for first order derivatives:
$
d / (d x) f g = f (d g) / (d x) + (d f) / (d x) g
$
We can apply the differential and apply chain rule again to obtain:
$
(d^2) / (d x^2) f g &= (d) / (d x) (f (d g) / (d x) + (d f) / (d x) g ) \
&= (d^2 f) / (d x^2) g + 2 (d f) / (d x) (d g) / (d x) + f (d^2 g) / (d x^2)
$<eq:manual-diff2>
and so on.
You could encode this rule in a Rust code like below #footnote[https://github.com/msakuta/rustograd/blob/c902c7066c19f6df336a2cc1af85e4f430bce99a/src/tape.rs#L364].
Note that we use generics for the value type, and it may not be `Copy`, so they are cloned when they are used more than once.
```rust
Mul(lhs, rhs) => {
let dlhs = derive(nodes, lhs, wrt)?;
let drhs = derive(nodes, rhs, wrt)?;
let d2lhs = derive2(nodes, lhs, wrt)?;
let d2rhs = derive2(nodes, rhs, wrt)?;
let vrhs = value(nodes, rhs)?;
let vlhs = value(nodes, lhs)?;
let cross = dlhs * drhs;
d2lhs * vrhs + vlhs * d2rhs + cross.clone() + cross
}
```
We could go as far as @fig:manual-diff2 with this approach.
Here we differentiate a Gaussian function up to the second order differentiation.
$
f(x) &= exp(-x^2) \
(d f) / (d x) &= -2 x exp(-x^2) \
(d^2 f) / (d x^2) &= (-2 + 4 x) exp(-x^2)
$
#figure(
image("second-derive.svg", width: 70%),
caption: [A Gaussian distribution and its up to the second order differentiations]
) <fig:manual-diff2>
But it has many obvious problems. It is not scalable, it only works for forward mode differentiation, it can't work for multivariate functions and it feels like not automatic at all.
= Higher Order Automatic Differentiation with Dual Numbers
Another approach that I found in a paper is to use dual numbers, but more than just 2.
To recap, a dual number is something similar to a complex number, having 2 components like $x + y epsilon$.
This $epsilon$ is kind of an imaginary number that represents infinitesimal amount of change.
Being an infinitesimal number, the dual number will be zero if squared: $epsilon^2 = 0$.
Using dual numbers, you can derive product rule, for example:
$
(f + f' epsilon) (g + g' epsilon) = f g + (f g' + g f') epsilon + epsilon^2
$
and you can bring $epsilon^2$ to zero to obtain
$
f g' + g f'
$
which corresponds to
$
d (f g) = f d g + g d f
$
The dual number is just a mathematical symbol to describe the definition of derivatives, that is,
$
f'(x) = lim_(epsilon -> 0) (f(x + epsilon) - f(x)) / epsilon
$
You could use extended dual to compute higher order differentials by having another dual number $x + a epsilon + b eta$.
The calculation should yield the same result as the manually calculated chain rules.
It corresponds to applying the definition of derivatives twice.
$
f''(x) = lim_(eta -> 0) (lim_(epsilon -> 0) (f(x + epsilon + eta) - f(x + eta)) / epsilon - f(x)) / eta
$<eq:diff2>
For example, you can derive the product rule by 3-dual numbers:
$
(x + a epsilon + m eta) (y + b epsilon + n eta) = \
x y + (y a + x b) epsilon + (y m + x n) eta + (y a m + x b n) epsilon eta + a b epsilon^2 + m n eta^2
$
Now, $epsilon$ and $eta$ represent different infinitesimal value (see @eq:diff2).
So they have asymmetric rules of products.
- $epsilon^2 = 2 eta$ (corresponds to $d/(d x) d/(d x)$)
- $epsilon eta = 0$ (corresponds to the third order differentiation, which is ignored)
- $eta^2 = 0$ (corresponds to even higher order differentiations)
So the final expression will be:
$
x y + (y a + x b) epsilon + (y m + x n + 2 a b) eta
$
Here, the coefficients of the $eta$ will be the second order differentiation, because the first and the second term will be subtracted by the definition of differentiation @eq:diff2.
$
y m + x n + 2 a b
$
Now, if you look at it carefully, it corresponds to @eq:manual-diff2.
Another way to look at it that was presented by the paper is to use matrices like below, although they are rarely used in production, because they are too redundant to represent on memory.
$
1 = mat(1, 0, 0; 0, 1, 0; 0, 0, 1), epsilon = mat(0, 2, 0; 0, 0, 2; 0, 0, 0), eta = mat(0, 0, 2; 0, 0, 0; 0, 0, 0)
$
The paper generalizes the method to arbitrary order of differentiation as follows.
First, we represent the $i$-th dual number as $bold(i)_j$.
Then we can write arbitrary function with linear combination of $bold(i)_j$ like below.
$
cal(D) (f) = sum_(j=0)^N f^((j)) bold(i)_j
$
Now, addition and subtraction are easy:
$
cal(D)(f_1 plus.minus f_2) = sum_(j=0)^N (f_i^((j)) plus.minus f_2^((j))) bold(i)_j = cal(D)(f_1) plus.minus cal(D)(f_2)
$
The multiplication is more complicated, but you can obtain:
$
cal(D)(f_1 f_2) = sum_(j=0)^N sum_(k=0)^(N-j) f_1^((j)) f_2^((k)) binom(j + k, k) bold(i)_(j + k)
$
Encoding these rules in Rust code is a bit of hussle, but we can define a type `Dvec` that can handle arbitrary order of differentiations as you can find in the repository #footnote[https://github.com/msakuta/rustograd/blob/dnum/src/dvec.rs].
You can see that the result @fig:dvec-diff2 agrees with the manual differentiation @fig:manual-diff2.
#figure(
image("second-derive-dvec.svg", width: 70%),
caption: [A Gaussian distribution differentiations using Dvec]
) <fig:dvec-diff2>
= Generating subgraphs
We can generate subgraphs from existing nodes.
In this way, we can support higher order differentiation or even a function that includes derivatives.
$
f(x) = g(x) + (d h(x))/(d x)
$
= Differentiation of $arctan(y,x)$
To compute differentiation of $arctan(y,x)$,
$
f(x) &= arctan(x) \
(dif f(x))/(dif x) &= ( (dif f^(-1)(x))/(dif x) )^(-1) \
&= ( (dif)/(dif x) tan(x) )^(-1) = ( (dif)/(dif x) (sin(x))/(cos(x)) )^(-1) \
&= ( (cos(x))/(cos(x)) - (sin(x))/(cos^2(x)) )^(-1) = ( (cos^2(x) - sin(x))/(cos^2(x)) )^(-1) \
&= (cos^2(x)) / (cos^2(x) - sin(x))
$
= Differentiation of Matrix Products
Let's say we have matrices $A in bb(R)^(n times m)$ and $B in bb(R)^(m times l)$, both potentially a function of some variable. How do we calculate the derivative $d (A B)$?
First, let's write the total derivative.
$
d {A B_(i j)} = d sum_(k=1)^m a_(i k) space b_(k j)
= sum_(k=1)^m (d a_(i k) space b_(k j) + a_(i k) space d b_(k j))
space (i in [1,n], j in [1,l])
$
Let's consider the case of derivative with respect to $a_(p q)$.
Note that this is a 4th order tensor with indices $i, j, p$ and $q$.
It's messy, but we will simplify quite a bit later.
$
(diff {A B_(i j)}) / (diff a_(p q)) = (sum_k b_(k j) space diff a_(i k)) / (diff a_(p q)) = b_(q j) delta_(i p)
$
Similarly, we can compute
$
(diff {A B_(i j)}) / (diff b_(p q)) = (sum_k a_(i k) space diff b_(k j)) / (diff b_(p q)) = a_(i p) delta_(j q)
$
The question is, how much contribution does each input variable has to the output variable.
We would have to accumulate the influence through every path that goes through the product.
$
sum_(i=1)^n sum_(j=1)^l (diff {A B_(i j)}) / (diff a_(p q)) &= sum_j b_(q j) \
sum_(i=1)^n sum_(j=1)^l (diff {A B_(i j)}) / (diff b_(p q)) &= sum_i a_(i p)
$ <eq:ab>
Actually, the story is a bit more complicated, because the matrix product is often an intermediate step in the chain of computations.
When we backpropagate, we have a term like below by the product rule.
$
f_(i j) (diff {A B_(i j)}) / (diff a_(p q))
$
where $f_(i j)$ is some arbitrary function.
Therefore, @eq:ab would be written like below, which is really dot products.
$
sum_(i=1)^n sum_(j=1)^l f_(i j) (diff {A B_(i j)}) / (diff a_(p q)) &= sum_j f_(i j) b_(q j) = bold(f)_([i,:]) bold(b)_([q,:])^T = F B^T \
sum_(i=1)^n sum_(j=1)^l f_(i j) (diff {A B_(i j)}) / (diff b_(p q)) &= sum_i f_(i j) a_(i p) = bold(f)_([:,j])^T bold(a)_([:,p]) = F^T A
$
Here, we use notation $bold(b)_([q,:])$ to indicate the $q$-th row vector of $B$ and $bold(a)_([:,p])$ to indicate the $p$-th column vector of $A$, similar to numpy or PyTorch notation,
because I don't know any better way of representing it...
Anyway, it ends up with simple enough matrix multiplications.
= Literature
There are many researches on this topic, but they are much less than the first order differentiation, and they tend to be mathematically abstract and hard to apply. These are the only few papers that I found useful (in the sense that is understandable and implementable by me)
https://kenndanielso.github.io/mlrefined/blog_posts/3_Automatic_differentiation/3_5_higher_order.html
https://pp.bme.hu/eecs/article/download/16341/8918/87511
|
|
https://github.com/MattiaOldani/The-useless-theorem | https://raw.githubusercontent.com/MattiaOldani/The-useless-theorem/main/template.typ | typst | #let project(title: "", abstract: [], author: "", body) = {
set document(author: author, title: title)
set page(
margin: (left: 25mm, right: 25mm, top: 25mm, bottom: 25mm),
numbering: "1",
number-align: center,
)
set text(font: "New Computer Modern", lang: "it")
set heading(numbering: "1.")
line(length: 100%, stroke: 2pt)
pad(
bottom: 4pt,
top: 4pt,
align(center)[
#block(text(1.75em, title))
#v(1em, weak: true)
],
)
line(length: 100%, stroke: 2pt)
pad(
top: 0.5em,
x: 2em,
align(center)[
#block(text(1.25em, author))
],
)
align(center)[#datetime.today().display("[day]-[month]-[year]")]
pad(
x: 3em,
top: 1em,
bottom: 0.4em,
align(center)[
#heading(
outlined: false,
numbering: none,
text(1em, smallcaps[Abstract]),
)
#set par(justify: true)
#set text(hyphenate: false)
#abstract
],
)
line(length: 100%, stroke: 2pt)
v(12pt)
set par(justify: true)
set text(hyphenate: false)
body
}
|
|
https://github.com/floriandejonckheere/utu-thesis | https://raw.githubusercontent.com/floriandejonckheere/utu-thesis/master/thesis/chapters/02-methodology.typ | typst | #import "@preview/acrostiche:0.3.1": *
#import "/helpers.typ": *
= Methodology <methodology>
This chapter describes the methodology used in this thesis.
To answer the first research question, an ad hoc review of grey literature is conducted, picking a select number of publications that define and discuss the modular monolith architecture.
An ad hoc review is a less formal review process, where the researcher discusses purposefully selected publications to gain an understanding of a specific topic @ralph_baltes_2022.
For the second research question, a systematic literature review is conducted to identify and summarize the state of the art in (semi-)automated modularization technologies.
Systematic literature reviews are more formal than ad hoc reviews, and follow a well-defined process to reduce bias and increase the reliability of the results @ralph_baltes_2022.
The third research question is answered by designing an approach based on the results of the systematic literature review, and evaluating it in the context of a case study.
The effectiveness of the approach is then assessed based on a select set of quality metrics.
==== Systematic literature review
A systematic literature review is used to identify, evaluate and interpret research literature for a given topic area, or research question @kitchenham_charters_2007.
The methodological nature of systematic literature reviews reduces sampling bias through a well-defined sequence of steps to identify and categorize existing literature, and applies techniques such as forward and reverse snowballing to reduce publication bias @ralph_baltes_2022.
Studies directly researching the topic area are called _primary_ studies, systematic studies aggregating and summarizing primary studies are called _secondary_ studies.
_Tertiary_ studies are systematic studies aggregating and summarizing secondary studies.
Systematic literature reviews often only consider primary studies as they are considered the most reliable source of information @ralph_baltes_2022, but may also include secondary studies if the primary studies are scarce, or as a means to identify primary studies.
We conducted the systematic literature review in this thesis using the three-step protocol as defined by #cite_full(<kitchenham_charters_2007>).
@slr_process enumerates and succinctly describes the three steps of the protocol.
#figure(
table(
columns: (auto, auto, auto),
inset: 10pt,
stroke: (x: none),
align: (center, left, left),
[], [*Step*], [*Activity*],
"1", "Plan", "Identify the need for the review, specifying the research questions, and developing a review protocol",
"2", "Conduct", "Identification and selection of literature, data extraction and synthesis",
"3", "Report", "Evaluation and reporting of the results",
),
caption: [Systematic literature review process]
) <slr_process>
==== Case study
For the case study, a #acr("DSRM") is adopted, which is a research paradigm for information systems research focused at creating and evaluating artifacts.
In particular, the research and design of the proposed solution follows the six-step #acr("DSRP") model @peffers_etal_2007.
The model is inspired by prior research and is designed to guide researchers through the process of analysis, creation, and evaluation of artifacts in information science.
The six steps of the process are:
+ *Problem identification and motivation*: research problem statement and justification for existence of a solution.
+ *Objectives*: definition of the objectives following the problem statement
+ *Design and development*: creation of the artifact
+ *Demonstration*: usage of the artifact to demonstrate its effectiveness in solving the problem
+ *Evaluation*: observation and measurement of how well the artifact supports a solution to the problem
+ *Communication*: transfer of knowledge about the artifact and the problem solution to the relevant audience
#figure(
include("/figures/02-methodology/dsrp.typ"),
caption: [Design Science Research Process @peffers_etal_2007]
) <dsrp>
@dsrp gives a visual overview of the #acr("DSRP") model.
The process is structured sequentially, however the authors suggest that researchers may proceed in a non-linear fashion, and start or stop at any step, depending on the context and requirements of the research.
In this thesis, we use the #acr("DSRP") as a guideline for the design, development, and evaluation of the microservice candidate identification approach used in the case study.
We focus in particular on the design and development, demonstration, and evaluation steps.
|
|
https://github.com/RedGl0w/TypHex | https://raw.githubusercontent.com/RedGl0w/TypHex/main/README.md | markdown | ## TypHex
TypHex is a small package to draw [hex board game](https://en.wikipedia.org/wiki/Hex_(board_game))'s grids in [Typst](https://typst.app/).
Currently, it only implement some function to draw hexagons and make a grid of them, and a basic [SGF (smart game format)](https://en.wikipedia.org/wiki/Smart_Game_Format) tokenizer / parser.
This allows the user to simply call `gridFromSGF` implemented in `TypHex.typ` with as parameter a SGF string (generated with [HexGUI](https://github.com/ryanbhayward/hexgui) or any other software with similar SGF generated) to draw the game grid.
### Exemple :
When executing `gridFromSGF("(;FF[4]SZ[11];AB[a1][b2][c3][d4]AW[b1][c2][b3][e4]PL[W])")` :
|
|
https://github.com/sora0116/unix_seminar | https://raw.githubusercontent.com/sora0116/unix_seminar/master/handout/perf/main.typ | typst | #import "@preview/big-todo:0.2.0": *
#set text(font: "<NAME>")
#set heading(numbering: "1.1")
#set page(numbering: "1")
#show raw: it => {
if (it.lang == "shell") {
block(fill: rgb("#1d2433"), width: 100%, inset: 10pt, radius: 10pt)[
#text(fill: rgb("#f6f6f6"))[#it]
]
} else {
it
}
}
#let perf(cmd) = raw(cmd, block: true, lang: "shell")
#let options(pre: [文法:], name: "option name", desc: "description", ..con) = {
pre
table(
columns: (2fr, 3fr),
align: (_, y) => if y==0 {center} else {left},
[#name], [#desc],
..con.pos().flatten()
)
}
#let sep(text) = table.cell(colspan: 2)[#align(center)[#text]]
#let syn(text) = raw(" (lldb) "+text, block: true, lang: "shell")
#align(center+horizon)[#text(size: 2em)[Perf]]
#align(center)[Chapter 3]
#counter(heading).update(0)
#pagebreak()
= 導入
PerfはLinux用のプロファイラツールです。
== コマンド
perfはgitのように`perf <command>`の形式で各種ツールを使用します。
サポートされるコマンドの一覧は`perf`で閲覧できます。
```shell
$ perf
usage: perf [--version] [--help] [OPTIONS] COMMAND [ARGS]
The most commonly used perf commands are:
annotate Read perf.data (created by perf record) and display annotated code
archive Create archive with object files with build-ids found in perf.data file
bench General framework for benchmark suites
buildid-cache Manage build-id cache.
buildid-list List the buildids in a perf.data file
c2c Shared Data C2C/HITM Analyzer.
config Get and set variables in a configuration file.
daemon Run record sessions on background
data Data file related processing
diff Read perf.data files and display the differential profile
evlist List the event names in a perf.data file
ftrace simple wrapper for kernel's ftrace functionality
inject Filter to augment the events stream with additional information
iostat Show I/O performance metrics
kallsyms Searches running kernel for symbols
kvm Tool to trace/measure kvm guest os
list List all symbolic event types
mem Profile memory accesses
record Run a command and record its profile into perf.data
report Read perf.data (created by perf record) and display the profile
script Read perf.data (created by perf record) and display trace output
stat Run a command and gather performance counter statistics
test Runs sanity tests.
top System profiling tool.
version display the version of perf binary
probe Define new dynamic tracepoints
```
一部のコマンドはカーネルで特殊なサポートを必要とするため使用できない場合があります。各コマンドのオプションの一覧を`-h`で出力することができます。
例:
```shell
$ perf stat -h
Usage: perf stat [<options>] [<command>]
-a, --all-cpus system-wide collection from all CPUs
-A, --no-aggr disable CPU count aggregation
-B, --big-num print large numbers with thousands' separators
```
== イベント
perfは測定可能なイベントのリストを表示することができます。イベントは複数のソースからなり、一つはコンテキストスイッチやマイナーフォルトなどのカーネルカウンタです。これをソフトウェアイベントと呼びます。
もう一つはPerformance Monitoring Unit(PMU)と呼ばれるハードウェアです。PMUはサイクル数、リタイアした命令、L1キャッシュミスなどのマイクロアーキテクチャイベントを測定するためのイベントリストを提供します。これらのイベントをハードウェアイベントと呼びます。
イベントの一覧は
```shell
$ perf list
```
で閲覧できます。
= statによるカウント
`perf stat`を使用することでプログラム実行時のイベントを集計できます。
```shell
$ perf stat -e <event>[,<event>]... <command>
```
で`command`実行時の`event`の集計を行えます。
= recordによるサンプリング
`perf record`を使用することでプロファイル情報を収集して、`perf stat`よりも細かいソースコード、命令単位レベルで情報を見ることができます。
```shell
$ perf record [<options>] <command>
```
#options(
(`-g`, [コールグラフをレコード]),
(`-o, --output <file>`, [出力ファイルを指定]),
)
= reportによるサンプルの解析
`perf record`で収集したサンプルを`report`コマンドで閲覧します。
```shell
$ perf report
```
#options(
(`-g, --call-graph`, [コールグラフを表示]),
(`-i, --input <file>`, [読み込むファイルを指定]),
(`--stdio`, [TUIではなく標準出力に表示]),
)
|
|
https://github.com/WinstonMDP/math | https://raw.githubusercontent.com/WinstonMDP/math/main/exers/o.typ | typst | #import "../cfg.typ": *
#show: cfg
$
"Prove that"
all("absolutely covergent series" sum_(n = 1)^oo beta_n):
b_n/b_(n + 1) = 1 + beta_n -> b_n "has a limit"
$
$b_(n + 1) = b_n/(1 + beta_n)$
$b_(n + 2) =
b_(n + 1)/(1 + beta_(n + 1)) = b_n/((1 + beta_(n + 1))(1 + beta_n))$
$b_n =
b_1/((1 + beta_1) ... (1 + beta_(n - 1))) =
b_1/(product_(n = 1)^oo (1 + beta_n))$
$qed$
|
|
https://github.com/LDemetrios/Typst4k | https://raw.githubusercontent.com/LDemetrios/Typst4k/master/src/test/resources/suite/syntax/newlines.typ | typst | // Test newline continuations.
--- newline-continuation-code ---
#{
"hello"
.clusters()
if false {
}
else {
("1", "2")
}
}
--- newline-continuation-markup ---
#"hello"
.codepoints()
#if false {
}
else {
("1", "2")
}
--- newline-continuation-method-blank ---
#test({
"hi 1"
.clusters()
}, ("h", "i", " ", "1"))
--- newline-continuation-method-line-comment-after ---
#test({
"hi 2"// comment
.clusters()
}, ("h", "i", " ", "2"))
--- newline-continuation-method-block-comment-after ---
#test({
"hi 3"/* comment */
.clusters()
}, ("h", "i", " ", "3"))
--- newline-continuation-method-line-comment-between ---
#test({
"hi 4"
// comment
.clusters()
}, ("h", "i", " ", "4"))
--- newline-continuation-method-block-comment-between ---
#test({
"hi 5"
/*comment*/.clusters()
}, ("h", "i", " ", "5"))
--- newline-continuation-method-comments-and-blanks ---
#test({
"hi 6"
// comment
/* comment */
.clusters()
}, ("h", "i", " ", "6"))
--- newline-continuation-if-else-comment ---
#test({
let foo(x) = {
if x < 0 { "negative" }
// comment
else { "non-negative" }
}
foo(1)
}, "non-negative")
|
|
https://github.com/manforowicz/resume | https://raw.githubusercontent.com/manforowicz/resume/main/resume.typ | typst | // Metadata
#set document(
title: "<NAME> - Resume",
author: "<NAME>",
date: datetime(
year: 2024,
month: 8,
day: 28,
)
)
// Style
#set page(paper: "us-letter")
#set text(font: "Cantarell", lang: "en")
#set par(leading: 0.75em)
#show link: underline
#show link: set text(blue)
// Header
#grid(
columns: (1fr, 1fr),
align: (left, right),
[
= #link("https://manforowicz.github.io/")[<NAME>]
#link("https://www.linkedin.com/in/m-anforowicz/")[www.linkedin.com/in/m-anforowicz/]
],
[
(425) 340-9709 \
#link("mailto:<EMAIL>", "<EMAIL>")
]
)
- 3rd-year computer science undergraduate searching for a 2nd software internship.
- Industry experience in: C, C++, Python, JavaScript, ESP-IDF, circuit design, GDB.
- Project experience in: Rust, Java, Typescript, SystemVerilog, Arduino, serial protocols.
- Native language proficiency in: English, Polish.
== EDUCATION
=== Computer Science --- University of Washington #h(1fr) 2022 - Expected June 2026
- GPA: 3.89
- Excelled in courses: Machine Learning, Systems Programming, Digital Design, Hardware-Software Interface, Computer Security, Operating Systems, Data Structures & Parallelism.
== EXPERIENCE
=== Software engineering intern at #link("https://www.wibotic.com/")[WiBotic] #h(1fr) June 2024 - September 2024
// Header
#grid(
columns: (7fr, 1fr),
align: (left, right),
[
- Wrote over 3000 lines of multithreaded firmware for a #link("https://github.com/wibotic/socketcand_translate")[CAN-to-ethernet adapter].
- Developed a fullstack web app for configuring the CAN-to-ethernet adapter.
- Designed and built PCBs to power 64 microcontrollers on a shared CAN bus $->$
- Created a Python test suite that caught bugs in production firmware.
- Diagnosed and fixed major bugs in a large embedded C++ codebase.
- Used Python multithreading to accelerate a test analytics PDF report generator.
],
image("circuit.jpg")
)
=== YouTube educator #h(1fr) 2022 - Present
- #link("https://youtu.be/_FuuYSM7yOo?si=-bUz7KSFfRh2WE0f")[The "Just One More Paradox"] - Over 3M views. Programmatically animated #link("https://github.com/manforowicz/Manim-Videos")[using Manim].
- #link("https://youtu.be/cGJYCe6mGR0?si=_fzZlMWUd3hXujSL")[PCB Magnetorquer Prototype - Husky Satellite Lab] - Includes #link("https://github.com/manforowicz/Magnetorquer-Calc")[optimization code I wrote].
=== Leader at student organizations --- University of Washington #h(1fr) 2022 - Present,
- At UW Husky Flying Club, leads a 4-person team in building remotely-operated aerial vehicles from foam composites. Teaches electronics, design, and implementation.
- Creates marketing websites that auto-deploy using GitHub continuous integration: #link("https://uw-programming.netlify.app/")[UW Competitive Programming Club] (#link("https://github.com/manforowicz/uwcp-site")[code]), #link("https://huskysat.org/team.html")[Husky Satellite Lab] (#link("https://github.com/uwCubeSat/hsl-website")[code]), #link("https://manforowicz.github.io/flock/")[personal site] (#link("https://github.com/manforowicz/manforowicz.github.io")[code]).
- At Husky Satellite Lab, lead a team to design and build CubeSat radio #link("https://github.com/UWCubeSat/radio-hw")[circuit boards].
=== Active hobbyist #h(1fr) 2022 - Present
- Creates open source projects such as #link("https://github.com/manforowicz/gday")[Gday], a tool for encrypted peer-to-peer file transfer.
- Published an interactive Rust web assembly #link("https://manforowicz.github.io/flock/")[simulation] on personal website.
- Is an FCC-certified amateur radio operator. Experiments with WSPR, IRLP, and APRS.
- Has built 4 #link("https://youtu.be/02VQIWccqr0")[remote-controlled aircraft], with onboard cameras and electronic payloads.
=== Competitive programmer #h(1fr) 2021 - Present
- One of 900 programmers worldwide who qualified to USACO Gold in 2022.
- Competes on an ICPC team at the University of Washington's Competitive Programming Club.
|
|
https://github.com/SkiFire13/master-thesis | https://raw.githubusercontent.com/SkiFire13/master-thesis/master/chapters/4-implementation.typ | typst | #import "../config/common.typ": *
#import "@preview/cetz:0.2.2": canvas, draw
= Implementation <section-implementation>
The final goal of this thesis was a concrete implementation of the algorithms explained in the previous sections. The implementation partly relies on the work done in LCSFE @flori which, as mentioned in the introduction, was based on a different algorithm for parity games. The final implementation is available in the repository #underline(link("https://github.com/SkiFire13/master-thesis-code"))
In this section we will explain our design choices, what was actually implemented, and we will present a performance comparison with some existing tools.
== Technologies used
Just like LCSFE, our implementation is written in Rust @rust, a modern systems programming language, focused on performance and correctness and whose goal is to rival languages like C and C++ while offering memory safety. Just like C and C++, Rust mainly follows the imperative paradigm, allowing mutations, loops and general side effects, but it also includes lot of functional programming related features, like algebraic data structures and most notably _enums_, pattern matching, which allows to exhaustively inspect those enums, and _closures_, which are anonymous function that can capture their outer environment, although with some limitations due to how the memory management works. Among other features there are _traits_, which work similarly to type classes in Haskell and fill the same use cases as interfaces in popular OOP languages like Java. It should also be mentioned that Rust programs are organized in _crates_, which make up the unit of compilation, and _modules_, which are a hierarchical division internal to a crate and help organize code and avoid name clashes.
The most interesting features however are its _ownership_ system and its borrow checker, which allow the compiler to guarantee memory safety without a garbage collection or other kind of runtime support. The ownership system enforces that every value has exactly one _owner_, which is responsible for freeing up its resources, making classes of issues like use-after-free impossible, and others like memory leaking much more difficult to hit. The borrow checker instead rules how borrows can be created and used. Every variable can be borrowed, creating either a shared reference or an exclusive references, which are pointers with a special meaning for the compiler. The borrow checker ensures that at any point in time there can be either multiple shared references or one exclusive reference pointing to a variable, but not both. Coupled with the fact that only exclusive references allow mutations, this system guarantees that references always point to valid data.
The borrowing rules however can become an obstacle when writing programs that perform lot of mutations, especially for programmers used to other imperative languages. It has been found however that data oriented designs in practice work pretty well with the borrow checker, due to the ability to replace pointers with indexes and thus restricting the places where borrows need to be created. This paradigm also helps creating cache efficient programs, which can often be faster. For this reason we tried to implement out algorithm with a data oriented design, which was mainly done by associating an auto-incrementing index to each vertex. Then informations associated with vertices, like their successors or remaining moves, was each stored in its own array indexed by the same index on vertices.
== Structure of the implementation
The implementation was split in multiple crates, just like in the original LCSFE implementation. It consists of one main _solver_ crate implementing the solving algorithm and multiple dependent crates, that translate specific problems into systems of fixpoint equations with logic formulas ready to be solved by the solver crate and offer a CLI interface for testing such functionalities.
#figure(
canvas({
import draw: *
let edge(pi, pf, a) = {
bezier(pi, pf, (pi, 50%, a, pf), fill: none, stroke: black, mark: (end: ">"))
}
let inner_edge(pi, pf, a) = {
bezier(pi, pf, (pi, 50%, a, pf), fill: none, stroke: black, mark: (start: ">", end: ">"))
}
content((-4, 4), box(stroke: black, inset: 0.6em)[_parity_])
content((0, 4), box(stroke: black, inset: 0.6em)[_mucalc_])
content((4, 4), box(stroke: black, inset: 0.6em)[_bisimilarity_])
content((1.5, 2), box(stroke: black, inset: 0.6em)[_aut_])
content((-1.8, 0), [_solver_])
content((0, 0), box(stroke: black, inset: 0.6em)[_local_])
content((-1.5, -2), box(stroke: black, inset: 0.6em)[_strategy_])
content((1.5, -2), box(stroke: black, inset: 0.6em)[_symbolic_])
rect((-2.5, 0.5), (2.6, -2.5), name: "s")
edge((-4, 3.63), (-1.3, 0.5), 0deg)
edge((0, 3.63), (0, 0.5), 0deg)
edge((4, 3.63), (1.3, 0.5), 0deg)
edge((0.3, 3.63), (1.2, 2.37), 0deg)
edge((3.7, 3.63), (1.8, 2.37), 0deg)
inner_edge((-0.2, -0.37), (-1.5, -1.63), 0deg)
inner_edge((0.2, -0.37), (1.5, -1.63), 0deg)
}),
caption: [Crates tree of the implementation]
)
The crates involved are the following:
- _parity_, which implements the parsing and translation from parity games to a system of fixpoint equations, which we saw in section @parity-implementation, and a binary crate for the associated CLI;
- _aut_, which implements the parsing of labelled transition system files from the AUT format (also called Aldebaran) and is consumed by both the _mucalc_ and _bisimilarity_ crates;
- _mucalc_, which implements the parsing of a subset of $mu$-calculus formulas, followed by their translation to a system of fixpoint equations and logic formulas as shown in @mucalculus-application[Sections] and @mucalculus-translation[], and along with a binary crate for the associated CLI;
- _bisimilarity_, which implements the translation from a bisimilarity problem between two states of two different labelled transition systems to a system of one fixpoint equation and then logic formulas as shown in @bisimilarity-application[Sections] and @bisimilarity-translation[], along with a binary crate for the associated CLI.
The _solver_ crate is also internally split into three main modules implementing the major pieces of functionality:
- _symbolic_, which defines the structures for systems of fixpoint equation and logic formulas, and more importantly implements formula iterators their simplification;
- _strategy_, which implements the strategy iteration algorithm;
- _local_, which implements the local algorithm and the expansion scheme, along with the improvement we made to them, connecting to the _symbolic_ module to generate new moves when necessary and to the _strategy_ module to perform the valuation and improvement steps.
== Testing with parity games <parity-implementation>
As mentioned in @parity-translation parity games can be translated to systems of fixpoint equations, and we used this fact to generate simple problems for testing our implementation.
The _parity_ crate implements this conversion from parity games to systems of fixpoint equations and then logic formulas, along with a parser for parity games specified in the pgsolver @pgsolver format, according to the following grammar:
#[
#show "<": sym.angle.l
#show ">": sym.angle.r
#let s = h(0.5em)
#let paritygame = mathstr("parity_game")
#let nodespec = mathstr("node_spec")
#let identifier = mathstr("identifier")
#let priority = mathstr("priority")
#let owner = mathstr("owner")
#let successors = mathstr("successors")
#let name = mathstr("name")
$
<paritygame> &::= [sans("parity") < identifier > #s sans(";")] #s <nodespec>^+ \
<nodespec> &::= <identifier> #s <priority> #s <owner> #s <successors> #s [<name>] #s sans(";") \
<identifier> &::= bb(N) \
<priority> &::= bb(N) \
<owner> &::= sans("0") | sans("1") \
<successors> &::= <identifier> #s (, #s <identifier>)^* \
<name> &::= sans("\"") #s ("any ASCII string not containing '\"'") #s sans("\"") \
$
]
For example the parity game shown in @parity-example would be specified in the following way:
```
parity 5
0 0 0 1,2;
1 2 1 0;
2 3 1 1,3;
3 5 0 4;
4 4 0 2,3;
```
The format consists of a header containing the identifier $sans("parity")$ followed by a number indicating how many vertices will be specified, which can be used to speed up the parsing of the file. Then each of the following lines specifies a vertex with, in order, its identifier, priority, controlling player, edges and optionally a name. For the sake of simplicity we assumed the names to never be present, since they are not required for solving the game and were not present in the games we exploited for our testing activity.
We used the parity game instances included in the Oink @oink collection of parity game solvers to test our implementation. These tests are pretty small, reaching a maximum of 24 vertices and 90 edges, but they include lot of tricky cases which help getting empiric evidence of the correctness of our implementation.
== Testing with $mu$-calculus
As mentioned in @mucalculus-application[Sections] and @mucalculus-translation[], $mu$-calculus formulas can be translated to systems of fixpoint equations and then to logic formulas. We implemented this in the _mucalc_ crate, which performs this translation after parsing a labeled transition system and a $mu$-calculus formula from two given files.
The labelled transition system is expected to be in the AUT (Aldebaran) format, according to the following grammar, which based on the one given in @aut_spec:
#[
#show "<": sym.angle.l
#show ">": sym.angle.r
#let s = h(0.5em)
#let aut = mathstr("aut")
#let header = mathstr("header")
#let initialstate = mathstr("initial-state")
#let transitionscount = mathstr("transitions-count")
#let statescount = mathstr("states-count")
#let transition = mathstr("transition")
#let fromstate = mathstr("from-state")
#let label = mathstr("label")
#let unquotedlabel = mathstr("unquoted-label")
#let quotedlabel = mathstr("quoted-label")
#let tostate = mathstr("to-state")
$
<aut> &::= <header> #s <transition>^* \
<header> &::= sans("des") #s sans("(") #s <initialstate> #s sans(",") #s <transitionscount> #s sans(",") #s <statescount> sans(")" #s) \
<initialstate> &::= bb(N) \
<transitionscount> &::= bb(N) \
<statescount> &::= bb(N) \
<transition> &::= sans("(") #s <fromstate> #s sans(",") #s <label> #s sans(",") #s <tostate> #s sans(")") \
<fromstate> &::= bb(N) \
<label> &::= <unquotedlabel> | <quotedlabel> \
<unquotedlabel> &::= ("any character except \"" #h(0.3em)) #s ("any character except ," #h(0.3em))^* \
<quotedlabel> &::= sans("\"") #s ("any character except \"" #h(0.3em))^* #s sans("\"") \
<tostate> &::= bb(N) \
$
]
The grammar consists of a header containing the literal "des" followed by the initial state number, the number of transitions and the number of states. After that, are all the transitions, encoded as a triple $(s, l a b e l, t)$, where the first and last components $s$ and $t$ are the source and target state of the transition, while the second component is the label, which can be quoted or not. For the sake of simplicity we have diverged from the specification at @aut_spec by considering labels as either a sequence of characters until the first comma or as sequence of characters delimited by quotes. In particular we have ignored character escaping and any restrictions on which characters are allowed to be used.
The given grammar for a $mu$-calculus formula mostly follows the definition previously given in @mucalculus-application:
#[
#show "<": sym.angle.l
#show ">": sym.angle.r
#let s = h(0.5em)
#let expr = mathstr("expr")
#let fixexpr = mathstr("fix-expr")
#let var = mathstr("var")
#let orexpr = mathstr("or-expr")
#let andexpr = mathstr("and-expr")
#let modalexpr = mathstr("modal-expr")
#let action = mathstr("action")
#let label = mathstr("label")
#let atom = mathstr("atom")
$
<expr> &::= <fixexpr> | <orexpr> \
<fixexpr> &::= (sans("mu") | sans("nu")) #s <var> #s sans(".") #s <orexpr> \
<var> &::= ("any identifier") \
<orexpr> &::= <andexpr> #s (#s sans("||") #s <andexpr> #s)^* \
<andexpr> &::= <modalexpr> #s (#s sans("&&") #s <modalexpr> #s)^* \
<modalexpr> &::= (sans("＜") #s <action> #s sans("＞") #s <atom>)
| ( #s sans("[") #s <action> #s sans("]") #s <atom> )
| atom \
<action> &::= sans("true") | <label> | sans("!") #s <label> \
<label> &::= ("any character except ＞ and ]" #h(0.3em)) \
<atom> &::= sans("true") | sans("false") | <var> | sans("(") #s <expr> #s sans(")")
$
]
Compared to the definition given in @mucalculus-application we have omitted support for arbitrary propositions. Arbitrary subsets of labels are also not supported, but are instead limited to singleton sets containing a label, their complement, signaled by a $sans(!)$ character preceding a label, or the set of all labels, represented by the $sans("true")$ action. From now on we will use $mu$-calculus formulas that follow this syntax. Several mathematical symbols have also been replaced with similar ASCII characters, and precedence rules have been encoded in the grammar.
The two grammars for labelled transition systems and $mu$-calculus formulas have been chosen to be mostly compatible with the ones used in LCSFE, from which their limitations also come from, in order to simplify a comparison between the two implementation. However the grammar for labelled transition systems has also been extended in order to allow for quoted labels in the labelled transition system grammar, which appeared in some instances used for testing, and more convenient precedence rules for the $mu$-calculus grammar, which helped when writing some more complex formulas.
=== Performance comparison
We compared the performance of our implementation with respect to LCSFE and mCRL2 on the mCRL2 examples used originally in @flori. All the tests were performed on a computer equipped with an AMD Ryzen 3700x and 32GB of DDR4 RAM running Windows 10. LCSFE and our implementation were compiled using the Rust release profile, which applies optimizations to the code produced.
We started with the "bridge referee" example from mCRL2, modeling the crossing of a bridge by a group of 4 adventurers with different speeds, with the additional restrictions that only 2 explorers can cross the bridge at a time and that they have to carry their only flashlight at every crossing. This leads to a labelled transition system with 102 states and 177 transitions, representing all the possible ways they can try crossing such bridge. The formula to check is $mu x. diam(#h(0em)"report"(17)) #h(0.3em) tt or diam(tt) #h(0.3em) x$, representing the fact that all 4 adventurers reach the other side in 17 minutes, which is signaled by the transition $"report(17)"$. The formula thus checks if it is possible to ever execute such transition.
Using the workflow suggested by mCRL2 we first converted the mCRL2 specification into its internal lps format using the `mcrl22lps` utility:
```cmd
> mcrl22lps bridge-referee.mcrl2 bridge.lps --timings
```
```
- tool: mcrl22lps
timing:
total: 0.024
```
Then, we bundled together the lps file and a file holding the formula specified above into a pbes file, another internal format, using the `lps2pbes` utility.
```cmd
> lps2pbes bridge.lps --formula=bridge_report_17.mcf \
bridge_report_17.pbes --timings
```
```
- tool: lps2pbes
timing:
total: 0.016
```
Finally, the `pbes2bool` was used to convert the pbes file into a boolean parity game and solve it. It should be noted that $mu$-calculus also admits an ad-hoc translation to parity games, which we would expect to be better than our generic approach.
```cmd
> pbes2bool bridge_report_17.pbes -rjittyc --timings
```
```
true
- tool: pbes2bool
timing:
instantiation: 0.009495
solving: 0.000028
total: 0.038349
```
We then verified the same formula with LCSFE and our implementation. We used mCRL2 again to convert the mCRL2 machine specification to a labelled transition system in AUT format we can use. To do this we reused the lps file previously generated to produce a lts file using the `lps2lts` utility:
```cmd
> lps2lts bridge.lps bridge.lts -rjittyc --timings
```
```
- tool: lps2lts
timing:
total: 0.035608
```
The lts file was then converted to an AUT file using the `ltsconvert` utility, which converts between different labelled transition systems formats:
```cmd
> ltsconvert bridge.lts bridge.aut --timings
```
```
- tool: ltsconvert
timing:
reachability check: 0.000
total: 0.002
```
Finally we verified the formula using LCSFE and our implementation
```cmd
> lcsfe-cli mu-ald bridge.aut bridge_report_17.mcf 0
```
```
Preprocessing took: 0.0004837 sec.
Solving the verification task took: 0.0000129 sec.
Result: The property is satisfied from state 0
```
```cmd
> mucalc bridge.aut bridge_report_17.mcf
```
```
Preprocessing took 432.1µs
Solve took 1.1076ms
The formula is satisfied
```
We used this small example to get some empirical evidence that our implementation for $mu$-calculus is correct, as it gives the same result as the other tools, and to also show the process we used to run all the tools involved. From now on we will omit the specific commands we ran and instead will only report the time required to run them.
We then tested the second formula that was used in @flori, which uses the bigger "gossip" labelled transition system, also an example from mCRL2 which models a group of $n$ girls sharing gossips through phone calls. We tested up to $n = 5$, which leads to 9152 states and 183041 transitions, after which the transition system began growing too big. The formula tested was $nu x. diam(tt) tt and boxx(tt) x$, which represents the lack of deadlocks. It should be noted that formulas checking for absence of deadlock that are satisfied, like this one, are a worst case for local algorithms because they require visiting the whole graph, thus vanishing the advantage of local algorithms which consists in the possibility of visiting only the states that are relevant.
#figure(
table(
columns: (auto,) * 5,
align: horizon,
inset: (x: 1em),
stroke: none,
table.header([$n$], [*mCRL2*], [*AUT generation*], [*Our solver*], [*LCSFE*]),
table.hline(),
[2], [67.8 ms], [54.7 ms], [132 #us], [65.5 #us],
[3], [68.5 ms], [59.2 ms], [212 #us], [195 #us],
[4], [72.0 ms], [117 ms], [2.30 ms], [4.38 ms],
[5], [1.47 s], [2.05 s], [202 ms], [5.90 s],
),
caption: [Gossips benchmark results]
) <table-gossips-benchmarks>
Our implementation scales much better than LCSFE, confirming that the different parity game solving algorithm does make a difference in this case, to the point where the bottleneck becomes the generation of the AUT file, which takes an order of magnitude more time than solving the parity game itself. Compared with mCRL2 our implementation overall takes a similar amount of time, most of which is however spent doing conversions to produce the AUT file using mCRL2 itself. This suggests that lazily generating the labelled transition system might be beneficial, though this was considered out of scope for our work. Overall the pure mCRL2 approach is slightly faster, probably due to the costs of the intermediate conversions to produce the AUT file or the overhead of using a local algorithm in a case where all states must be explored regardless.
We also compared our tool with LCSFE on a set of randomly generated transition systems given the number of states, the number of transitions for each state, and the number of labels. For sake of simplicity the labels have been given a natural number starting from $0$ as their name. We used the two tools to test a _fairness_ formula on these transition systems, that is a formula in the shape $nu x. mu y. (P and diam(Act) x) or diam(Act) y$, which is satisfied when there exist a path in the labelled transition system where $P$ is true infinitely often. We choose such formula because it represents a common property to verify, it actually uses nested fixpoints, and also because it does not require exploring the whole transition system to verify, hence favoring local solvers. As a formula $P$ we choose $diam(0) tt and diam(1) tt and diam(2) tt$, that is we require a state to be able to do three transitions with respectively the labels $0$, $1$ and $2$, because it is an arbitrary condition that we can manipulate how often it is satisfied by changing the number of transitions and labels. We then tested on a number of states ranging from $1000$ to $10000$, while the number of transitions and labels tested was respectively 10/10 and 20/100, representing a case where the condition $P$ was satisfied quite often and a bit rarer.
#let size_cell(s, t, l) = (
table.cell(align: right)[#s],
[/],
table.cell(align: center)[#t],
[/],
table.cell(align: left)[#l]
)
#figure(
table(
columns: (auto, 0em, auto, 0em, auto, auto, auto),
align: center + horizon,
inset: (x: 1em),
stroke: none,
table.header(table.cell(colspan: 5)[*Size (states/ \ transitions/labels)*], [*Our solver*], [*LCSFE*]),
table.hline(),
..size_cell(1000, 10, 10), [2.74 ms], [21.8 ms],
..size_cell(2500, 10, 10), [5.10 ms], [59.9 ms],
..size_cell(5000, 10, 10), [10.2 ms], [120 ms],
..size_cell(10000, 10, 10), [18.5 ms], [250 ms],
..size_cell(1000, 20, 100), [5.63 ms], [26.6 ms],
..size_cell(2500, 20, 100), [13.8 ms], [67.7 ms],
..size_cell(5000, 20, 100), [40.1 ms], [142 ms],
..size_cell(10000, 20, 100), [48.6 ms], [298 ms],
),
caption: [Random LTS benchmark results]
) <table-random-fairness-benchmarks>
Again we can see our tool improving compared to LCSFE, though this time by not so much. This could be attributed to a difference in either the efficiency of the algorithm of the one of the implementation though.
Finally, we also ran our solver on some of the instances in the VLTS benchmark suite to understand the limitations and the strengths of our implementation. For each chosen instance we verified the $mu$-calculus formulas $nu x. diam(tt) tt and boxx(tt) x$, which checks for absence of deadlocks, and $mu x. diam(tt) x or (nu y. diam(#h(0em)"tau"#h(0em)) y)$, which checks for the presence of livelocks, that is cycles consisting of only tau transitions. For each instance we ran the solver 5 times, ignored the slowest and quickest ones and reported a mean of the remaining 3.
#[
#set text(size: 10pt)
#figure(
table(
columns: (auto, 4.5em, 4.5em, 4.5em, auto, 4.5em, auto),
align: horizon,
inset: (x: 0.3em),
stroke: none,
table.header([*Name*], [*States count*], [*Trans. count*], [*Deadlocks?*], [*Deadlock\ solve time*], [*Livelocks?*], [*Livelock\ solve time*]),
table.hline(),
`vasy_0_1`, [289], [1224], [no], [4.93 ms], [no], [6.98 ms],
`cwi_1_2`, [1952], [2387], [no], [8.74 ms], [no], [72.9 ms],
`vasy_52_318`, [52268], [318126], [no], [443 s], [yes], [75.2 ms],
`vasy_69_520`, [69754], [520633], [yes], [122 ms], [no], [6.59 s],
`vasy_720_390`, [720247], [390999], [yes], [82 ms], [no], [3.64 s],
),
caption: [VLTS benchmark results]
) <table-vlts-benchmarks>
]
The various labelled transition systems reported in @table-vlts-benchmarks have different sizes, and some have deadlocks and livelocks while others do not, which greatly influences the results and makes the various results not directly comparable to one another. We can for example see that checking for the absence of deadlocks when they are not present quickly becomes very slow, like in `vasy_52_318` where in particular we observed that even single iterations of the strategy iteration algorithm become quite slow.
Checking for the presence of livelocks also becomes pretty slow when they are not present, however when they are the local nature of the algorithm allows us to skip checking a lot of positions, ultimately making the algorithm much faster.
In the `cwi_1_2` we observed the computation of play profiles for newly expanded vertices to be especially effective, allowing the valuation step to be performed only once.
The `vasy_720_390` instance is also interesting because it is not connected, with only 87740 states which are actually reachable from the initial one. This is a favorable case for local algorithms, and in fact the time required to verify the formulas is proportional to the number of actually reachable states rather than the full amount.
== Testing with bisimilarity
We also briefly tested performance of our bisimilarity checker implementation. For that we used some of the instances mentioned above, in particular `vasy_0_1` and `cwi_1_2` because bigger instances were too slow to check. For each instance we obtained a reduced version of them according to strong bisimilarity and then used our implementation to check whether random states in the original instance were bisimilar with the ones in the reduced one.
#figure(
table(
columns: (auto, auto, auto, auto),
align: center + horizon,
inset: (x: 1em),
stroke: none,
table.header(table.cell(rowspan: 2)[*Name*], table.cell(rowspan: 2)[*Bisimilar*], table.cell(colspan: 2)[*Non bisimilar*], [*Min*], [*Max*]),
table.hline(),
`vasy_0_1`, [15.4 ms], [540 #us], [80 ms],
`cwi_1_2`, [5.63 s], [1.17 ms], [5.73 s],
),
caption: [Bisimilarity benchmark results]
) <table-bisimilarity-benchmarks>
We splitted the results based on whether the two states were bisimilar or not, as that influences how many states the local algorithm has to consider. We also noticed that when checking non bisimilar states the time needed varied a lot, which we suspect was due to some states having lot of transitions with the same label and thus causing lot of pairs of states to be checked before becoming distinguishable.
It should be noted that strong bisimilarity admits an algorithm that runs in $O(M log N)$ @bisimilaritymlogn time, where $N$ is the number of states and $M$ the number of transitions. In comparison, for states that are bisimilar the solver needs to visit at least as many vertexes as states, similarly to the deadlock case for $mu$-calculus, leading to a complexity of $O(N dot M)$ for each the improvement step, let alone the whole algorithm.
Ultimately the goal was to show that the powerset game was flexible enough, and being able to solve bisimilarity too, although a bit inefficiently, does confirm it.
|
|
https://github.com/satoqz/dhbw-template | https://raw.githubusercontent.com/satoqz/dhbw-template/main/README.md | markdown | MIT License | # DHBW Thesis Template
A thesis template for work at DHBW created in [Typst](https://github.com/typst/typst), focused on simplicity.
[**Preview**](./example.pdf)
> [!NOTE]
> This template is only intended for students of the faculty of technology, specifially
> computer science students. Especially if you're part of the faculty of economics, you
> should probably consult a lawyer before you even type a single character.
|
https://github.com/frectonz/the-pg-book | https://raw.githubusercontent.com/frectonz/the-pg-book/main/book/178.%20genius.html.typ | typst | genius.html
The Bus Ticket Theory of Genius
November 2019Everyone knows that to do great work you need both natural ability
and determination. But there's a third ingredient that's not as
well understood: an obsessive interest in a particular topic.To explain this point I need to burn my reputation with some group
of people, and I'm going to choose bus ticket collectors. There
are people who collect old bus tickets. Like many collectors, they
have an obsessive interest in the minutiae of what they collect.
They can keep track of distinctions between different types of bus
tickets that would be hard for the rest of us to remember. Because
we don't care enough. What's the point of spending so much time
thinking about old bus tickets?Which leads us to the second feature of this kind of obsession:
there is no point. A bus ticket collector's love is disinterested.
They're not doing it to impress us or to make themselves rich, but
for its own sake.When you look at the lives of people who've done great work, you
see a consistent pattern. They often begin with a bus ticket
collector's obsessive interest in something that would have seemed
pointless to most of their contemporaries. One of the most striking
features of Darwin's book about his voyage on the Beagle is the
sheer depth of his interest in natural history. His curiosity seems
infinite. Ditto for Ramanujan, sitting by the hour working out on
his slate what happens to series.It's a mistake to think they were "laying the groundwork" for the
discoveries they made later. There's too much intention in that
metaphor. Like bus ticket collectors, they were doing it
because they liked it.But there is a difference between Ramanujan and a bus ticket
collector. Series matter, and bus tickets don't.If I had to put the recipe for genius into one sentence, that might
be it: to have a disinterested obsession with something that matters.Aren't I forgetting about the other two ingredients? Less than you
might think. An obsessive interest in a topic is both a proxy for
ability and a substitute for determination. Unless you have
sufficient mathematical aptitude, you won't find series interesting.
And when you're obsessively interested in something, you don't need
as much determination: you don't need to push yourself as hard when
curiosity is pulling you.An obsessive interest will even bring you luck, to the extent
anything can. Chance, as Pasteur said, favors the prepared mind,
and if there's one thing an obsessed mind is, it's prepared.The disinterestedness of this kind of obsession is its most important
feature. Not just because it's a filter for earnestness, but because
it helps you discover new ideas.The paths that lead to new ideas tend to look unpromising. If they
looked promising, other people would already have explored them.
How do the people who do great work discover these paths that others
overlook? The popular story is that they simply have better vision:
because they're so talented, they see paths that others miss. But
if you look at the way great discoveries are made, that's not what
happens. Darwin didn't pay closer attention to individual species
than other people because he saw that this would lead to great
discoveries, and they didn't. He was just really, really interested
in such things.Darwin couldn't turn it off. Neither could Ramanujan. They didn't
discover the hidden paths that they did because they seemed promising,
but because they couldn't help it. That's what allowed them to
follow paths that someone who was merely ambitious would have
ignored.What rational person would decide that the way to write great novels
was to begin by spending several years creating an imaginary elvish
language, like Tolkien, or visiting every household in southwestern
Britain, like Trollope? No one, including Tolkien and Trollope.The bus ticket theory is similar to Carlyle's famous definition of
genius as an infinite capacity for taking pains. But there are two
differences. The bus ticket theory makes it clear that the source
of this infinite capacity for taking pains is not infinite diligence,
as Carlyle seems to have meant, but the sort of infinite interest
that collectors have. It also adds an important qualification: an
infinite capacity for taking pains about something that matters.So what matters? You can never be sure. It's precisely because no
one can tell in advance which paths are promising that you can
discover new ideas by working on what you're interested in.But there are some heuristics you can use to guess whether an
obsession might be one that matters. For example, it's more promising
if you're creating something, rather than just consuming something
someone else creates. It's more promising if something you're
interested in is difficult, especially if it's more difficult for
other people than it is for you. And the obsessions of talented
people are more likely to be promising. When talented people become
interested in random things, they're not truly random.But you can never be sure. In fact, here's an interesting idea
that's also rather alarming if it's true: it may be that to do great
work, you also have to waste a lot of time.In many different areas, reward is proportionate to risk. If that
rule holds here, then the way to find paths that lead to truly great
work is to be willing to expend a lot of effort on things that turn
out to be every bit as unpromising as they seem.I'm not sure if this is true. On one hand, it seems surprisingly
difficult to waste your time so long as you're working hard on
something interesting. So much of what you do ends up being useful.
But on the other hand, the rule about the relationship between risk
and reward is so powerful that it seems to hold wherever risk occurs.
Newton's case, at least, suggests that the risk/reward rule holds
here. He's famous for one particular obsession of his that turned
out to be unprecedentedly fruitful: using math to describe the
world. But he had two other obsessions, alchemy and theology, that
seem to have been complete wastes of time. He ended up net ahead.
His bet on what we now call physics paid off so well that it more
than compensated for the other two. But were the other two necessary,
in the sense that he had to take big risks to make such big
discoveries? I don't know.Here's an even more alarming idea: might one make all bad bets? It
probably happens quite often. But we don't know how often, because
these people don't become famous.It's not merely that the returns from following a path are hard to
predict. They change dramatically over time. 1830 was a really good
time to be obsessively interested in natural history. If Darwin had
been born in 1709 instead of 1809, we might never have heard of
him.What can one do in the face of such uncertainty? One solution is
to hedge your bets, which in this case means to follow the obviously
promising paths instead of your own private obsessions. But as with
any hedge, you're decreasing reward when you decrease risk. If you
forgo working on what you like in order to follow some more
conventionally ambitious path, you might miss something wonderful
that you'd otherwise have discovered. That too must happen all the
time, perhaps even more often than the genius whose bets all fail.The other solution is to let yourself be interested in lots of
different things. You don't decrease your upside if you switch
between equally genuine interests based on which seems to be working
so far. But there is a danger here too: if you work on too many
different projects, you might not get deeply enough into any of
them.One interesting thing about the bus ticket theory is that it may
help explain why different types of people excel at different kinds
of work. Interest is much more unevenly distributed than ability.
If natural ability is all you need to do great work, and natural
ability is evenly distributed, you have to invent elaborate theories
to explain the skewed distributions we see among those who actually
do great work in various fields. But it may be that much of the
skew has a simpler explanation: different people are interested in
different things.The bus ticket theory also explains why people are less likely to
do great work after they have children. Here interest has to compete
not just with external obstacles, but with another interest, and
one that for most people is extremely powerful. It's harder to find
time for work after you have kids, but that's the easy part. The
real change is that you don't want to.But the most exciting implication of the bus ticket theory is that
it suggests ways to encourage great work. If the recipe for genius
is simply natural ability plus hard work, all we can do is hope we
have a lot of ability, and work as hard as we can. But if interest
is a critical ingredient in genius, we may be able, by cultivating
interest, to cultivate genius.For example, for the very ambitious, the bus ticket theory suggests
that the way to do great work is to relax a little. Instead of
gritting your teeth and diligently pursuing what all your peers
agree is the most promising line of research, maybe you should try
doing something just for fun. And if you're stuck, that may be the
vector along which to break out.I've always liked Hamming's famous double-barrelled question: what
are the most important problems in your field, and why aren't you
working on one of them? It's a great way to shake yourself up. But
it may be overfitting a bit. It might be at least as useful to ask
yourself: if you could take a year off to work on something that
probably wouldn't be important but would be really interesting,
what would it be?The bus ticket theory also suggests a way to avoid slowing down as
you get older. Perhaps the reason people have fewer new ideas as
they get older is not simply that they're losing their edge. It may
also be because once you become established, you can no longer mess
about with irresponsible side projects the way you could when you
were young and no one cared what you did.The solution to that is obvious: remain irresponsible. It will be
hard, though, because the apparently random projects you take up
to stave off decline will read to outsiders as evidence of it. And
you yourself won't know for sure that they're wrong. But it will
at least be more fun to work on what you want.It may even be that we can cultivate a habit of intellectual bus
ticket collecting in kids. The usual plan in education is to start
with a broad, shallow focus, then gradually become more specialized.
But I've done the opposite with my kids. I know I can count on their
school to handle the broad, shallow part, so I take them deep.When they get interested in something, however random, I encourage
them to go preposterously, bus ticket collectorly, deep. I don't
do this because of the bus ticket theory. I do it because I want
them to feel the joy of learning, and they're never going to feel
that about something I'm making them learn. It has to be something
they're interested in. I'm just following the path of least resistance;
depth is a byproduct. But if in trying to show them the joy of
learning I also end up training them to go deep, so much the better.Will it have any effect? I have no idea. But that uncertainty may
be the most interesting point of all. There is so much more to learn
about how to do great work. As old as human civilization feels,
it's really still very young if we haven't nailed something so
basic. It's exciting to think there are still discoveries to make
about discovery. If that's the sort of thing you're interested in.
Notes[1] There are other types of collecting that illustrate this point
better than bus tickets, but they're also more popular. It seemed
just as well to use an inferior example rather than offend more
people by telling them their hobby doesn't matter.[2] I worried a little about using the word "disinterested," since
some people mistakenly believe it means not interested. But anyone
who expects to be a genius will have to know the meaning of such a
basic word, so I figure they may as well start now.[3] Think how often genius must have been nipped in the bud by
people being told, or telling themselves, to stop messing about and
be responsible. Ramanujan's mother was a huge enabler. Imagine if
she hadn't been. Imagine if his parents had made him go out and get
a job instead of sitting around at home doing math.On the other hand, anyone quoting the preceding paragraph to justify
not getting a job is probably mistaken.[4] 1709 Darwin is to time what the Milanese Leonardo is to space.[5] "An infinite capacity for taking pains" is a paraphrase of what
Carlyle wrote. What he wrote, in his History of Frederick the Great,
was "... it is the fruit of 'genius' (which means transcendent
capacity of taking trouble, first of all)...." Since the paraphrase
seems the name of the idea at this point, I kept it.Carlyle's History was published in 1858. In 1785 H�rault de S�chelles
quoted Buffon as saying "Le g�nie n'est qu'une plus grande aptitude
� la patience." (Genius is only a greater aptitude for patience.)[6] Trollope was establishing the system of postal routes. He himself
sensed the obsessiveness with which he pursued this goal.
It is amusing to watch how a passion will grow upon a man. During
those two years it was the ambition of my life to cover the
country with rural letter-carriers.
Even Newton occasionally sensed the degree of his obsessiveness.
After computing pi to 15 digits, he wrote in a letter to a friend:
I am ashamed to tell you to how many figures I carried these
computations, having no other business at the time.
Incidentally, Ramanujan was also a compulsive calculator. As Kanigel
writes in his excellent biography:
One Ramanujan scholar, <NAME>, later told how Ramanujan's
research into number theory was often "preceded by a table of
numerical results, carried usually to a length from which most
of us would shrink."
[7] Working to understand the natural world counts as creating
rather than consuming.Newton tripped over this distinction when he chose
to work on theology. His beliefs did not allow him to see it, but
chasing down paradoxes in nature is fruitful in a way that chasing
down paradoxes in sacred texts is not.[8] How much of people's propensity to become interested in a topic
is inborn? My experience so far suggests the answer is: most of
it. Different kids get interested in different things, and it's
hard to make a child interested in something they wouldn't otherwise
be. Not in a way that sticks. The most you can do on behalf of a
topic is to make sure it gets a fair showing � to make it clear to
them, for example, that there's more to math than the dull drills
they do in school. After that it's up to the child.Thanks to <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, <NAME>, and my 7 year old for reading drafts of this.Spanish TranslationRussian TranslationKorean TranslationArmenian Translation
|
|
https://github.com/hyskr/touying-bjtu | https://raw.githubusercontent.com/hyskr/touying-bjtu/main/lib.typ | typst | MIT License | // University theme - modified to fit BUAA
// Inspired by https://github.com/QuadnucYard/touying-theme-seu
#import "@preview/touying:0.4.2": *
#let buaa-nav-bar(self: none) = states.touying-progress-with-sections(dict => {
let (current-sections, final-sections) = dict
current-sections = current-sections.filter(section => section.loc != none).map(section => (
section,
section.children,
)).flatten().filter(item => item.kind == "section")
final-sections = final-sections.filter(section => section.loc != none).map(section => (
section,
section.children,
)).flatten().filter(item => item.kind == "section")
let current-index = current-sections.len() - 1
set text(size: 0.5em)
for (i, section) in final-sections.enumerate() {
set text(fill: if i != current-index {
gray
} else {
white
})
box(inset: 0.5em)[#link(section.loc, utils.section-short-title(section))<touying-link>]
}
})
#let buaa-outline(self: none) = states.touying-progress-with-sections(dict => {
let (current-sections, final-sections) = dict
current-sections = current-sections.filter(section => section.loc != none).map(section => (
section,
section.children,
)).flatten().filter(item => item.kind == "section")
final-sections = final-sections.filter(section => section.loc != none).map(section => (
section,
section.children,
)).flatten().filter(item => item.kind == "section")
let current-index = current-sections.len() - 1
for (i, section) in final-sections.enumerate() {
if i == 0 {
continue
}
set text(fill: if current-index == 0 or i == current-index {
self.colors.primary
} else {
self.colors.primary.lighten(80%)
})
block(
spacing: 1.5em,
[#link(section.loc, utils.section-short-title(section))<touying-link>],
)
}
})
#let slide(
self: none,
title: auto,
subtitle: auto,
header: auto,
footer: auto,
display-current-section: auto,
..args,
) = {
if title != auto {
self.buaa-title = title
}
if subtitle != auto {
self.buaa-subtitle = subtitle
}
if header != auto {
self.buaa-header = header
}
if footer != auto {
self.buaa-footer = footer
}
if display-current-section != auto {
self.buaa-display-current-section = display-current-section
}
(self.methods.touying-slide)(
..args.named(),
self: self,
title: title,
setting: body => {
show: args.named().at("setting", default: body => body)
align(horizon, body)
},
..args.pos(),
)
}
#let title-slide(self: none, ..args) = {
// self = utils.empty-page(self)
let info = self.info + args.named()
info.authors = {
let authors = if "authors" in info {
info.authors
} else {
info.author
}
if type(authors) == array {
authors
} else {
(authors,)
}
}
let content = {
if info.logo != none {
align(right, info.logo)
}
show: align.with(center + horizon)
block(
fill: self.colors.primary,
inset: 1.5em,
radius: 0.5em,
breakable: false,
{
text(size: 1.2em, fill: self.colors.neutral-lightest, weight: "bold", info.title)
if info.subtitle != none {
parbreak()
text(size: 1.0em, fill: self.colors.neutral-lightest, weight: "bold", info.subtitle)
}
},
)
// authors
grid(
columns: (1fr,) * calc.min(info.authors.len(), 3),
column-gutter: 1em,
row-gutter: 1em,
..info.authors.map(author => text(fill: black, author)),
)
v(0.5em)
// institution
if info.institution != none {
parbreak()
text(size: 0.7em, info.institution)
}
// date
if info.date != none {
parbreak()
text(size: 1.0em, utils.info-date(self))
}
}
(self.methods.touying-slide)(self: self, repeat: none, content)
}
#let outline-slide(self: none) = {
self.buaa-title = context if text.lang == "zh" [目录] else [Outline]
let content = {
set align(horizon)
set text(weight: "bold")
hide([-])
buaa-outline(self: self)
}
(self.methods.touying-slide)(self: self, repeat: none, section: (title: context if text.lang == "zh" [目录] else [Outline]), content)
}
#let new-section-slide(self: none, short-title: auto, title) = {
self.buaa-title = context if text.lang == "zh" [目录] else [Outline]
let content = {
set align(horizon)
set text(weight: "bold")
hide([-]) // magic
buaa-outline(self: self)
}
(self.methods.touying-slide)(self: self, repeat: none, section: (title: title, short-title: short-title), content)
}
#let ending-slide(self: none, title: none, body) = {
let content = {
set align(center + horizon)
if title != none {
block(
fill: self.colors.tertiary,
inset: (top: 0.7em, bottom: 0.7em, left: 3em, right: 3em),
radius: 0.5em,
text(size: 1.5em, fill: self.colors.neutral-lightest, title),
)
}
body
}
(self.methods.touying-slide)(self: self, repeat: none, content)
}
#let slides(self: none, title-slide: true, slide-level: 1, ..args) = {
if title-slide {
(self.methods.title-slide)(self: self)
}
(self.methods.touying-slides)(self: self, slide-level: slide-level, ..args)
}
#let register(
self: themes.default.register(),
aspect-ratio: "4-3",
progress-bar: true,
footer-columns: (25%, 25%, 1fr, 5em),
footer-a: self => self.info.author,
footer-b: self => utils.info-date(self),
footer-c: self => if self.info.short-title == auto {
self.info.title
} else {
self.info.short-title
},
footer-d: self => {
states.slide-counter.display() + " / " + states.last-slide-number
},
..args,
) = {
// color theme
self.base-color = rgb("#023174")
self = (self.methods.colors)(
self: self,
primary: self.base-color,
primary-dark: rgb("#004078"),
secondary: rgb("#ffffff"),
tertiary: rgb("#005bac"),
neutral-lightest: rgb("#ffffff"),
neutral-darkest: self.base-color.darken(65%),
)
// marker
self.buaa-knob-marker = box(
width: 0.5em,
place(
dy: 0.1em,
circle(
fill: gradient.radial(self.colors.primary.lighten(100%), self.colors.primary.darken(40%), focal-center: (30%, 30%)),
radius: 0.25em,
),
),
)
// save the variables for later use
self.buaa-enable-progress-bar = progress-bar
self.buaa-progress-bar = self => states.touying-progress(ratio => {
grid(
columns: (ratio * 100%, 1fr),
rows: 2pt,
components.cell(fill: self.colors.primary),
components.cell(fill: self.colors.neutral-lightest),
)
})
self.buaa-navigation = self => {
grid(
align: center + horizon,
columns: (1fr, auto, auto),
rows: 1.8em,
components.cell(fill: self.colors.neutral-darkest, buaa-nav-bar(self: self)),
block(fill: self.colors.neutral-darkest, inset: 4pt, height: 100%, image("assets/vi/bjtu-logo.svg")),
)
}
self.buaa-title = none
self.buaa-subtitle = none
self.buaa-footer = self => {
let cell(fill: none, it) = rect(
width: 100%,
height: 100%,
inset: 1mm,
outset: 0mm,
fill: fill,
stroke: none,
align(horizon, text(fill: self.colors.neutral-lightest, it)),
)
grid(
columns: footer-columns,
rows: (1.5em, auto),
cell(fill: self.colors.neutral-darkest, utils.call-or-display(self, footer-a)),
cell(fill: self.colors.neutral-darkest, utils.call-or-display(self, footer-b)),
cell(fill: self.colors.primary, utils.call-or-display(self, footer-c)),
cell(fill: self.colors.primary, utils.call-or-display(self, footer-d)),
)
}
self.buaa-header = self => {
if self.buaa-title != none {
block(
width: 100%,
height: 1.8em,
fill: gradient.linear(self.colors.primary, self.colors.neutral-darkest),
place(left + horizon, text(fill: self.colors.neutral-lightest, weight: "bold", size: 1.3em, self.buaa-title), dx: 1.5em),
)
}
}
// set page
let header(self) = {
set align(top)
grid(
rows: (auto, auto),
utils.call-or-display(self, self.buaa-navigation),
utils.call-or-display(self, self.buaa-header),
)
}
let footer(self) = {
set text(size: .5em)
set align(center + bottom)
grid(
rows: (auto, auto),
utils.call-or-display(self, self.buaa-footer),
if self.buaa-enable-progress-bar {
utils.call-or-display(self, self.buaa-progress-bar)
},
)
}
self.page-args += (
paper: "presentation-" + aspect-ratio,
header: header,
footer: footer,
header-ascent: 0em,
footer-descent: 0em,
margin: (top: 4.5em, bottom: 3.5em, x: 2.5em),
)
// register methods
self.methods.slide = slide
self.methods.title-slide = title-slide
self.methods.outline-slide = outline-slide
self.methods.new-section-slide = new-section-slide
self.methods.touying-new-section-slide = new-section-slide
self.methods.ending-slide = ending-slide
self.methods.slides = slides
self.methods.touying-outline = (self: none, enum-args: (:), ..args) => {
states.touying-outline(self: self, enum-args: (tight: false) + enum-args, ..args)
}
self.methods.alert = (self: none, it) => text(fill: self.colors.primary, it)
self.methods.tblock = (self: none, title: none, it) => {
grid(
columns: 1,
row-gutter: 0pt,
block(
fill: self.colors.primary-dark,
width: 100%,
radius: (top: 6pt),
inset: (top: 0.4em, bottom: 0.3em, left: 0.5em, right: 0.5em),
text(fill: self.colors.neutral-lightest, weight: "bold", title),
),
rect(
fill: gradient.linear(self.colors.primary-dark, self.colors.primary.lighten(90%), angle: 90deg),
width: 100%,
height: 4pt,
),
block(
fill: self.colors.primary.lighten(90%),
width: 100%,
radius: (bottom: 6pt),
inset: (top: 0.4em, bottom: 0.5em, left: 0.5em, right: 0.5em),
it,
),
)
}
self.methods.init = (self: none, lang: "en", font: ("Linux Libertine",), body) => {
set text(size: 19pt, font: font)
set heading(outlined: false)
set list(marker: self.buaa-knob-marker)
show strong: it => text(weight: "bold", it)
show figure.caption: set text(size: 0.6em)
show footnote.entry: set text(size: 0.6em)
show link: it => if type(it.dest) == str {
set text(fill: self.colors.primary)
it
} else {
it
}
show: if lang == "zh" {
import "@preview/cuti:0.2.1": show-cn-fakebold
show-cn-fakebold
} else {
it => it
}
set text(lang: lang)
show figure.where(kind: table): set figure.caption(position: top)
body
}
self
}
|
https://github.com/soul667/typst | https://raw.githubusercontent.com/soul667/typst/main/PPT/typst-slides-fudan/themes/polylux/themes/themes.typ | typst | #import "simple.typ"
#import "clean.typ"
#import "bipartite.typ"
#import "university.typ"
#import "metropolis.typ"
|
|
https://github.com/fenjalien/metro | https://raw.githubusercontent.com/fenjalien/metro/main/tests/num/exponent/exponent-product/test.typ | typst | Apache License 2.0 | #import "/src/lib.typ": num, metro-setup
#set page(width: auto, height: auto)
#num(e: 2)[1]
#num(e: 2, exponent-product: sym.dot)[1] |
https://github.com/lucannez64/Notes | https://raw.githubusercontent.com/lucannez64/Notes/master/Algebre_Lineaire_Serie_7.typ | typst | #import "@preview/bubble:0.1.0": *
#import "@preview/fletcher:0.4.3" as fletcher: diagram, node, edge
#import "@preview/cetz:0.2.2": canvas, draw, tree
#import "@preview/cheq:0.1.0": checklist
#import "@preview/typpuccino:0.1.0": macchiato
#import "@preview/wordometer:0.1.1": *
#import "@preview/tablem:0.1.0": tablem
#show: bubble.with(
title: "Algèbre Linéaire Série 7",
subtitle: "16/10/2024",
author: "<NAME>",
affiliation: "EPFL",
year: "2024/2025",
class: "Génie Mécanique",
logo: image("JOJO_magazine_Spring_2022_cover-min-modified.png"),
)
#set page(footer: context [
#set text(8pt)
#set align(center)
#text("page "+ counter(page).display())
]
)
#set heading(numbering: "1.1")
#show: checklist.with(fill: luma(95%), stroke: blue, radius: .2em)
= Exercice 1
==
Supposons que $A C = I_n$
Si A a un inverse alors $exists!E space E A = I_n$
Supposons que $ C A != I_n $
Ainsi $ (C A - I_n)D != 0 $
$ A(C A - I_n)D != 0 $
$ A C A D - A D != 0 $
$ A D - A D != 0 $
$ 0 != 0 $ Absurde Donc $A C = I_n arrow.long.l.r.double C A = I_n $ et C est l'inverse de A par définition
==
Supposons que $C A = I_n$
Si A a un inverse alors $exists!E space A E = I_n$
Supposons que $ A C != I_n $
Ainsi $ C(A C - I_n)D != 0 $
$ C(A C - I_n)D != 0 $
$ C A C D - C D != 0 $
$ C D - C D != 0 $
$ 0 != 0 $ Absurde Donc $C A = I_n arrow.long.l.r.double A C = I_n $ et C est l'inverse de A par définition
Par double implication $A$ est inversible d'inverse $C$
= Exercice 2
On $A B(U) = I_n$
et $V(A B) = I_n $
Par associativité $ A(B U) = I_n $ d'après le théorème précédent A est inversible d'inverse $B U$
$ (V A)B = I_n $ d'après le théorème précédent B est inversible d'inverse $V A$
= Exercice 3
$det(A)= b c^2 - c b^2 -a c^2 + c a^2 + a b^2 - b a^2 = c^2(b-a)+b^2(a-c)+ a^2(c- b) = (b-a)(c-a)(c-b)$
$(b-a)(c-a)(c-b) != 0$
$arrow.double.long c!=b!=a!=c$
==
$ A => mat(1, 1, 1, 1; 0, b-a, c-a, d-a; 0, b(b-a), c(c-a), d(d-a); 0, b^2(b-a), c^2(c-a), d^2(d-a);) $
$ det(A) = (b-a)(c-a)(d-a)(c-b)(d-b)(d-c) $
== Généralisation
$ det(A) = product_(0<=i<j<=n)^n (c_j-c_i) $
= Exercice 4
$ t = 7 $
$ s = 14 $
= Exercice 5
$ det(A) = 16 $
= Exercice 6
==
F
==
V
==
F
==
F
= Exercice 7
==
$ det(C) = -15 det(A) $
$ det(2 B) = 2^3B $
$ det(D) = -120 det(A)det(B) $
==
$ det(C) = 4^3(-1) det(A) $
$ det(D^-1) = 1/4det(B)^-1 $
$ det(C D^-1) = -16 det(A)det(B)^-1 $
= Exercice 8
==
S4S
==
S4S
==
S4S
==
S4S
==
$ f(x) = 0 in FF $
$ f(x)+g(x) in RR $
$ alpha f(x) in RR $
Donc $FF$ est un espace vectoriel
==
$ 0 in PP $ car $f(x) = 0 = p(t) = 0$ monome nulle
Question a
==
On peut dire que $C(RR)$ est un sous ensemble de $FF$
Or d'après l'analyse $f+g$ est continue si f et g sont continue donc $f+g in C(RR)$
$f(x) = 0$ est continue et $alpha f(x)$ est continue pour tout $alpha in RR$ si f est continue
donc $C(RR)$ est un sev de $FF$, un espace vectoriel.
==
$f(x) = 0 in C^1(RR)$ car $f(x) = 0$ a pour dérivée lui même donc sa dérivée est continue
$f +g in C^1(RR)$ et $alpha f in C^1(RR)$ d'après l'analyse
donc $C^1(RR)$ est un sev de $C(RR)$
|
|
https://github.com/cetz-package/cetz-venn | https://raw.githubusercontent.com/cetz-package/cetz-venn/master/tests/helper.typ | typst | Apache License 2.0 | #import "@preview/cetz:0.2.2"
#import "/src/lib.typ" as venn
/// Test case canvas surrounded by a red border
#let test-case(body, ..canvas-args, args: none) = {
if type(body) != function {
body = _ => { body }
args = (none,)
} else {
assert(type(args) == array and args.len() > 0,
message: "Function body requires args set!")
}
for arg in args {
block(stroke: 2pt + red,
cetz.canvas(..canvas-args, {
body(arg)
})
)
}
}
|
https://github.com/frectonz/the-pg-book | https://raw.githubusercontent.com/frectonz/the-pg-book/main/book/219.%20google.html.typ | typst | google.html
How to Start Google
March 2024(This is a talk I gave to 14 and 15 year olds about what to do now
if they might want to start a startup later. Lots of schools think
they should tell students something about startups. This is what I
think they should tell them.)Most of you probably think that when you're released into the
so-called real world you'll eventually have to get some kind of
job. That's not true, and today I'm going to talk about a trick you
can use to avoid ever having to get a job.The trick is to start your own company. So it's not a trick for
avoiding work, because if you start your own company you'll
work harder than you would if you had an ordinary job. But you will
avoid many of the annoying things that come with a job, including
a boss telling you what to do.It's more exciting to work on your own project than someone else's.
And you can also get a lot richer. In fact, this is the standard
way to get
really rich. If you look at the lists of the richest
people that occasionally get published in the press, nearly all of
them did it by starting their own companies.Starting your own company can mean anything from starting a barber
shop to starting Google. I'm here to talk about one extreme end of
that continuum. I'm going to tell you how to start Google.The companies at the Google end of the continuum are called startups
when they're young. The reason I know about them is that my wife
Jessica and I started something called Y Combinator that is basically
a startup factory. Since 2005, Y Combinator has funded over 4000
startups. So we know exactly what you need to start a startup,
because we've helped people do it for the last 19 years.You might have thought I was joking when I said I was going to tell
you how to start Google. You might be thinking "How could we
start Google?" But that's effectively what the people who did start
Google were thinking before they started it. If you'd told Larry
Page and <NAME>, the founders of Google, that the company they
were about to start would one day be worth over a trillion dollars,
their heads would have exploded.All you can know when you start working on a startup is that it
seems worth pursuing. You can't know whether it will turn into
a company worth billions or one that goes out of business. So when I
say I'm going to tell you how to start Google, I mean I'm going to
tell you how to get to the point where you can start a company that
has as much chance of being Google as Google had of being Google.
[1]How do you get from where you are now to the point where you can
start a successful startup? You need three things. You need to be
good at some kind of technology, you need an idea for what you're
going to build, and you need cofounders to start the company with.How do you get good at technology? And how do you choose which
technology to get good at? Both of those questions turn out to have
the same answer: work on your own projects. Don't try to guess
whether gene editing or LLMs or rockets will turn out to be the
most valuable technology to know about. No one can predict that.
Just work on whatever interests you the most. You'll work much
harder on something you're interested in than something you're doing
because you think you're supposed to.If you're not sure what technology to get good at, get good at
programming. That has been the source of the median startup for the
last 30 years, and this is probably not going to change in the next
10.Those of you who are taking computer science classes in school may
at this point be thinking, ok, we've got this sorted. We're already
being taught all about programming. But sorry, this is not enough.
You have to be working on your own projects, not just learning stuff
in classes. You can do well in computer science classes without
ever really learning to program. In fact you can graduate with a
degree in computer science from a top university and still not be
any good at programming. That's why tech companies all make you
take a coding test before they'll hire you, regardless of where you
went to university or how well you did there. They know grades and
exam results prove nothing.If you really want to learn to program, you have to work on your
own projects. You learn so much faster that way. Imagine you're
writing a game and there's something you want to do in it, and you
don't know how. You're going to figure out how a lot faster than
you'd learn anything in a class.You don't have to learn programming, though. If you're wondering
what counts as technology, it includes practically everything you
could describe using the words "make" or "build." So welding would
count, or making clothes, or making videos. Whatever you're most
interested in. The critical distinction is whether you're producing
or just consuming. Are you writing computer games, or just playing
them? That's the cutoff.<NAME>, the founder of Apple, spent time when he was a teenager
studying calligraphy — the sort of beautiful writing that
you see in medieval manuscripts. No one, including him, thought
that this would help him in his career. He was just doing it because
he was interested in it. But it turned out to help him a lot. The
computer that made Apple really big, the Macintosh, came out at
just the moment when computers got powerful enough to make letters
like the ones in printed books instead of the computery-looking
letters you see in 8 bit games. Apple destroyed everyone else at
this, and one reason was that Steve was one of the few people in
the computer business who really got graphic design.Don't feel like your projects have to be serious. They can
be as frivolous as you like, so long as you're building things
you're excited about. Probably 90% of programmers start out building
games. They and their friends like to play games. So they build
the kind of things they and their friends want. And that's exactly
what you should be doing at 15 if you want to start a startup one
day.You don't have to do just one project. In fact it's good to learn
about multiple things. <NAME> didn't just learn calligraphy.
He also learned about electronics, which was even more valuable.
Whatever you're interested in. (Do you notice a theme here?)So that's the first of the three things you need, to get good at
some kind or kinds of technology. You do it the same way you get
good at the violin or football: practice. If you start a startup
at 22, and you start writing your own programs now, then by the
time you start the company you'll have spent at least 7 years
practicing writing code, and you can get pretty good at anything
after practicing it for 7 years.Let's suppose you're 22 and you've succeeded: You're now really
good at some technology. How do you get
startup ideas? It might
seem like that's the hard part. Even if you are a good programmer,
how do you get the idea to start Google?Actually it's easy to get startup ideas once you're good at technology.
Once you're good at some technology, when you look at the world you
see dotted outlines around the things that are missing. You start
to be able to see both the things that are missing from the technology
itself, and all the broken things that could be fixed using it, and
each one of these is a potential startup.In the town near our house there's a shop with a sign warning that
the door is hard to close. The sign has been there for several
years. To the people in the shop it must seem like this mysterious
natural phenomenon that the door sticks, and all they can do is put
up a sign warning customers about it. But any carpenter looking at
this situation would think "why don't you just plane off the part
that sticks?"Once you're good at programming, all the missing software in the
world starts to become as obvious as a sticking door to a carpenter.
I'll give you a real world example. Back in the 20th century,
American universities used to publish printed directories with all
the students' names and contact info. When I tell you what these
directories were called, you'll know which startup I'm talking
about. They were called facebooks, because they usually had a picture
of each student next to their name.So <NAME> shows up at Harvard in 2002, and the university
still hasn't gotten the facebook online. Each individual house has
an online facebook, but there isn't one for the whole university.
The university administration has been diligently having meetings
about this, and will probably have solved the problem in another
decade or so. Most of the students don't consciously notice that
anything is wrong. But Mark is a programmer. He looks at this
situation and thinks "Well, this is stupid. I could write a program
to fix this in one night. Just let people upload their own photos
and then combine the data into a new site for the whole university."
So he does. And almost literally overnight he has thousands of
users.Of course Facebook was not a startup yet. It was just a... project.
There's that word again. Projects aren't just the best way to learn
about technology. They're also the best source of startup ideas.Facebook was not unusual in this respect. Apple and Google also
began as projects. Apple wasn't meant to be a company. <NAME>
just wanted to build his own computer. It only turned into a company
when <NAME> said "Hey, I wonder if we could sell plans for this
computer to other people." That's how Apple started. They weren't
even selling computers, just plans for computers. Can you imagine
how lame this company seemed?Ditto for Google. Larry and Sergey weren't trying to start a company
at first. They were just trying to make search better. Before Google,
most search engines didn't try to sort the results they gave you
in order of importance. If you searched for "rugby" they just gave
you every web page that contained the word "rugby." And the web was
so small in 1997 that this actually worked! Kind of. There might
only be 20 or 30 pages with the word "rugby," but the web was growing
exponentially, which meant this way of doing search was becoming
exponentially more broken. Most users just thought, "Wow, I sure
have to look through a lot of search results to find what I want."
Door sticks. But like Mark, Larry and Sergey were programmers. Like
Mark, they looked at this situation and thought "Well, this is
stupid. Some pages about rugby matter more than others. Let's figure
out which those are and show them first."It's obvious in retrospect that this was a great idea for a startup.
It wasn't obvious at the time. It's never obvious. If it was obviously
a good idea to start Apple or Google or Facebook, someone else would
have already done it. That's why the best startups grow out of
projects that aren't meant to be startups. You're not trying to
start a company. You're just following your instincts about what's
interesting. And if you're young and good at technology, then your
unconscious instincts about what's interesting are better than your
conscious ideas about what would be a good company.So it's critical, if you're a young founder, to build things for
yourself and your friends to use. The biggest mistake young founders
make is to build something for some mysterious group of other people.
But if you can make something that you and your friends truly want
to use — something your friends aren't just using out of
loyalty to you, but would be really sad to lose if you shut it down
— then you almost certainly have the germ of a good startup
idea. It may not seem like a startup to you. It may not be obvious
how to make money from it. But trust me, there's a way.What you need in a startup idea, and all you need, is something
your friends actually want. And those ideas aren't hard to see once
you're good at technology. There are sticking doors everywhere.
[2]Now for the third and final thing you need: a cofounder, or cofounders.
The optimal startup has two or three founders, so you need one or
two cofounders. How do you find them? Can you predict what I'm going
to say next? It's the same thing: projects. You find cofounders by
working on projects with them. What you need in a cofounder is
someone who's good at what they do and that you work well with, and
the only way to judge this is to work with them on things.At this point I'm going to tell you something you might not want
to hear. It really matters to do well in your classes, even the
ones that are just memorization or blathering about literature,
because you need to do well in your classes to get into a good
university. And if you want to start a startup you should try to
get into the best university you can, because that's where the best
cofounders are. It's also where the best employees are. When Larry
and Sergey started Google, they began by just hiring all the smartest
people they knew out of Stanford, and this was a real advantage for
them.The empirical evidence is clear on this. If you look at where the
largest numbers of successful startups come from, it's pretty much
the same as the list of the most selective universities.I don't think it's the prestigious names of these universities that
cause more good startups to come out of them. Nor do I think it's
because the quality of the teaching is better. What's driving this
is simply the difficulty of getting in. You have to be pretty smart
and determined to get into MIT or Cambridge, so if you do manage
to get in, you'll find the other students include a lot of smart
and determined people.
[3]You don't have to start a startup with someone you meet at university.
The founders of Twitch met when they were seven. The founders of
Stripe, Patrick and <NAME>, met when John was born. But
universities are the main source of cofounders. And because they're
where the cofounders are, they're also where the ideas are, because
the best ideas grow out of projects you do with the people who
become your cofounders.So the list of what you need to do to get from here to starting a
startup is quite short. You need to get good at technology, and the
way to do that is to work on your own projects. And you need to do
as well in school as you can, so you can get into a good university,
because that's where the cofounders and the ideas are.That's it, just two things, build stuff and do well in school.Notes[1]
The rhetorical trick in this sentence is that the "Google"s
refer to different things. What I mean is: a company that has as
much chance of growing as big as Google ultimately did as Larry and
Sergey could have reasonably expected Google itself would at the
time they started it. But I think the original version is zippier.[2]
Making something for your friends isn't the only source of
startup ideas. It's just the best source for young founders, who
have the least knowledge of what other people want, and whose own
wants are most predictive of future demand.[3]
Strangely enough this is particularly true in countries like
the US where undergraduate admissions are done badly. US admissions
departments make applicants jump through a lot of arbitrary hoops
that have little to do with their intellectual ability. But the
more arbitrary a test, the more it becomes a test of mere determination
and resourcefulness. And those are the two most important qualities
in startup founders. So US admissions departments are better at
selecting founders than they would be if they were better at selecting
students.Thanks to <NAME>, <NAME>, <NAME>, <NAME>, and <NAME> for reading drafts of this.
|
|
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/unify/0.1.0/lib.typ | typst | Apache License 2.0 | #let re-num = regex("^(-?\d+\.?\d*)(((\+(\d+\.?\d*)-(\d+\.?\d*)))|((((\+-)|(-\+))(\d+\.?\d*))))?(e(-?\d+))?$")
#let _format-num(value, exponent: none, upper: none, lower: none) = {
/// Format a number.
/// - `value`: Value of the number.
/// - `exponent`: Exponent in the exponential notation.
/// - `upper`: Upper uncertainty.
/// - `lower`: Lower uncertainty.
let formatted-value = ""
formatted-value += str(value)
if upper != none and lower != none {
if upper != lower {
formatted-value += "^(+" + str(upper) + ")"
formatted-value += "_(-" + str(lower) + ")"
} else {
formatted-value += " plus.minus " + str(upper)
}
} else if upper != none {
formatted-value += " plus.minus " + str(upper)
} else if lower != none {
formatted-value += " plus.minus " + str(lower)
}
if not (upper == none and lower == none) {
formatted-value = "lr((" + formatted-value
formatted-value += "))"
}
if exponent != none {
formatted-value += " dot 10^(" + str(exponent) + ")"
}
formatted-value
}
#let num(value) = {
/// Format a number.
/// - `value`: String with the number.
value = str(value).replace(" ", "")
let match-value = value.match(re-num)
assert.ne(match-value, none, message: "invalid string")
let captures-value = match-value.captures
let upper = none
let lower = none
if captures-value.at(11) != none {
upper = captures-value.at(11)
lower = none
} else {
upper = captures-value.at(4)
lower = captures-value.at(5)
}
let formatted = _format-num(
captures-value.at(0),
exponent: captures-value.at(13),
upper: upper,
lower: lower
)
formatted = "$" + formatted + "$"
eval(formatted)
}
#let _fix-csv(path, delimiter: ",") = {
/// Load a CSV file with pre- or postfixes.
/// - `path`: Path of the CSV file.
/// - `delimiter`: Passed to the `csv` function.
let array = csv(path, delimiter: delimiter)
let dict = (:)
for line in array {
dict.insert(line.at(0), line.at(1))
}
dict
}
#let _unit-csv(path, delimiter: ",") = {
/// Load a CSV file with units.
/// - `path`: Path of the CSV file.
/// - `delimiter`: Passed to the `csv` function.
let array = csv(path, delimiter: delimiter)
let units = (:)
let units-space = (:)
for line in array {
units.insert(line.at(0), line.at(1))
if line.at(2) == "false" or line.at(2) == "0" {
units-space.insert(line.at(0), false)
} else {
units-space.insert(line.at(0), true)
}
}
(units, units-space)
}
#let prefixes = _fix-csv("prefixes.csv")
#let (units, units-space) = _unit-csv("units.csv")
#let postfixes = _fix-csv("postfixes.csv")
#let _format-unit(string, space: "#h(0.166667em)") = {
/// Format a unit.
/// - `string`: String containing the unit.
/// - `space`: Space between units.
let formatted = ""
// whether per was used
let per = false
// whether waiting for a postfix
let post = false
// whether a unit is finished
let unit-finished = false
// one unit
let unit = ""
let split = string.split(" ")
split.push("")
for u in split {
// expecting postfix
if post {
// add postfix
if u in postfixes {
if per {
unit += "^(-"
} else {
unit += "^("
}
unit += postfixes.at(u)
unit += ") \" \""
per = false
post = false
formatted += unit
unit = ""
unit-finished = false
continue
// add per
} else if per {
unit += "^(-1) \" \""
per = false
post = false
formatted += unit
unit = ""
unit-finished = false
// finish unit
} else {
post = false
formatted += unit
unit = ""
unit-finished = false
}
}
// detected per
if u == "per" {
per = true
// add prefix
} else if u in prefixes {
unit += prefixes.at(u)
// add unit
} else if u in units {
unit += units.at(u)
if units-space.at(u) {
unit = space + unit
}
post = true
}
}
formatted
}
#let unit(value, unit, raw-unit: false, space: "#h(0.166667em)") = {
/// Format a unit.
/// - `value`: String containing the number.
/// - `unit`: String containing the unit.
/// - `raw-unit`: Whether to transform the unit or keep the raw string.
/// - `space`: Space between units.
value = str(value).replace(" ", "")
let match-num = value.match(re-num)
assert.ne(match-num, none, message: "invalid string")
let captures-num = match-num.captures
let upper = none
let lower = none
if captures-num.at(11) != none {
upper = captures-num.at(11)
lower = none
} else {
upper = captures-num.at(4)
lower = captures-num.at(5)
}
let formatted-value = _format-num(
captures-num.at(0),
exponent: captures-num.at(13),
upper: upper,
lower: lower
)
let formatted-unit = ""
if raw-unit {
formatted-unit = space + unit
} else {
formatted-unit = _format-unit(unit, space: space)
}
let formatted = "$" + formatted-value + formatted-unit + "$"
eval(formatted)
}
#let _format-range(
lower, upper, exponent-lower: none, exponent-upper: none,
delimiter: "-", space: "#h(0.16667em)", force-parentheses: false
) = {
/// Format a range.
/// - `(lower, upper)`: Strings containing the numbers.
/// - `(exponent-lower, exponent-upper)`: Strings containing the exponentials in exponential notation.
/// - `delimiter`: Symbol between the numbers.
/// - `space`: Space between the numbers and the delimiter.
/// - `force-parentheses`: Whether to force parentheses around the range.
let formatted-value = ""
formatted-value += lower
if exponent-lower != exponent-upper and exponent-lower != none {
formatted-value += "dot 10^(" + str(exponent-lower) + ")"
}
formatted-value += space + delimiter + space + upper
if exponent-lower != exponent-upper and exponent-upper != none {
formatted-value += "dot 10^(" + str(exponent-upper) + ")"
}
if exponent-lower == exponent-upper and (exponent-lower != none and exponent-upper != none) {
formatted-value = "lr((" + formatted-value
formatted-value += ")) dot 10^(" + str(exponent-lower) + ")"
} else if force-parentheses {
formatted-value = "lr((" + formatted-value
formatted-value += "))"
}
formatted-value
}
#let range(lower, upper, delimiter: "-", space: "#h(0.16667em)") = {
lower = str(lower).replace(" ", "")
let match-lower = lower.match(re-num)
assert.ne(match-lower, none, message: "invalid string")
let captures-lower = match-lower.captures
upper = str(upper).replace(" ", "")
let match-upper = upper.match(re-num)
assert.ne(match-upper, none, message: "invalid string")
let captures-upper = match-upper.captures
let formatted = _format-range(
captures-lower.at(0),
captures-upper.at(0),
exponent-lower: captures-lower.at(13),
exponent-upper: captures-upper.at(13),
delimiter: delimiter,
space: space,
)
formatted = "$" + formatted + "$"
eval(formatted)
}
#let unitrange(
lower, upper, unit, raw-unit: false, delimiter: "-",
space: "", unit-space: "#h(0.16667em)"
) = {
/// Format a range with a unit.
/// - `(lower, upper)`: Strings containing the numbers.
/// - `unit`: String containing the unit.
/// - `raw-unit`: Whether to transform the unit or keep the raw string.
/// - `delimiter`: Symbol between the numbers.
/// - `space`: Space between the numbers and the delimiter.
/// - `unit-space`: Space between units.
lower = str(lower).replace(" ", "")
let match-lower = lower.match(re-num)
assert.ne(match-lower, none, message: "invalid string")
let captures-lower = match-lower.captures
upper = str(upper).replace(" ", "")
let match-upper = upper.match(re-num)
assert.ne(match-upper, none, message: "invalid string")
let captures-upper = match-upper.captures
let formatted-value = _format-range(
captures-lower.at(0),
captures-upper.at(0),
exponent-lower: captures-lower.at(13),
exponent-upper: captures-upper.at(13),
delimiter: delimiter,
space: space,
force-parentheses: true
)
let formatted-unit = ""
if raw-unit {
formatted-unit = space + unit
} else {
formatted-unit = _format-unit(unit, space: unit-space)
}
let formatted = "$" + formatted-value + formatted-unit + "$"
eval(formatted)
}
|
https://github.com/ClazyChen/Table-Tennis-Rankings | https://raw.githubusercontent.com/ClazyChen/Table-Tennis-Rankings/main/history_CN/2023/WS-11.typ | typst |
#set text(font: ("Courier New", "NSimSun"))
#figure(
caption: "Women's Singles (1 - 32)",
table(
columns: 4,
[排名], [运动员], [国家/地区], [积分],
[1], [孙颖莎], [CHN], [3628],
[2], [陈梦], [CHN], [3437],
[3], [王曼昱], [CHN], [3406],
[4], [陈幸同], [CHN], [3313],
[5], [早田希娜], [JPN], [3302],
[6], [王艺迪], [CHN], [3225],
[7], [朱雨玲], [MAC], [3222],
[8], [伊藤美诚], [JPN], [3120],
[9], [何卓佳], [CHN], [3111],
[10], [钱天一], [CHN], [3092],
[11], [韩莹], [GER], [3090],
[12], [木原美悠], [JPN], [3080],
[13], [蒯曼], [CHN], [3078],
[14], [张瑞], [CHN], [3070],
[15], [伯纳黛特 斯佐科斯], [ROU], [3054],
[16], [张本美和], [JPN], [3044],
[17], [桥本帆乃香], [JPN], [3037],
[18], [平野美宇], [JPN], [3036],
[19], [刘炜珊], [CHN], [3036],
[20], [范思琦], [CHN], [3028],
[21], [郑怡静], [TPE], [3025],
[22], [石川佳纯], [JPN], [3014],
[23], [杨晓欣], [MON], [2976],
[24], [小盐遥菜], [JPN], [2964],
[25], [陈熠], [CHN], [2961],
[26], [田志希], [KOR], [2960],
[27], [申裕斌], [KOR], [2958],
[28], [芝田沙季], [JPN], [2935],
[29], [阿德里安娜 迪亚兹], [PUR], [2919],
[30], [长崎美柚], [JPN], [2915],
[31], [单晓娜], [GER], [2902],
[32], [森樱], [JPN], [2901],
)
)#pagebreak()
#set text(font: ("Courier New", "NSimSun"))
#figure(
caption: "Women's Singles (33 - 64)",
table(
columns: 4,
[排名], [运动员], [国家/地区], [积分],
[33], [朱芊曦], [KOR], [2889],
[34], [安藤南], [JPN], [2886],
[35], [佐藤瞳], [JPN], [2886],
[36], [奥拉万 帕拉南], [THA], [2884],
[37], [石洵瑶], [CHN], [2857],
[38], [高桥 布鲁娜], [BRA], [2845],
[39], [妮娜 米特兰姆], [GER], [2836],
[40], [边宋京], [PRK], [2830],
[41], [曾尖], [SGP], [2827],
[42], [刘佳], [AUT], [2810],
[43], [倪夏莲], [LUX], [2804],
[44], [袁嘉楠], [FRA], [2792],
[45], [李昱谆], [TPE], [2785],
[46], [李时温], [KOR], [2775],
[47], [大藤沙月], [JPN], [2775],
[48], [邵杰妮], [POR], [2773],
[49], [李雅可], [CHN], [2772],
[50], [<NAME>], [ROU], [2769],
[51], [郭雨涵], [CHN], [2765],
[52], [伊丽莎白 萨玛拉], [ROU], [2759],
[53], [徐奕], [CHN], [2758],
[54], [覃予萱], [CHN], [2757],
[55], [傅玉], [POR], [2757],
[56], [金河英], [KOR], [2755],
[57], [徐孝元], [KOR], [2752],
[58], [DIACONU Adina], [ROU], [2746],
[59], [吴洋晨], [CHN], [2743],
[60], [王晓彤], [CHN], [2743],
[61], [李恩惠], [KOR], [2732],
[62], [<NAME>-Yin], [TPE], [2725],
[63], [王 艾米], [USA], [2723],
[64], [琳达 伯格斯特罗姆], [SWE], [2719],
)
)#pagebreak()
#set text(font: ("Courier New", "NSimSun"))
#figure(
caption: "Women's Singles (65 - 96)",
table(
columns: 4,
[排名], [运动员], [国家/地区], [积分],
[65], [朱成竹], [HKG], [2717],
[66], [梁夏银], [KOR], [2714],
[67], [<NAME>], [SRB], [2705],
[68], [齐菲], [CHN], [2705],
[69], [玛利亚 肖], [ESP], [2697],
[70], [普利西卡 帕瓦德], [FRA], [2696],
[71], [韩菲儿], [CHN], [2691],
[72], [崔孝珠], [KOR], [2682],
[73], [笹尾明日香], [JPN], [2679],
[74], [索菲亚 波尔卡诺娃], [AUT], [2679],
[75], [PESOTSKA Margaryta], [UKR], [2673],
[76], [SAWETTABUT Suthasini], [THA], [2672],
[77], [范姝涵], [CHN], [2666],
[78], [金娜英], [KOR], [2664],
[79], [杜凯琹], [HKG], [2654],
[80], [陈思羽], [TPE], [2643],
[81], [玛妮卡 巴特拉], [IND], [2638],
[82], [张安], [USA], [2638],
[83], [WINTER Sabine], [GER], [2636],
[84], [杨屹韵], [CHN], [2636],
[85], [斯丽贾 阿库拉], [IND], [2623],
[86], [朱思冰], [CHN], [2622],
[87], [KIM Byeolnim], [KOR], [2613],
[88], [ZARIF Audrey], [FRA], [2612],
[89], [WAN Yuan], [GER], [2607],
[90], [苏蒂尔塔 穆克吉], [IND], [2597],
[91], [BAJOR Natalia], [POL], [2589],
[92], [GODA Hana], [EGY], [2587],
[93], [艾希卡 穆克吉], [IND], [2586],
[94], [HUANG Yi-Hua], [TPE], [2585],
[95], [#text(gray, "SOO Wai Yam Minnie")], [HKG], [2584],
[96], [纵歌曼], [CHN], [2584],
)
)#pagebreak()
#set text(font: ("Courier New", "NSimSun"))
#figure(
caption: "Women's Singles (97 - 128)",
table(
columns: 4,
[排名], [运动员], [国家/地区], [积分],
[97], [张墨], [CAN], [2582],
[98], [CIOBANU Irina], [ROU], [2577],
[99], [NOMURA Moe], [JPN], [2574],
[100], [布里特 伊尔兰德], [NED], [2567],
[101], [KAMATH <NAME>], [IND], [2566],
[102], [刘杨子], [AUS], [2561],
[103], [CHENG Hsien-Tzu], [TPE], [2560],
[104], [杨蕙菁], [CHN], [2559],
[105], [ZHANG Xiangyu], [CHN], [2558],
[106], [AKAE Kaho], [JPN], [2550],
[107], [克里斯蒂娜 卡尔伯格], [SWE], [2549],
[108], [STEFANOVA Nikoleta], [ITA], [2548],
[109], [MALOBABIC Ivana], [CRO], [2535],
[110], [GHORPADE Yashaswini], [IND], [2531],
[111], [<NAME>], [CZE], [2530],
[112], [BRATEYKO Solomiya], [UKR], [2530],
[113], [<NAME>], [MAS], [2527],
[114], [BALAZOVA Barbora], [SVK], [2524],
[115], [LOEUILLETTE Stephanie], [FRA], [2524],
[116], [SU Pei-Ling], [TPE], [2523],
[117], [蒂娜 梅谢芙], [EGY], [2522],
[118], [陈沂芊], [TPE], [2517],
[119], [GHOSH Swastika], [IND], [2512],
[120], [GUISNEL Oceane], [FRA], [2511],
[121], [POTA Georgina], [HUN], [2508],
[122], [<NAME>], [HUN], [2508],
[123], [LUT<NAME>], [FRA], [2501],
[124], [<NAME>], [FRA], [2500],
[125], [<NAME>], [CZE], [2498],
[126], [<NAME>], [UKR], [2492],
[127], [<NAME>], [AUS], [2490],
[128], [#text(gray, "<NAME>")], [FRA], [2488],
)
) |
|
https://github.com/dipamsen/typst-playground | https://raw.githubusercontent.com/dipamsen/typst-playground/main/README.md | markdown | # Typst Playground
Demo app to render Typst on the web, using typst.ts.
|
|
https://github.com/VisualFP/docs | https://raw.githubusercontent.com/VisualFP/docs/main/SA/project_documentation/content/meeting_minutes/week_07.typ | typst | = Project Meeting 31.10.2023 08:15 - 09:15 (MS Teams)
== Participants
- Prof. Dr. <NAME>
- <NAME>
- <NAME>
== Agenda
- Discussion of Advisor's thoughts on the current design concept for visual function composition
- Discussion of Unification & Lambda Calculus
- Look at ML Type Inference
- Look at #link("https://www.youtube.com/watch?v=x3evzO8O9e8&ab_channel=OST%E2%80%93OstschweizerFachhochschule")[talk by <NAME> from Zurihac 2019] about type inference
- VisualFP should use ML or Lisp style language as storage format
- Look at the books "Types and Programming Languages" and "Advanced Topics in Types and Programming Languages" by <NAME>
- Discussion of expectations for PoC
- Simple meta-language
- Simple unification-language
- UI to define functions, types and holes
- UI and business logic should be separated to make a possible switch to a different UI framework easier
- The PoC doesn't have to be "ready for use". It's more about trying out libraries, etc.
- Maybe take a look at #link("https://github.com/reflex-frp")[reflex-frp]
|
|
https://github.com/christopherkenny/tufte | https://raw.githubusercontent.com/christopherkenny/tufte/main/_extensions/tufte/typst-template.typ | typst | Other | #let wideblock(content) = block(width: 100% + 2.5in, content)
#let tufte(
title: none,
subtitle: none,
shorttitle: none,
document-number: none,
authors: none,
date: datetime.today(),
abstract: none,
publisher: none,
abstract-title: none,
margin: (left: 1in, right: 3.5in, y: 1.5in),
paper: "us-letter",
lang: "en",
region: "US",
font: (),
fontsize: 11pt,
codefont: "DejaVu Sans Mono",
sansfont: "Gill Sans MT",
sectionnumbering: none,
toc: false,
toc_title: none,
toc_depth: none,
toc_indent: 1.5em,
draft: false,
footer-content: none,
distribution: none,
doc,
) = {
// Document metadata
if authors != none {
set document(
title: title,
author: authors.map(author => to-string(author.name)),
)
} else {
set document(title: title)
}
// Just a suttle lightness to decrease the harsh contrast
set text(fill: luma(30))
// Tables and figures
show figure: set figure.caption(separator: [.#h(0.5em)])
show figure.caption: set align(left)
show figure.caption: set text(font: sansfont)
show figure.where(kind: table): set figure.caption(position: top)
show figure.where(kind: table): set figure(numbering: "I")
show figure.where(kind: "quarto-float-tbl"): set figure.caption(position: top)
show figure.where(kind: "quarto-float-tbl"): set figure(numbering: "I")
show figure.where(kind: image): set figure(
supplement: [Figure],
numbering: "1",
)
show figure.where(kind: "quarto-float-fig"): set figure(
supplement: [Figure],
numbering: "1",
)
show figure.where(kind: raw): set figure.caption(position: top)
show figure.where(kind: raw): set figure(supplement: [Code], numbering: "1")
show raw: set text(font: "Lucida Console", size: 10pt)
// Equations
set math.equation(numbering: "(1)")
show math.equation: set block(spacing: 0.65em)
show link: underline
// Lists
set enum(
indent: 1em,
body-indent: 1em,
)
show enum: set par(justify: false)
set list(
indent: 1em,
body-indent: 1em,
)
show list: set par(justify: false)
// Headings
set heading(numbering: none)
show heading.where(level: 1): it => {
v(2em, weak: true)
text(size: 14pt, weight: "bold", it)
v(1em, weak: true)
}
show heading.where(level: 2): it => {
v(1.3em, weak: true)
text(size: 13pt, weight: "regular", style: "italic", it)
v(1em, weak: true)
}
show heading.where(level: 3): it => {
v(1em, weak: true)
text(size: fontsize, style: "italic", weight: "thin", it)
v(0.65em, weak: true)
}
// show heading: it => {
// if it.level <= 3 {
// it
// } else { }
// }
// Page setup
set page(
paper: "us-letter",
margin: (
left: 1in,
right: 3.5in,
top: 1.5in,
bottom: 1.5in,
),
header: context {
set text(font: sansfont)
block(
width: 100% + 3.5in - 1in,
{
if counter(page).get().first() > 1 {
if document-number != none {
document-number
}
h(1fr)
if shorttitle != none {
upper(shorttitle)
} else {
upper(title)
}
if publisher != none {
linebreak()
h(1fr)
upper(publisher)
}
}
},
)
},
footer: context {
set text(font: sansfont, size: 8pt)
block(
width: 100% + 3.5in - 1in,
{
if counter(page).get().first() == 1 {
if type(footer-content) == array {
footer-content.at(0)
linebreak()
} else {
footer-content
linebreak()
}
if draft [
Draft document, #date.
]
if distribution != none [
Distribution limited to #distribution.
]
} else {
if type(footer-content) == array {
footer-content.at(1)
linebreak()
} else {
footer-content
linebreak()
}
if draft [
Draft document, #date.
]
if distribution != none [
Distribution limited to #distribution.
]
linebreak()
[Page #counter(page).display()]
}
},
)
},
background: if draft {
rotate(
45deg,
text(font: sansfont, size: 200pt, fill: rgb("FFEEEE"))[DRAFT],
)
},
)
set par(
// justify: true,
leading: 0.65em,
first-line-indent: 1em
)
show par: set block(spacing: 0.65em)
// frontmatter
if title != none {
wideblock({
set text(
hyphenate: false,
size: 20pt,
font: sansfont,
)
set par(
justify: false,
leading: 0.2em,
first-line-indent: 0pt,
)
upper(title)
set text(size: fontsize)
v(-0.65em)
upper(subtitle)
})
}
if authors != none {
wideblock({
set text(font: sansfont, size: fontsize)
v(1em)
for i in range(calc.ceil(authors.len() / 3)) {
let end = calc.min((i + 1) * 3, authors.len())
let is-last = authors.len() == end
let slice = authors.slice(i * 3, end)
grid(
columns: slice.len() * (1fr,),
gutter: fontsize,
..slice.map(author => align(
left,
{
upper(author.name)
if "university" in author [
\ #author.university
]
if "email" in author [
\ #to-string(author.email)
]
},
))
)
if not is-last {
v(16pt, weak: true)
}
}
})
}
if date != none {
upper(date)
linebreak()
if document-number != none {
document-number
}
}
if abstract != none {
wideblock({
set text(font: sansfont)
set par(hanging-indent: 3em)
h(3em)
abstract
})
}
if toc {
wideblock({
v(1em)
set text(font: sansfont)
outline(indent: 1em, title: none, depth: 2)
})
}
// Finish setting up sidenotes
set-page-properties()
set-margin-note-defaults(
stroke: none,
side: right,
margin-right: 2.35in,
margin-left: 1.35in,
)
// Body text
set text(
lang: lang,
region: region,
font: font,
style: "normal",
weight: "regular",
hyphenate: true,
size: fontsize,
)
show cite.where(form: "prose"): notecite
doc
}
#set table(
inset: 6pt,
stroke: none,
)
|
https://github.com/jneug/schule-typst | https://raw.githubusercontent.com/jneug/schule-typst/main/tests/kl/test.typ | typst | MIT License | #import "@local/schule:1.0.0": kl
#import kl: *
#import "@preview/finite:0.3.0": automaton, layout, transition-table, cetz, draw, powerset
#show: klausur.with(
autor: "<NAME>",
kuerzel: "Ngb",
titel: "1. Klausur",
reihe: "Automaten und formale Sprachen",
nummer: "1",
fach: "Informatik",
kurs: "Q1 LK",
version: "2023-09-10",
fontsize: 10pt,
dauer: 225,
datum: "11.09.2023",
loesungen: "seite",
)
#let vielErfolg = align(right, text(2em, kl.theme.primary, font: "Comic Neue")[Viel Erfolg!])
#let img(src, ..args) = image("2023-Q2.2/" + src, ..args)
#let b = $#h(.2em)|#h(.2em)$
#aufgabe(titel: "Endliche Automaten")[
@abb:automat1 zeigt den Übergangsgraphen eines endlichen Automaten $G$.
#figure(
automaton(
(
q0: (q1: 0, q2: 0),
q2: (q3: 1, q4: 0),
q4: (q2: 0, q5: 0, q6: 0),
q6: (q7: 1),
q1: (q3: 1, q4: 0),
q3: (q1: 1, q5: 1, q6: 1),
q5: (q7: 1),
q7: (),
),
layout: layout.group.with(
grouping: (
("q0",),
("q1", "q2", "q3", "q4", "q5", "q6"),
("q7",),
),
spacing: 2,
layout: (
layout.linear,
layout.grid.with(columns: 3, spacing: 2.6),
layout.linear,
),
),
style: (
transition: (curve: 0),
q1-q3: (curve: 1),
q3-q1: (curve: 1),
q2-q4: (curve: 1),
q4-q2: (curve: 1),
q1-q4: (label: (pos: .95)),
q2-q3: (label: (pos: .95, dist: -.33)),
q3-q6: (label: (pos: .95)),
q4-q5: (label: (pos: .95, dist: -.33)),
),
),
caption: [Übergangsgraph eines nicht-deterministischen endlichen Automaten $G$.],
) <abb:automat1>
#teilaufgabe[
#operator[Begründe], das es sich bei $G$ um einen nichtdeterministischen endlichen Automaten (NEA) handelt und #operator[erkläre], wie sich die formale Definition eines NEA zu der eines deterministischen endlichen Automaten (DEA) unterschiedet.
#erwartung("Begründet, dass es nicht eindeutige Übergänge im Automaten gibt bzw. Übergänge im Automaten fehlen.", 2)
#erwartung("Erklärt die Unterschiede zwischen NEAs und DEAs.", 4)
#loesung[
- Es gibt Zustände, von denen mehrere Übergänge mit demselben Buchstaben wegführen. (zum Beispiel $q_3$ mit $1$ nach $q_1$, $q_5$ und $q_6$).
- Es gibt Zustände, für die nicht für alle Buchstaben aus $Sigma$ ein Übergang definiert ist. (Zum Beispiel hat $q_0$ keinen Übergang für $1$.)
Die Formale Definition eines NEA unterschiedet sich zu einem DEA nur darin, dass die eindeutige _Übergangsfunktion_ des DEA eine _Übergangsrelation_ wird, die zu einer Kombination aus Zustand und Buchstabe auch mehrere Folgezustände (oder gar keinen) enthalten kann.
In der allgemeinen Definition eines NEA dürfen auch mehrere Startzustände vorhanden sein, wobei wir nur welche mit einem eindeutigen Startzustand betrachten.
]
]
#teilaufgabe[
#operator[Gib] die vollständige formale Beschreibung des NEA $G$ #operator[an]. (Die Übergänge kannst Du in Form einer Übergangstabelle notieren.)
#erwartung([Gibt das 5-Tupel des NEA $G$ an], 6)
#loesung[
#grid(
columns: (1fr, 1fr),
[
$G = (Q, s, Sigma, F, delta)$
- $Q = {q_0, q_1, dots, q_7}$
- $Sigma = {0, 1}$
- $s = q_0$
- $F = {q_7}$
],
[
$delta =$
#transition-table((
q0: (q1: 0, q2: 0),
q1: (q3: 1, q4: 0),
q2: (q3: 1, q4: 0),
q4: (q2: 0, q5: 0, q6: 0),
q6: (q7: 1),
q3: (q1: 1, q5: 1, q6: 1),
q5: (q7: 1),
q7: (),
))
],
)
]
]
#teilaufgabe[
#operator[Zeige], dass die Worte `011111` und `0001` vom Automaten aus @abb:automat1 akzeptiert werden, indem du jeweils eine akzeptierende Zustandsfolge (Ableitung) #operator[angibst].
#erwartung([Gibt eine Ableitung für das Wort `011111` an.], 2)
#erwartung([Gibt eine Ableitung für das Wort `0001` an.], 2)
#loesung[
Ableitungen:
- Ableitung `011111`: $q_0, q_1, q_3, q_1, q_3, q_5, q_7$
- Ableitung `0001`: $q_0, q_2, q_4, q_6, q_7$
]
]
#teilaufgabe[
#operator[Gib] die beiden kürzesten Wörter #operator[an], die der Automat akzeptiert. (Für diese ist kein Ableitung notwendig)
#erwartung([Gibt die kürzesten Wörter `0001` und `0111` an.], 2)
#loesung[
`0001` und `0111`
]
]
#teilaufgabe[
#operator[Beschreibe] möglichst präzise mit eigenen Worten, welche Sprache vom Automaten $G$ akzeptiert wird.
#erwartung([Beschreibt präzise die Sprache $L(G)$.], 4)
#loesung[
Worte der Sprache $L(G)$ beginnen immer mit $0$ und enden mit $1$. Dazwischen wiederholen sich immer doppelte $0$ oder doppelte $1$ (also $00$ oder $11$) beliebig oft, aber mindestens einmal.
]
]
#teilaufgabe[
#operator[Gib] die Sprache $L(G)$ in Mengenschreibweise #operator[an].
#erwartung([Gibt die Sprache $L(G)$ in Mengenschreibweise an.], 4)
#loesung[
$ L(G) = {0 (00|11)^n 1 | 0 < n in NN} $
]
]
]
#aufgabe(titel: "Potenzmengenkonstruktion")[
Bei der Übertragung von binär codierten Daten werden Datenpakete mit mindestens drei Bit immer mit einem Terminatorsymbol aus zwei Nullen (`00`) abgeschlossen. Die Daten zuvor können beliebige Kombinationen aus `1` und `0` sein.
Der Automat $G_D$ in @abb:automat2 akzeptiert die Sprache
$L_D = { w | w #text[ist ein gültiges Datenpaket] }$.
#figure(
automaton(
(
q0: (q1: (0, 1)),
q1: (q2: (0, 1), q0: (0, 1)),
q2: (q3: (0, 1), q0: (0, 1)),
q3: (q4: 0, q0: (0, 1)),
q4: (q5: 0),
q5: (),
),
layout: layout.linear.with(spacing: 1.2),
style: (
q1-q0: (curve: .5, label: (pos: .2)),
q2-q0: (curve: 1, label: (pos: .15)),
q3-q0: (curve: 1.5, label: (pos: .1)),
),
),
caption: [Übergangsgraph eines nicht-deterministischen endlichen Automaten $G_D$.],
) <abb:automat2>
#teilaufgabe[
#operator[Wende] die Potenzmengenkonstruktion auf den NEA $G_D$ an und #operator[gib] den Übergangsgraphen eines äquivalenten DEAs #operator[an], der die Sprache $L_D$ akzeptiert.
#operator[Zeige], dass die Worte `0100100` und `00000000` von Deinem DEA akzeptiert werden.
#erwartung([Erstellt einen vollständigen DEA, der genau die Sprache $L_D$ akzeptiert.], 8)
#erwartung([Gibt Ableitung im DEA für die Worte `0100100` und `00000000` an.], 2)
#loesung[
#grid(
columns: (auto, 1fr),
gutter: 5mm,
[
*Übergangstabelle*
#transition-table((
q0: (q1: (0, 1)),
q1: (q2: (0, 1), q0: (0, 1)),
q2: (q3: (0, 1), q0: (0, 1)),
q3: (q4: 0, q0: (0, 1)),
q4: (q5: 0),
q5: (),
))],
[
*Potenzmengenkonstruktion*
#transition-table(
powerset((
q0: (q1: (0, 1)),
q1: (q2: (0, 1), q0: (0, 1)),
q2: (q3: (0, 1), q0: (0, 1)),
q3: (q4: 0, q0: (0, 1)),
q4: (q5: 0),
q5: (),
)),
)
],
)
*Übergangsdiagramm*
#figure(
automaton(
powerset((
q0: (q1: (0, 1)),
q1: (q2: (0, 1), q0: (0, 1)),
q2: (q3: (0, 1), q0: (0, 1)),
q3: (q4: 0, q0: (0, 1)),
q4: (q5: 0),
q5: (),
)),
final: ("{q0,q1,q2,q3,q5}", "{q0,q1,q2,q3,q4,q5}"),
layout: (
"{q0}": (0, 0),
"{q1}": (2, 0),
"{q0,q2}": (4, 0),
"{q0,q1,q3}": (6, 0),
"{q0,q1,q2}": (6, -2),
"{q0,q1,q2,q3}": (4, -3),
"{q0,q1,q2,q4}": (8, 0),
"{q0,q1,q2,q3,q4}": (4, -6),
"{q0,q1,q2,q3,q5}": (8, -4),
"{q0,q1,q2,q3,q4,q5}": (1, -3),
),
style: (
transition: (curve: 0),
"{q0,q1,q2,q4}-{q0,q1,q2,q3}": (curve: 1.2),
),
),
)
Ableitungen:
- Ableitung `0100100`: ${q_0}, {q_1}, {q_0,q_2}, {q_0,q_1,q_3}, {q_0,q_1,q_2,q_4}, {q_0,q_1,q_2,q_3},$ ${q_0,q_1,q_2,q_3,q_4},{q_0,q_1,q_2,q_3,q_4,q_5}$
- Ableitung `00000000`: ${q_0}, {q_1}, {q_0,q_2}, {q_0,q_1,q_3}, {q_0,q_1,q_2,q_4}, {q_0,q_1,q_2,q_3,q_5},$ ${q_0,q_1,q_2,q_3,q_4}, {q_0,q_1,q_2,q_3,q_4,q_5}, {q_0,q_1,q_2,q_3,q_4,q_5}$
]
]
Damit auch mehrere Datenpakete hintereinander übertragen werden können, soll das Format geändert werden. Der Terminator eines Paketes soll nun aus viermal `0` bestehen (`0000`), dafür dürfen die Datenbits zuvor nicht viermal `0` hintereinander enthalten. Akzeptierte Worte sind beispielsweise `11010000`, `11110000` oder auch `000000`.Nicht akzeptiert werden `000010000` oder `111000`. Jedes Paket muss mindestens ein Datenbit enthalten (`0000` ist also nicht gültig).
#teilaufgabe[
#operator[Entwickele] eine reguläre Grammatik, die die neue Sprache für Datenpakete produziert und #operator[gib] ihre formale Definition vollständig #operator[an].
#erwartung([Entwickelt eine Grammatik, die die Sprache produziert.], 6)
#loesung[
$G = (N,T,S,P)$
- $N = {S, A, B, C}$
- $T = {0, 1}$
- $P:$
- $S #sym.arrow.r 0 A #b 1 A$
- $A #sym.arrow.r 0 B #b 1 A$
- $B #sym.arrow.r 0 C #b 1 A$
- $C #sym.arrow.r 0 D #b 1 A$
- $D #sym.arrow.r 0 #b 1 A$
]
]
Damit ein Empfänger die Korrektheit der Daten überprüfen kann, soll den Datenpaketen ein _Prüfbit_ angehängt werden. Als Prüfbit kann beispielsweise `1` gewählt werden, wenn die Anzahl an `1` im Datenpaket gerade ist, ansonsten ist das Prüfbit `0`. Das Prüfbit sorgt also dafür, dass die Anzhal der `1` im Datenpaket immer ungerade ist. Man nennt diese Art eines Prüfbits "Paritätsbit".
#teilaufgabe[
#operator[Entscheide begründet], ob es einen endlichen Automaten geben kann, der genau die Datenpakete mit Prüfbit akzeptiert, die ein korrektes Paritätsbit angehängt bekommen haben.
#erwartung(
[Begründet, dass ein solcher Automat existieren kann, da ein DEA zwar nicht zählen kann, aber in diesem Fall nur gerade / ungerade entscheiden muss, was möglich ist.],
4,
)
#loesung[
Es kann einen solchen Automaten geben, da der Automat nicht die Anzahl der `1` "zählen" muss, sondern nur, ob die `1` immer paarweise vorkommen. Dies lässt sich mittels zweier Zustände prüfen, die immer untereinander wechseln.
#automaton((
q0: (q1: 1, q0: 0),
q1: (q0: 1, q1: 0),
))
]
]
]
#aufgabe(titel: "Kommentare in Quelltexten")[
In höheren Programmiersprachen gibt es in der Regel zwei Arten, den Quelltext mit Kommentaren zu versehen: Zeilen- und Blockkommentare. In Java werden Zeilenkommentare mit `//` eingeleitet. Sie können an einer beliebigen Stelle im Quellcode stehen und ab dem Kommentar bis zum Zeilenende bzw. dem Ende des Quelltextes. Gültige Blockkommentare werden mit `/*` begonnen und enden mit `*/`. die Zeichen `/` und `*` können auch in anderen Kontexten im Quellcode vorkommen.
#operator[Entwickle] einen deterministischen endlichen Automaten über dem Alphabet $Sigma = { \/, *, \#, z }$, der einen Quelltext darauf prüft, ob er nur gültige (oder keine) Kommentare enthält. (Also alle Worte mit keinen oder gültigen Kommentaren akzeptiert.)
Dabei steht das Symbol "\#" für ein Zeilenende und "z" für ein beliebiges Zeichen, das nicht eines der anderen Zeichen des obigen Alphabets ist.
#hinweis[Es reicht die Angabe eines Übergangsgraphen.]
#erwartung([Zeichnet einen vollständigen DEA, der genau die Kommentar-Sprache akzeptiert.], 10)
#loesung[
#set align(center)
#automaton(
(
q0: (q0: "#,*,z", q1: "/"),
q1: (q0: "#,z,", q2: "/", q3: "*"),
q2: (q0: "#", q2: "*,/,z"),
q3: (q4: "*", q3: "#,/,z"),
q4: (q0: "/", q4: "*", q3: "#,z"),
),
layout: (
q0: (0, 0),
q1: (6, 0),
q2: (3, 4),
q3: (6, -6),
q4: (0, -6),
),
style: (
q0-q0: (anchor: top + left),
q1-q2: (curve: -1),
q2-q0: (curve: -1),
q3-q3: (anchor: right),
q4-q4: (anchor: left),
),
)
]
]
#aufgabe(titel: "Cockatil-Misch-Maschine")[
In der Bar "DIY-Drinks" können sich die Gäste an einer Cocktail-Misch-Maschine selber eigene Cocktails mischen lassen. Damit die Mischungen auf jeden Fall einigermaßen schmecken, arbeitet die Machine mit einem Mischautomaten, der bestimmte Verhältnisse der Zutaten einhalten soll.
Als Zutaten können verschiedene Liköre (`l`), Säfte (`s`) und süße Sirupsorten (`i`) eingemischt werden. Der Automat in @abb:automat-cocktails prüft bei der Eingabe, ob ein Rezept dem Mischverhältnis entspricht.
#figure(
cetz.canvas({
import cetz.draw: *
import draw: *
set-style(transition: (curve: 0))
state((0, 0), "q0", initial: true)
state((5, 0), "q1")
state((9, 0), "q2", final: true)
transition("q0", "q0", label: (text: [$(\#,l): A A \#$\ $(A,l): A A A$], dist: .5))
transition("q0", "q1", label: (text: [$(\#,s): X \#$\ $(A,s): X$\ $(A,i): epsilon$], dist: .75))
transition("q1", "q1", label: (text: [$(X,s): epsilon$\ $(A,s): X$\ $(A,i): epsilon$], dist: .75))
transition("q1", "q2", label: (text: [$(\#,epsilon): epsilon$]))
}),
caption: [Übergangsgraph eines deterministischen endlichen Kellerautomaten $G_3$.],
) <abb:automat-cocktails>
#teilaufgabe[
#operator[Beschreibe] die Lesweise und Bedeutung der Übergänge $(\#,l): A A \#$ und $(\#,epsilon): epsilon$ anhand des Automaten $G_3$.
#operator[Gib] an, nach welchem Mischverhältnis Likör, Saft und Sirup gemischt werden.
#erwartung([Beschreibt die Lesart für Übergänge in einem Kellerautomaten.], 4)
#erwartung([Gibt die Verhältnisse an.], 2)
#loesung[
$(\#,l): A A \#$ bedeutet, dass das kellersymbol $\#$ ist und als Eingabesymbol ein $l$ gelesen wird. Wenn dies der Fall ist, dann werden die Symbole rechts auf den Keller gelegt zwar von rechts nach links gelesen. Also zuerst ein $\#$ und dann zweimal $A$.
Der erste Übergang stellt die erste Auswahl einer Zutat dar, da der Keller noch leer ist. In diesem Fall wurde eine Einheit Likör gewählt.
Der zweite Übergang stellt das Ende eines gültigen Rezepts dar, denn der ÜBergang führt zum einzigen akzeptierenden Zustand und kann nur ausgeführt werden, wenn Keller und Eingabewort leer sind.
]
]
Die folgende kontextfreie Grammatik produziert gültige Cocktail-Rezepte.
#set enum(numbering: n => $p_#n$)
1. $S #sym.arrow.r l A #b s X$
2. $A #sym.arrow.r B C$
3. $B #sym.arrow.r s X #b i #b l A C$
4. $C #sym.arrow.r s X #b i$
5. $X #sym.arrow.r s$
(Beachte: Eine kontextfreie Grammatik unterliegt nicht den Einschränkungen einer regulären Grammatik und darf auf der rechten Seite auch mehr als ein Nichtterminal stehen haben.)
#teilaufgabe[
Produziere mit Hilfe der Grammatik ein Rezept für einen alkoholischen und einen alkoholfreien Cocktail.
#erwartung([Produziert zwei Worte der Sprache (eines mit `l`am Anfang und eines mit `s`.], 2)
#loesung[
*alkoholisch* (eine Einheit Likör und zwei Einheiten Sirup):
$S #sym.arrow.r l A #sym.arrow.r l B C #sym.arrow.r l i C #sym.arrow.r l i i$
*nicht-alkoholisch* (zwei Einheiten Saft):
$S #sym.arrow.r s X #sym.arrow.r s s$
]
]
#teilaufgabe[
#operator[Entwickele] schrittweise eine Ableitung für das Rezept `lllssissssiss`, indem Du für jede Ersetzung die angewandte Produktion ($p_1$ bis $p_5$) notierst.
#erwartung([Gibt eine schrittweise Ableitung des Wortes an.], 4)
#loesung[
/ $p_1$: $S #sym.arrow.r l A$
/ $p_2$: $#hide[S ]#sym.arrow.r l B C$
/ $p_3$: $#hide[S ]#sym.arrow.r l l A C C$
/ $p_2$: $#hide[S ]#sym.arrow.r l l B C C C$
/ $p_3$: $#hide[S ]#sym.arrow.r l l l A C C C C$
/ $p_2$: $#hide[S ]#sym.arrow.r l l l B C C C C C$
/ $p_3$: $#hide[S ]#sym.arrow.r l l l s X C C C C C$
/ $p_5$: $#hide[S ]#sym.arrow.r l l l s s C C C C C$
/ $p_4$: $#hide[S ]#sym.arrow.r l l l s s i C C C C$
/ $p_4$: $#hide[S ]#sym.arrow.r l l l s s i s X C C C$
/ $p_5$: $#hide[S ]#sym.arrow.r l l l s s i s s C C C$
/ $p_4$: $#hide[S ]#sym.arrow.r l l l s s i s s s X C C$
/ $p_5$: $#hide[S ]#sym.arrow.r l l l s s i s s s s C C$
/ $p_4$: $#hide[S ]#sym.arrow.r l l l s s i s s s s i C$
/ $p_4$: $#hide[S ]#sym.arrow.r l l l s s i s s s s i s X$
/ $p_5$: $#hide[S ]#sym.arrow.r l l l s s i s s s s i s s$
]
]
#teilaufgabe[
#operator[Erkläre] anhand des Automaten $G_3$, warum Gäste der Bar, die keinen Alkohol trinken wollen, eher enttäuscht sind vom Angebot der Bar.
#erwartung([Erklärt, dass nicht-alkoholische Cocktails nur aus zwei Einheiten Saft bestehen können.], 2)
#loesung[
Der Automat kann derzeit nur alkoholfreie Cocktails mischen, die aus zweimal Saft bestehen.
]
]
Um ihren Gästen eine größere Auswahl zu bieten, hat "DIY-Drinks" einen neuen Automaten in Auftrag gegeben, der nur nicht-alkoholische Cocktails mixt. Dazu soll je zwei Einheiten Saft (`s`) mit einer Einheit Sodawasser (`w`) und jede Einheit Sirup (`i`) mit zwei Einheiten Sodawasser (`w`) gemischt werden. Zunächst wählen die Kunden Säfte und Sirup aus und am Ende wir das Sodawasser zugegeben.
#teilaufgabe[
#operator[Entwickele] den Übergangsgraphen eines Kellerautomaten, der Rezepte der neuen Maschine akzeptiert.
#erwartung([Entwickelt einen Automaten zur Sprache.], 6)
#loesung[
Es reicht, wenn der Automat nur Rezepte akzeptiert, die zweimal `s` hintereinander erkennen und einmal `s` gefolgt von `i` nicht.
*eingeschränkte Lösung*
#cetz.canvas({
import cetz.draw: set-style
import draw: *
set-style(transition: (curve: 0))
state((0, 0), "q0", initial: true)
state((5, 0), "q1")
state((9, 0), "q2", final: true)
transition(
"q0",
"q0",
label: (text: [$(\#,s): X \#$\ $(\#,i): A A \#$\ $(X,s): A$\ $(A,s): X A$\ $(A,i): A A A$], dist: 1.25),
)
transition("q0", "q1", label: (text: [$(A,w): epsilon$]))
transition("q1", "q1", label: (text: [$(A,w): epsilon$]))
transition("q1", "q2", label: (text: [$(\#,epsilon): epsilon$]))
})
*Lösung mit beliebigen `s` und `i` Kombinationen*
#cetz.canvas({
import cetz.draw: set-style
import draw: *
set-style(transition: (curve: .8))
state((0, 0), "q0", initial: true)
state((5, 0), "q1")
state((9, 0), "q2", final: true)
state((4, -4), "q3")
transition("q0", "q0", label: (text: [$(\#,i): A A \#$\ $(A,i): A A A$], dist: .75))
transition("q0", "q1", label: (text: [$(A,w): epsilon$]))
transition("q1", "q1", label: (text: [$(A,w): epsilon$]))
transition("q1", "q2", label: (text: [$(\#,epsilon): epsilon$]))
transition("q0", "q3", label: (text: [$(\#,s): \#$]))
transition("q3", "q3", label: (text: [$(\#,i): A A \#$\ $(A,i): A A A$]))
transition("q3", "q0", label: (text: [$(\#,s): A$]))
})
]
]
Da die Zutaten der ersten Misch-Maschine $G_3$ in @abb:automat-cocktails recht teuer sind, soll eine neue Version der Maschine die Cocktails am Ende des Mischvorgangs pro Anteil Likör mit vier Anteilen Sodawasser auffüllen.
#teilaufgabe[
#operator[Beurteile], ob eine solche Änderung am aktuellen Modell des Automaten umsetzbar ist und #operator[begründe] Deine Antwort.
#erwartung([Begründet, dass die neue Sprache für Rezepte nicht mehr kontextfrei ist.], 4)
#loesung[
Die Änderung ist mit einem Kellerautomaten nicht umsetzbar, da der Keller leer ist, nachdem Saft / Sirup eingefüllt wurde und der Automat nicht mehr feststellen kann, wie viel Likör zuvor eingefüllt wurde. Es handelt sich also um eine kontextsensitive Sprache.
]
]
]
#vielErfolg
#anhang[
= Dokumentation
#info.docs.display("list")
]
|
https://github.com/frectonz/the-pg-book | https://raw.githubusercontent.com/frectonz/the-pg-book/main/book/138.%20vw.html.typ | typst | vw.html
Snapshot: Viaweb, June 1998
January 2012A few hours before the Yahoo acquisition was announced in June 1998
I took a snapshot of Viaweb's
site. I thought it might be interesting to look at one day.The first thing one notices is is how tiny the pages are. Screens
were a lot smaller in 1998. If I remember correctly, our frontpage
used to just fit in the size window people typically used then.Browsers then (IE 6 was still 3 years in the future) had few fonts
and they weren't antialiased. If you wanted to make pages that
looked good, you had to render display text as images.You may notice a certain similarity between the Viaweb and Y Combinator logos. We did that
as an inside joke when we started YC. Considering how basic a red
circle is, it seemed surprising to me when we started Viaweb how
few other companies used one as their logo. A bit later I realized
why.On the Company
page you'll notice a mysterious individual called <NAME>.
<NAME> (aka Rtm) was so publicity averse after the
Worm that he
didn't want his name on the site. I managed to get him to agree
to a compromise: we could use his bio but not his name. He has
since relaxed a bit
on that point.Trevor graduated at about the same time the acquisition closed, so in the
course of 4 days he went from impecunious grad student to millionaire
PhD. The culmination of my career as a writer of press releases
was one celebrating
his graduation, illustrated with a drawing I did of him during
a meeting.(Trevor also appears as Trevino
Bagwell in our directory of web designers merchants could hire
to build stores for them. We inserted him as a ringer in case some
competitor tried to spam our web designers. We assumed his logo
would deter any actual customers, but it did not.)Back in the 90s, to get users you had to get mentioned in magazines
and newspapers. There were not the same ways to get found online
that there are today. So we used to pay a PR
firm $16,000 a month to get us mentioned in the press. Fortunately
reporters liked
us.In our advice about
getting traffic from search engines (I don't think the term SEO
had been coined yet), we say there are only 7 that matter: Yahoo,
AltaVista, Excite, WebCrawler, InfoSeek, Lycos, and HotBot. Notice
anything missing? Google was incorporated that September.We supported online transactions via a company called
Cybercash,
since if we lacked that feature we'd have gotten beaten up in product
comparisons. But Cybercash was so bad and most stores' order volumes
were so low that it was better if merchants processed orders like phone orders. We had a page in our site trying to talk merchants
out of doing real time authorizations.The whole site was organized like a funnel, directing people to the
test drive.
It was a novel thing to be able to try out software online. We put
cgi-bin in our dynamic urls to fool competitors about how our
software worked.We had some well
known users. Needless to say, Frederick's of Hollywood got the
most traffic. We charged a flat fee of $300/month for big stores,
so it was a little alarming to have users who got lots of traffic.
I once calculated how much Frederick's was costing us in bandwidth,
and it was about $300/month.Since we hosted all the stores, which together were getting just
over 10 million page views per month in June 1998, we consumed what
at the time seemed a lot of bandwidth. We had 2 T1s (3 Mb/sec)
coming into our offices. In those days there was no AWS. Even
colocating servers seemed too risky, considering how often things
went wrong with them. So we had our servers in our offices. Or
more precisely, in Trevor's office. In return for the unique
privilege of sharing his office with no other humans, he had to
share it with 6 shrieking tower servers. His office was nicknamed
the Hot Tub on account of the heat they generated. Most days his
stack of window air conditioners could keep up.For describing pages, we had a template language called RTML, which
supposedly stood for something, but which in fact I named after
Rtm. RTML was Common Lisp augmented by some macros and libraries,
and concealed under a structure editor that made it look like it
had syntax.Since we did continuous releases, our software didn't actually have
versions. But in those days the trade press expected versions, so
we made them up. If we wanted to get lots of attention, we made
the version number an
integer. That "version 4.0" icon was generated by our own
button generator, incidentally. The whole Viaweb site was made
with our software, even though it wasn't an online store, because
we wanted to experience what our users did.At the end of 1997, we released a general purpose shopping search
engine called Shopfind. It
was pretty advanced for the time. It had a programmable crawler
that could crawl most of the different stores online and pick out
the products.
|
|
https://github.com/pauladam94/ENS-Rennes-Typst-Slides-Template | https://raw.githubusercontent.com/pauladam94/ENS-Rennes-Typst-Slides-Template/main/README.md | markdown | # ENS-Rennes-Typst-Slides-Template
Typst Slide Template for ENS Rennes
You have to download all of the files in your Tyspt Project.
Then you write in the main.typ your presentation. There is already example of what you can do with the template (and how to do it).
|
|
https://github.com/polarkac/MTG-Stories | https://raw.githubusercontent.com/polarkac/MTG-Stories/master/stories/011%20-%20Journey%20into%20Nyx/004_Thank%20the%20Gods.typ | typst | #import "@local/mtgstory:0.2.0": conf
#show: doc => conf(
"Thank the Gods",
set_name: "Journey into Nyx",
story_date: datetime(day: 30, month: 04, year: 2014),
author: "<NAME>",
doc
)
"Thank the gods!" the red-faced midwife exclaimed as Raissa's son began to emerge. The baby fought Raissa savagely as she pushed. He bucked with his tiny hooves, and the nubs of his new horns dug into her tender insides. #emph[Selfish!] Raissa thought, imagining the boy grasping the cord and trying to shimmy back up its length to hide behind her heart. As she struggled, her anger grew.
#v(0.35em)
#line(length: 100%, stroke: rgb(90%, 90%, 90%))
#v(0.35em)
At three months into the pregnancy, the midwife had announced that there would be twins, a divination that puffed her up like a haughty hen. But Raissa had already known this; the starfish had revealed this to her. It was also the starfish that showed her that one twin was a boy and one was a girl.
Raissa had visited the briny tidal pool often as she carried the twins. She gingerly picked her way down the jagged cliffs, her small hooves slipping on pebbles as she clung to the stones, inching toward the blue-green shore where she consulted the magical creature. Along the way, she collected clams to place in the pool next to the opalescent creature. The offerings made, its scintillant spiny surface swirled in a beautiful and mesmerizing dance until she tasted salt and felt herself floating like a mote in the pool, the starfish looming gargantuan before her. Looking up at the watery surface above her, images formed on its rippling underside, showing her visions of things she could not otherwise know.
#figure(image("004_Thank the Gods/01.jpg", width: 100%), caption: [Sigiled Starfish| Art by <NAME>], supplement: none, numbering: none)
At five months, Raissa saw in the vision that the boy was outgrowing the girl, although this was something her own body told, a maternal foreknowledge that permitted her a small sense of power in her life that had become all but commandeered by the needs of her unborn children.
At six months, the watery vision disturbed Raissa greatly. Floating in their womb-world, the wriggling boy crowded the tiny girl, forcing her into deep recesses. The girl shrank in the boy's overbearing presence until he completely eclipsed Raissa's view of girl.
Shocked, Raissa kicked toward the surface of the dream, breaching it like a panicked fish. She lay gasping in the harsh white light and air of the shoreline. After several minutes, she gathered herself and stumbled home, massaging her swollen belly and feeling only the presence of one child within her.
Two weeks passed, and she could no longer resist returning to make offerings to the starfish to peer into the secrets within her. Now, a single child swam inside her, a fattened boy growing large in the stolen space. He seemed to dance in her belly—yes, she could feel him cavorting within her, full of glee, as she floated in the vision.
Raissa was not disturbed by this, however; in fact, she felt a surge of pride—pride in her son's tenacity, his unfettered exuberance, and his strength. Raissa began to sway to the rhythm of his triumphant kicks.
At eight months, the starfish's dancing silver sigils shifted in color and wove a dream of incomprehensible breadth, drenched in waves of verdant green and splayed fans of fiery red. The vision pulsed with places she had never seen, places she understood that she would never see—fantastic and foul places that were no part of Theros.
#figure(image("004_Thank the Gods/02.jpg", width: 100%), caption: [Mana Confluence| Art by <NAME>right], supplement: none, numbering: none)
The worlds spun like a child's mobile around her son, who stood defiantly at the center, now fully grown. His haunches, fleeced in wiry auburn fur, flexed like a charging bull's. Thick horns curved from the back of his head, a mighty coiling crown of bone. The vision overwhelmed Raissa with its staggering portent. Her son would be a king! Again, pride washed through her; however, this time, down deep in the dark trenches of her mind, a cold current flowed.
#v(0.35em)
#line(length: 100%, stroke: rgb(90%, 90%, 90%))
#v(0.35em)
At last, Raissa felt the child relent to her increasing frustration and anger. That anger gave her strength, which she used to finally expel him, howling, from her body. The midwife's placid expression darkened as she pulled the baby and it kicked at her. Raissa's anger quickly dissolved into love when the midwife, cursing under her breath as she lifted the squirming child and struggled to swaddle him, finally thrust him into Raissa's arms.
"Thank the gods," the midwife muttered as she turned and hurried from the room.
Raissa's silk robe clung to her skin, soaked and cold with exertion. She shivered, and she called out weakly for the midwife to bring a blanket, but the woman was already beyond earshot, having disappeared into the cellar to drink from the Setessan Order of Midwives's store of symposium wine.
#figure(image("004_Thank the Gods/03.jpg", width: 100%), caption: [Voyaging Satyr| Art by <NAME>], supplement: none, numbering: none)
Raissa lay on the straw mattress, exhausted, and considered her situation. She had sought the assistance of the women of Setessa when giving birth. Most satyr women, once sufficiently recovered, would simply abandon their children to the care of Setessa and return to the carefree revels of Skola Valley, the satyr home. Her sister had done just that when she had become pregnant. Should she do the same? Raissa looked down at the pink face of her boy and knew she could not. This child was special, and he would need her to fulfill the destiny she had witnessed.
She hugged the child close.
#v(0.35em)
#line(length: 100%, stroke: rgb(90%, 90%, 90%))
#v(0.35em)
"Thank the gods!" her neighbors exclaimed, when Raissa staggered from the burning house, her six-year-old son in her arms. They rushed to her and took the boy from her arms as she collapsed, coughing convulsively, her silk robe seared and smoking. "Thank the gods," they repeated, and Raissa clenched her teeth. #emph[The gods, indeed.] Raissa wanted to rebuke the people who offered those thanks, the same people who whispered about her and her child when they thought she could not hear. And what had the gods done for her, except curse her with this nearly feral child she could not control? He had caused them to be cast out of Setessa when he shoved the son of one of the Karametra temple's ruling council to his death from a high rope bridge among the trees. But Raissa could only gasp and cough up blackened fluid.
#emph[I should have left him and returned to the Valley] , she thought bitterly.
When she had her breath again, she climbed to her feet and snatched the boy from their arms. She turned and limped with him down the road, still coughing, leaving the muttering of the crowd behind her.
"You are strong," said the boy. Raissa looked down at him. He smiled up at her, blinking soot from his wide, bright green eyes. Once again, Raissa's anger toward her son drained away, and love swelled in the space.
She pried from his small hand the charred, oil-soaked tinder he had used to set her bed alight while she napped and tossed it away.
#figure(image("004_Thank the Gods/04.jpg", width: 100%), caption: [], supplement: none, numbering: none)
After an hour of walking, despair settled over Raissa. She placed the boy on the ground and rested, watching as he clopped off to play near the trees at the edge of the road. She had no place to go, now. She had been walking with no destination in mind, and sunset was only a couple of hours away. Where would they sleep? The boy, now wielding a sharp stick like a sword, leaped back and forth across the ditch at the side of the road. What would they eat?
Raissa looked up for an answer, almost out of habit, as if she would see there not the vault of Nyx arching above, but the rippling reassuring dreams of the starfish's visions. There was only the empty meaningless sky.
#emph[Am I punished because I do not pay tribute to the gods?] Raissa knelt where she stood. "Is this what you want?" she asked the open air. She closed her eyes against the unsympathetic stare of the heavens. She clasped her hands together. "Would this satisfy you, to show you that you have broken us?"
Raissa listened to her son humming and leaping at the edge of the road. "Shall I submit?" she said, more quietly.
All was quiet. Then, she heard her son next to her shout, "Strong!" The boy struck her in the side of her head with his stick. Pain burst behind her eyelids, white and searing, and she cried out. He scooted away, giggling. A warm trickle oozed down the side of her face.
#v(0.35em)
#line(length: 100%, stroke: rgb(90%, 90%, 90%))
#v(0.35em)
Raissa did not know the path forward for herself or her son, but she knew where she could learn it. It had been a year since she visited the tidal pools. She hoped the starfish would still be there, although it had been so long she worried that it had moved on to other pools in search of sustenance once her offerings of clams had stopped.
Raissa picked her way carefully down the cliffs, while her son hopped and skittered and laughed his way down ahead of her. At the shore, she showed him how to search for clams. They gathered several, and she led him over weathered stones to the secluded tidal pools. She checked the pool she had always visited, but the starfish was gone.
She searched the other pools, going farther and farther out from the first one. Then, in a shallow depression near the edge of the rocky ground, she found the starfish. It glinted silver and orange in the long evening rays of the sun. Raissa placed her clams in the pool around the starfish, and her son did the same. His large eyes widened as the starfish shifted, and its surface flushed with green and red. Together, Raissa and her son floated into the dream.
She saw a night sky above her, Nyx itself, full of constellations that glided about with a life of their own. They flirted with, welcomed, threatened, and retreated from one another in a mighty drama that amazed Raissa.
Then, it all stopped. The constellations, their elegant movements arrested, hung motionless before her and her son. Slowly, their heads turned. They faced Raissa—no, they were facing her son!—and outrage flared in their eyes. Their mouths opened, and in unison their withering voices erupted in a terrible chorus of condemnation. They raised their weapons. Their hands filled with storms, and lightning arced from their fingers as they advanced on her son. Raissa reached out to grab her son, but he was not there. She saw him, ascending on a roiling cloud of acrid red and green power toward the advancing ranks of the empyreal host, in his grip a gleaming staff. Raissa recoiled and covered her face.
#figure(image("004_Thank the Gods/05.jpg", width: 100%), caption: [Extinguish All Hope | Art by Chase Stone], supplement: none, numbering: none)
The vision went dark. She tasted salt and something metallic in her mouth.
"Strong!"
The darkness lifted. Her son was laughing, a harsh laugh that seemed full of spite and embers, not the bright innocence of a child. He held aloft his sharp stick in a victorious pose. A glistening gray ichor trickled down the length of the stick, down his arm, and dripped into the pool from his elbow to make dark clouds in the water. At the end of the stick writhed the impaled gray body of the starfish.
|
|
https://github.com/gianzamboni/cancionero | https://raw.githubusercontent.com/gianzamboni/cancionero/main/wip/evil-like-me.typ | typst | #import "../theme.typ": *;
== Evil Like Me
=== <NAME> & <NAME>
Look at you, look at me, \
I don’t know who to be, mother \
Is it wrong? Is it right? \
Be a thief in the night?, mother \
Tell me what to do
#newVerse
I was once like you, my child, slightly insecure \
Argued with my mother too, thought I was mature \
But I put my heart aside and I used my head \
Now I think it's time you learned \
What dear old mamma said
#newVerse
Don’t you wanna be evil like me? \
Don’t you wanna be mean? \
Don't you wanna make mischief your daily routine?
#newVerse
Well you can spend your life attending to the poor \
But when you're evil doing less is doing more
#newVerse
Don't you wanna be ruthless and rotten and mad? \
Don't you wanna be very, very good at being bad? \
I have tried my whole life long \
To do the worst I can
#newVerse
Clawed my way to victory \
Built my master plan \
Now the time has come, my dear \
For you to take your place \
Promise me you’ll try to be \
An absolute disgrace
#newVerse
Don't you wanna be evil like me? \
Don't you wanna be cruel? \
Don't you wanna be nasty and brutal and cool? \
#newVerse
And when you grab that wand that's when your reign begins \
Who wants an evil queen without a sack of sins? \
Don't you wanna be heartless and hardened as stone? \
Don't you wanna be finger licking' evil to the bone?
#newVerse
This is not for us to ponder \
This was preordained \
You and I shall rule together \
Freedom soon regain \
Mistress of the universe, powerful and strong
#newVerse
Daughter, hear me \
Help me, join me \
Won't you sing along?
#newVerse
Now we're gonna be evil! \
It's true! \
Never gonna think twice \
And we're gonna be spiteful \
Yes, spiteful!
#newVerse
That's nice \
In just an hour or two \
Our future's safe and sure \
This mother-daughter act is going out on tour
|
|
https://github.com/gforges/PowerMEMs_template | https://raw.githubusercontent.com/gforges/PowerMEMs_template/main/template_proceeding_power_mems.typ | typst | #let template_proceeding(
title: none,
authors: (),
abstract: [],
keywords: [],
affiliations: (),
corps_du_texte,
) = {
set math.equation(numbering:"(1)",number-align:horizon)
set page(
paper: "a4",
margin: (x: 1.9cm, y: 1.9cm),
)
set text(
lang: "En",
font: "Times New Roman",
size: 10pt,
)
show bibliography: set block(height: 0.7em, below: 0.7em)
show figure.caption: emph
show figure.caption: set align(start)
show figure.where(kind: table): set figure.caption(position: top)
show figure.caption.where(kind: table): set align(center)
show table: set par(justify: false)
set table(
fill: (x,y) =>
if x >=1 and y == 1 or x>=1 and y ==3 or x>=1 and y ==5 {
gray.lighten(40%)
},
align: horizon
)
show heading: set block(spacing: 1em)
show heading.where(level: 1): it => block(text(size: 12pt,strong(upper(it.body))) + v(-0.5em))
show heading.where(level: 2): it => block(text(size: 10pt, strong(it.body))+ v(-0.4em))
set align(center)
strong[#upper(text(14pt, title))]
linebreak()
text(12pt, style: "italic", authors.enumerate().map(((i, author)) => author.name + super[#(author.affiliation.join(",") )]).join(", "))
linebreak()
text(12pt, affiliations.enumerate().map(((i, affiliations)) => super[#(affiliations.number.join(",") )] + affiliations.name + [ ]).join("and" + linebreak()))
set align(left)
set par(
justify: true,
)
show: columns.with(2, gutter: 0.635cm)
[
= Abstract
#h(0.635cm)
#text(abstract)
= keywords
#h(0.635cm)
#text(keywords)
]
corps_du_texte
}
|
|
https://github.com/typst-doc-cn/typst-doc-cn | https://raw.githubusercontent.com/typst-doc-cn/typst-doc-cn/main/README.md | markdown | # Typst 中文文档网站
社区驱动的非官方 Typst 中文文档.
https://typst-doc-cn.github.io/docs/
GitHub Repo：https://github.com/typst-doc-cn/typst-doc-cn.github.io
Gitee 镜像：https://gitee.com/orangex4/typst-doc-cn.github.io
## 贡献
1. Fork 仓库 https://github.com/typst-doc-cn/typst-doc-cn.github.io
2. 更改 `./docs/src` 目录下的 Markdown 文件 (不用修改文件名和主标题)
3. 更改 `./docs/i18n` 目录下的 Yaml 文件
4. 示例 (example) 里的英文不需要翻译成中文
5. 发起一个 Pull Request
6. 如果需要的话，也可以在文档的末尾处留下翻译者的名字
PS: Reference 中的 *CONTENT* 和 *COMPUTE* 部分需要深入到 `./library/src/text/misc.rs` 这类代码文件中的注释中修改.
如果想要贡献的话, 可以加入 QQ 群 793548390 联系 OrangeX4, 我们会使用石墨文档进行协作.
当然也可以直接尝试翻译和发起 Pull Request.
## 技术细节
Typst 的文档生成是与 Typst 源码紧耦合的, 具体体现在:
1. Typst 开发者使用 Rust 写了一个 `docs` 模块, 文档生成的大部分工作都在这里进行;
2. Typst 的文档是使用一种 Markdown 的方言以及 Yaml 文件生成的, `docs/src` 路径下的文件;
3. `docs` 模块里的函数被执行后, 会动态地生成示例图片, 就像你们示例代码对应的右边的示例图片, 均为编译时生成的;
4. 参考部分对应的大部分页面, 例如 [`lorem`](https://typst-doc-cn.github.io/docs/reference/text/lorem/) 函数, 对应的 Markdown 部分是写在 `lorem` 函数对应的 Rust 代码文件的注释里的, 有点像 `docstring`;
5. Typst Repo 里面只有 `docs` 模块的代码, 没有对应的文档网页生成的代码, 那部分还没有开源;
因此我做了以下事情以生成这个 Typst 中文文档网页:
1. 修改了 `docs` 模块的部分代码, 在 `assets` 路径下生成了一个所有文档对应的 `docs.json` 文件, 这个文件里面的结构相对复杂, 但是包含了生成一个文档网站的全部内容;
2. `docs.json` 里面有多种类型的结构:
1. 最简单的是 `html` 类型, 对应概览和教程, 以及参考的 `LANGUAGE` 大部分;
2. 还有 `type` 类型, 对应的就是类型对应的页面;
3. 还有 `func` 类型, 对应的就是函数对应的页面, 里面内容繁杂, 东西很多;
4. 其他还有三种类型 `category`, `funcs`, `symbol`;
3. 我依照官网的 HTML 和 CSS 文件, 使用 `jinja2` 的语法写了几个 HTML 模板, 放在 `templates` 路径下;
4. 然后我写了 `gen.py`, 用于将 `docs.json` 使用模板转换为最终的 Web 网站, 放在 `dist` 路径下;
5. 根据 `docs.json` 里的内容, 生成了 `i18n` 目录便于翻译;
6. 写了一个 GitHub Action 用于将生成 `dist` 部署到 GitHub Pages 上.
## 本地生成
本地生成是非必须的, 但是它很适合你在本地查看生成的网页是否正确.
首先你需要 clone 本仓库, 并安装 `cargo` 工具链, 以及 Python 和 Python 包 `jinja2`.
```sh
cargo test --package typst-docs --lib -- tests::test_docs --exact --nocapture
python ./gen.py
```
最后编译得到的文件位于 `./dist`.
|
|
https://github.com/hewliyang/fyp-typst | https://raw.githubusercontent.com/hewliyang/fyp-typst/main/ablations.typ | typst | #set heading(numbering: "1.")
#import "@preview/showybox:2.0.1": showybox
= Ablations
In this section, we describe retraining the NISQA architecture from scratch on naturalness MOS with the newer self-attention layers described in @Mittag_2021 instead of the BiLSTM @Mittag_2020 architecture to investigate it's behavior and sensitivity to different pre-training data. We would also like to observe the impact of removing @prahallad2014blizzard and @prahallad2015blizzard from the train set.
All experiments were conducted on an AWS EC2 `g4dn.xlarge` instance with 4 vCPUs, 16 GB of memory and a single Nvidia Tesla T4 with 16 GB of VRAM.
== Training
Since, the original pre-training corpus was not released in @Mittag_2020, we utilize a similar synthetic corpus described in @Mittag_2021 as the *NISQA Corpus*.
Overall, it includes over 14,000 stimuli with a total of over 97,000 human ratings for MOS-N. But we only use a subset shown below as the other datasets mainly focused on VoIP distortions, which may be out of distribution for our use case.
#figure(
caption: "Subset of NISQA Corpus used in pre-training",
kind: table,
[
#set text(size: 10.5pt)
#table(
columns: 6,
[Dataset], [Language], [Files], [Individual Speakers], [Files per Condition], [Votes per File],
[NISQA_TRAIN_SIM], [`en`], [10,000], [2,322], [1], [~5],
[NISQA_VAL_SIM], [`en`], [2,500], [938], [1], [~5],
[NISQA_TRAIN_LIVE], [`en`], [1,020], [486], [1], [~5],
[NISQA_VAL_LIVE], [`en`], [200], [102], [1], [~5],
)],
)
The hyperparameters for mel-spectrogram construction are the same defaults used in NISQA. In particular:
#showybox(
frame: (
border-color: red.darken(50%),
title-color: red.lighten(60%),
body-color: red.lighten(80%),
),
title-style: (
color: black,
weight: "regular",
align: center,
),
shadow: (
offset: 3pt,
),
title: "Mel Spectrogram Hyperparameters",
```
ms_sr: null
ms_fmax: 20000
ms_n_fft: 4096
ms_hop_length: 0.01
ms_win_length: 0.02
ms_n_mels: 48
ms_seg_length: 15
ms_seg_hop_length: 4
ms_max_segments: 1300 duration. increase if you apply the model to longer samples
ms_channel: null
```,
)
During pretraining, the `NISQA_VAL_SIM` and `NISQA_VAL_LIVE` are used as validations set to determine early stopping. The BiLSTM decoder network is switched out for the newer self-attention network.
Apart from reducing batch size to 32 due to VRAM limitations, yet again the default hyperparameters are used.
#showybox(
frame: (
border-color: red.darken(50%),
title-color: red.lighten(60%),
body-color: red.lighten(80%),
),
title-style: (
color: black,
weight: "regular",
align: center,
),
shadow: (
offset: 3pt,
),
title: "Pre-training Hyperparameters",
```
tr_epochs: 50 # number of max training epochs
tr_early_stop: 5 # if val RMSE nor correlation does not improve
tr_bs: 32
tr_bs_val: 32
tr_lr: 0.001 # learning rate of ADAM optimiser
tr_lr_patience: 15 # decrease lr if val RMSE or correlation does not improve
```,
)
The model is then fine tuned on the Blizzard Challenge and VCC datasets described in @sec-dataset-curation using the same hyperparameters until convergence. We try to approximate the NISQA training and validation sets as close as possible, using the same train-validation splits.
The loss curves are described in the following chart:
#figure(
caption: [Train & validation loss curves],
kind: image,
[#image("assets/training-run.svg")],
)
== Evaluation & Analysis
The results on the training and validation set at the per-stimuli level are as follows:
The results slightly underperform the original NISQA findings using the CNN-BiLSTM architecture, perhaps due to difference in pretraining data and the absence of the 2014 @prahallad2014blizzard and 2015 @itu_bs1534-3_2015 Blizzard challenges in the train sets.
However, it seems that the phenomenon of poor performance on out-of-distribution data at the stimuli level remains although the in-distribution PRCC is relatively higher - indicative of some overfitting.
#figure(
caption: "Training and Validation Sets Performance Metrics",
kind: table,
[
#table(
columns: 3,
[Dataset], [$r$], [$"RMSE"$],
table.cell([*Train*]), table.cell(stroke: (left: 0pt), []), table.cell(stroke: (left: 0pt), []),
[Blizzard_2008_TRAIN], [0.84], [0.48],
[Blizzard_2009_TRAIN], [0.84], [0.49],
[Blizzard_2010_TRAIN], [0.95], [0.44],
[Blizzard_2011_TRAIN], [0.87], [0.43],
[Blizzard_2013_TRAIN], [0.88], [0.46],
[Blizzard_2019_TRAIN], [0.91], [0.39],
[Blizzard_2020_TRAIN], [0.73], [0.51],
[Blizzard_2021_TRAIN], [0.89], [0.41],
[VCC_2018_HUB_TRAIN], [0.74], [0.56],
[VCC_2018_SPO_TRAIN], [0.74], [0.59],
[*Validation*], table.cell(stroke: (left: 0pt), []), table.cell(stroke: (left: 0pt), []),
[Blizzard_2008_VAL], [0.70], [0.60],
[Blizzard_2009_VAL], [0.46], [0.62],
[Blizzard_2010_VAL], [0.68], [0.67],
[Blizzard_2012_VAL], [0.50], [0.85],
[Blizzard_2016_VAL], [0.84], [0.51],
[VCC_2018_HUB_VAL], [0.64], [0.66],
[VCC_2018_SPO_VAL], [0.66], [0.65],
)],
)
As for testing, regretfully, the VCC 2016 @toda2016voice did not distribute stimuli level metrics. Instead, we test on the PhySyQx @7336888 dataset instead. It is important to recall however that it only contains 36 stimuli.
On the PhySyQx dataset, our model achieves an $r = 0.79$ at the per-stimuli level, once again slightly underperforming the original implementation.
Overall, we validate that the work of @Mittag_2020 is indeed reproducible, but are concerned with the poor out of domain performance at the stimuli level, particularly in the validation sets. |
|
https://github.com/kairosiot/software.2024.11-Document_Template | https://raw.githubusercontent.com/kairosiot/software.2024.11-Document_Template/main/tests/long-part-title/test.typ | typst | Other | #import "../../typst-orange.typ": project, part, chapter, my-bibliography, appendices
#let mainColor = rgb("#F36619")
#set text(font: "Lato")
#show math.equation: set text(font: "Fira Math")
#show raw: set text(font: "Fira Code")
#show: project.with(
title: "Exploring the Physical Manifestation of Humanity’s Subconscious Desires",
subtitle: "A Practical Guide",
date: "Anno scolastico 2023-2024",
author: "<NAME>",
mainColor: mainColor,
lang: "en",
cover: image("./background.png"),
imageIndex: image("./orange1.jpg"),
listOfFigureTitle: "List of Figures",
listOfTableTitle: "List of Tables",
supplementChapter: "Chapter",
part_style: 0,
copyright: [
Copyright © 2023 <NAME>
PUBLISHED BY PUBLISHER
#link("https://github.com/flavio20002/typst-orange-template", "TEMPLATE-WEBSITE")
Licensed under the Apache 2.0 License (the “License”).
You may not use this file except in compliance with the License. You may obtain a copy of
the License at https://www.apache.org/licenses/LICENSE-2.0. Unless required by
applicable law or agreed to in writing, software distributed under the License is distributed on an
“AS IS” BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and limitations under the License.
_First printing, July 2023_
]
)
#part("This is a very long part title to test the layout")
#chapter("This is a very long chapter title to test the layout", image: image("./orange2.jpg"))
== This is a very very very very very very very very very long section title to test the layout
=== This is a very very very very very very very very very long subsection title to test the layout
#part("This is a very long part title to test the layout")
#chapter("This is a very long chapter title to test the layout", image: image("./orange2.jpg"))
== This is a very very very very very very very very very long section title to test the layout
=== This is a very very very very very very very very very long subsection title to test the layout
#part("This is a very long part title to test the layout")
#chapter("This is a very long chapter title to test the layout", image: image("./orange2.jpg"))
== This is a very very very very very very very very very long section title to test the layout
=== This is a very very very very very very very very very long subsection title to test the layout
#part("This is a very long part title to test the layout")
#chapter("This is a very long chapter title to test the layout", image: image("./orange2.jpg"))
#part("This is a very long part title to test the layout")
#chapter("This is a very long chapter title to test the layout", image: image("./orange2.jpg"))
#part("This is a very long part title to test the layout")
#chapter("This is a very long chapter title to test the layout", image: image("./orange2.jpg"))
#lorem(100) |
https://github.com/An-314/Notes-of-DSA | https://raw.githubusercontent.com/An-314/Notes-of-DSA/main/stack%26queue.typ | typst | = 栈与队列Stack & Queue
== 栈Stack
=== 接口与实现
栈（stack）是受限的序列
- 只能在栈顶（top）插入和删除
- 栈底（bottom）为盲端
- 后进先出（LIFO），先进后出（FILO）
基本接口是
- `size()` / `empty()`
- `push()` 入栈
- `pop()` 出栈
- `top()` 查顶
- 扩展接口： `getMax(`)...
直接基于向量或列表派生
```cpp
template <typename T> class Stack: public Vector<T> { //原有接口一概沿用
public:
void push( T const & e ) { insert( e ); } //入栈
T pop() { return remove( size() – 1 ); } //出栈
T & top() { return (*this)[ size() – 1 ]; } //取顶
}; //以向量首/末端为栈底/顶——颠倒过来呢？
```
如此实现的栈各接口，均只需$O(1)$时间
=== 调用栈
#figure(
image("fig\栈\1.png",width: 70%),
caption: "调用栈",
)
#figure(
image("fig\栈\2.png",width: 80%),
caption: "调用栈",
)
#figure(
image("fig\栈\3.png",width: 80%),
caption: "调用栈——递归深度",
)
递归算法所需的空间主要取决于*递归深度*，而非递归实例总数。
==== 消除递归
为隐式地维护调用栈，需花费额外的时间、空间。为节省空间，可
- 显式地维护调用栈
- 将递归算法改写为迭代版本
```cpp
int fib( int n )
{ return (n < 2) ? n : fib(n - 1) + fib(n - 2); }
int fib( int n ) { //O(1)空间
int f = 0, g = 1;
while ( 0 < n-- )
{ g += f; f = g - f; }
return f;
}
```
通常，消除递归只是在常数意义上优化空间，但也可能有实质改进。
==== 尾递归
尾递归是在递归实例中，作为最后一步的递归调用。
```cpp
fac(n) {
if (1 > n) return 1; //base
return n * fac( n-1 ); //tail recursion
}
```
#figure(
image("fig\栈\4.png",width: 50%),
caption: "尾递归",
)
一旦抵达递归基，便会
- 引发一连串的return（且返回地址相同）
- 调用栈相应地连续pop
尾递归优化：时间复杂度有常系数改进，空间复杂度或有渐近改进。
```cpp
fac(n) { //尾递归
if (1 > n) return 1;
return n * fac( n-1 );
}//O(n)时间 + O(n)空间
fac(n) { //统一转换为迭代
int f = 1; //记录子问题的解
next: //转向标志，模拟递归调用
if (1 > n) return f;
f *= n--;
goto next; //模拟递归返回
}//O(n)时间 + O(1)空间
fac(n) { //简捷
int f = 1;
while (1 < n)
f *= n--;
return f;
}//O(n)时间 + O(1)空间
```
=== 进制转换
常用短除法，进行进制转换。
#figure(
image("fig\栈\5.png",width: 80%),
caption: "进制转换",
)
位数$m$并不确定，如何正确记录并输出转换结果？具体地
- 如何支持足够大的$m$，同时空间也不浪费？
- 自低而高得到的数位，如何自高而低输出？
若使用向量，则扩容策略必须得当；若使用列表，则多数接口均被闲置。使用栈， 既可满足以上要求， 亦可有效控制计算成本。
```cpp
void convert( Stack<char> & S, __int64 n, int base ) {
char digit[] = "0123456789ABCDEF"; //数位符号，如有必要可相应扩充
while ( n > 0 ) //由低到高，逐一计算出新进制下的各数位
{ S.push( digit[ n % base ] ); n /= base; } //余数入栈， n更新为除商
} //新进制下由高到低的各数位，自顶而下保存于栈S中
main() {
Stack<char> S; convert( S, n, base ); //用栈记录转换得到的各数位
while ( ! S.empty() ) printf( "%c", S.pop() ); //逆序输出
}
```
=== 括号匹配
括号匹配的问题难以用减而之治和分而治之的思想由外而内解决。
颠倒以上思路：消去一对紧邻的左右括号，不影响全局的匹配判断
$
L |( " " )| R => L | R
$
顺序扫描表达式，用栈记录已扫描的部分的左括号。反复迭代：凡遇"("，则进栈；凡遇")"，则出栈。
```cpp
bool paren( const char exp[], Rank lo, Rank hi ) { //exp[lo, hi)
Stack<char> S; //使用栈记录已发现但尚未匹配的左括号
for ( Rank i = lo; i < hi; i++ ) //逐一检查当前字符
if ( '(' == exp[i] ) S.push( exp[i] ); //遇左括号：则进栈
else if ( ! S.empty() ) S.pop(); //遇右括号：若栈非空，则弹出对应的左括号
else return false; //否则（遇右括号时栈已空），必不匹配
return S.empty(); //最终栈空， 当且仅当匹配
}
```
#figure(
image("fig\栈\6.png",width: 80%),
caption: "括号匹配",
)
当括号为单一的一种的时候，甚至可以用一个计数器进行简化。
=== 栈混洗 Stack Permutation
有栈$A = (a_1, a_2, ..., a_n)$，栈$B = S = Phi$：
每次可以
- 将 $A$ 的顶元素弹出并压入 $S$ ，或
- 将 $S$ 的顶元素弹出并压入 $B$
最终所有元素都从 $A$ 移动到 $B$，且$B$为$A$的一个排列$B = (a_(p_1), a_(p_2), ..., a_(p_n))$。
#figure(
image("fig\栈\7.png",width: 80%),
caption: "栈混洗",
)
$B$中的排列是有限制的，满足要求的排列有
$
"Catalan"(n) = 1/(n+1) mat(2n; n)
$
个。这是因为，设$n$个元素的栈混洗排列有$"SP"(n)$个，则有递推关系
$
"SP"(n) = sum_(i=1)^n "SP"(i-1) dot "SP"(n-i)
$
*栈混洗排列的充要条件*：不存在312的模式。即在栈混洗排列中，任意三个连续元素$a_i, a_j, a_k$，满足$i < j < k$，有$a_i < a_k < a_j$。
这样可以得到一个$O(n^3)$的检验算法。
可以简化成当且仅当对于任意$i < j$，不含模式$[ ..., j+1, ..., i, ..., j, ... >$。
这样可以得到一个$O(n^2)$的检验算法。
事实上，可以直接用栈来模拟，这样可以得到一个$O(n)$的检验算法。
*括号匹配*的合法排列就是栈混洗排列。
=== 中缀表达式
减而治之：优先级高的局部执行计算，并被代以其数值；运算符渐少，直至得到最终结果。`val(S) = val( SL + str(v0) + SR )`。
延迟缓冲：仅根据表达式的前缀，不足以确定各运算符的计算次序；只有获得足够的后续信息，才能确定其中哪些运算符可以执行。
求值算法 = 栈 + 线性扫描
- 自左向右扫描表达式，用栈记录已扫描的部分，以及中间结果；栈内最终所剩的那个元素，即表达式之值。
```cpp
If (栈的顶部存在可优先计算的子表达式)
Then 令其退栈并计算；计算结果进栈
Else 当前字符进栈，转入下一字符
```
- 优先级高的局部执行计算，并被代以其数值；运算符渐少，直至得到最终结果。
```cpp
double evaluate( char* S, char* RPN ) { //S保证语法正确
Stack<double> opnd; Stack<char> optr; //运算数栈、运算符栈
optr.push('\0'); //哨兵
while ( ! optr.empty() ) { //逐个处理各字符，直至运算符栈空
if ( isdigit( *S ) ) //若为操作数（可能多位、小数），则
readNumber( S, opnd ); //读入
else //若为运算符，则视其与栈顶运算符之间优先级的高低
switch( priority( optr.top(), *S ) ) { /* 分别处理 */ }
} //while
return opnd.pop(); //弹出并返回最后的计算结果
}
```
其中优先级的比较可以用一个表格来实现
```cpp
const char pri[N_OPTR][N_OPTR] = { //运算符优先等级 [栈顶][当前]
/* -- + */ '>', '>', '<', '<', '<', '<', '<', '>', '>',
/* | - */ '>', '>', '<', '<', '<', '<', '<', '>', '>',
/* 栈 * */ '>', '>', '>', '>', '<', '<', '<', '>', '>',
/* 顶 / */ '>', '>', '>', '>', '<', '<', '<', '>', '>',
/* 运 ^ */ '>', '>', '>', '>', '>', '<', '<', '>', '>',
/* 算 ! */ '>', '>', '>', '>', '>', '>', ' ', '>', '>',
/* 符 ( */ '<', '<', '<', '<', '<', '<', '<', '=', ' ',
/* | ) */ ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ',
/* --\0 */ '<', '<', '<', '<', '<', '<', '<', ' ', '='
// + - * / ^ ! ( ) \0
// |-------------- 当前运算符 --------------|
};
```
'<'：静待时机
```cpp
switch( priority( optr.top(), *S ) ) {
case '<': //栈顶运算符优先级更低
optr.push( *S ); S++; break; //计算推迟，当前运算符进栈
case '=':
/* ...... */
case '>': {
/* ...... */
break;
} //case '>'
} //
```
#figure(
image("fig\栈\8.png",width: 80%),
caption: "中缀表达式求值——'<'",
)
'>'：时机已到
```cpp
switch( priority( optr.top(), *S ) ) {
/* ...... */
case '>': {
char op = optr.pop();
if ( '!' == op ) opnd.push( calcu( op, opnd.pop() ) ); //一元运算符
else { double opnd2 = opnd.pop(), opnd1 = opnd.pop(); //二元运算符
opnd.push( calcu( opnd1, op, opnd2 ) ); //实施计算，结果入栈
} //为何不直接： opnd.push( calcu( opnd.pop(), op, opnd.pop() ) )？
break;
} //case '>'
} //switch
```
#figure(
image("fig\栈\9.png",width: 80%),
caption: "中缀表达式求值——'>'",
)
'='：终须了断
```cpp
switch( priority( optr.top(), *S ) ) {
case '<':
/* ...... */
case '=': //优先级相等（当前运算符为右括号，或尾部哨兵'\0'）
optr.pop(); S++; break; //脱括号并接收下一个字符
case '>': {
/* ...... */
break;
} //case '>'
} //switch
```
#figure(
image("fig\栈\10.png",width: 80%),
caption: "中缀表达式求值——'='",
)
=== 逆波兰表达式Reverse Polish Notation(RNP)
在由运算符（operator）和操作数（operand）组成的表达式中，不使用括号（parenthesis-free），即可表示带优先级的运算关系。
例如：
```
0 !+ 123 + 4 *( 5 * 6 !+ 7 !/ 8 )/ 9
123 + 4 5 6 !* 7 ! 8 /+* 9 /+
```
- 相对于日常使用的中缀式（infix）， RPN亦称作后缀式（postfix）；
- 作为补偿，须额外引入一个起分隔作用的元字符（比如空格），较之原表达式，未必更短。
NRP的求值很容易，只需要一个栈即可。
```cpp
引入栈S //存放操作数
逐个处理下一元素x
if ( x是操作数 ) 将x压入S
else //运算符无需缓冲
从S中弹出x所需数目的操作数
执行相应的计算，结果压入S //无需顾及优先级！
返回栈顶 // 只要输入的RPN语法正确，此时的栈顶亦是栈底，对应于最终的计算结果
```
#figure(
image("fig\栈\11.png",width: 80%),
caption: "逆波兰表达式求值",
)
==== 中缀表达式转换为逆波兰表达式
如果要用程序自动转换，可以在刚才求值的基础上修改。
其实后缀表达式的运算就是在中缀表达式计算的时候，按照优先级的顺序排出来的序列。
```cpp
double evaluate( char* S, char* RPN ) { //RPN转换
/* ................................. */
while ( ! optr.empty() ) { //逐个处理各字符，直至运算符栈空
if ( isdigit( * S ) ) //若当前字符为操作数，则直接
{ readNumber( S, opnd ); append( RPN, opnd.top() ); } //将其接入RPN
else //若当前字符为运算符
switch( priority( optr.top(), *S ) ) {
/* ................................. */
case '>': { //且可立即执行，则在执行相应计算的同时
char op = optr.pop(); append( RPN, op ); //将其接入RPN
/* ................................. */
} //case '>'
/* ................................. */
} //switch
/* ................................. */
} //while
/* ................................. */
return opnd.pop(); //弹出并返回最后的计算结果
}
```
手动转换的方法：
#figure(
image("fig\栈\12.png",width: 80%),
caption: "中缀表达式转换为逆波兰表达式",
)
#figure(
image("fig\栈\13.png",width: 80%),
caption: "中缀表达式转换为逆波兰表达式",
)
== 队列Queue
=== 接口与实现
队列（queue）也是受限的序列
- 先进先出（FIFO）
- 后进后出（LILO）
提供接口：
- 只能在队尾插入（查询）： `enqueue()` / `rear()`
- 只能在队头删除（查询）： `dequeue() `/ `front()`
- 扩展接口： `getMax()`...
基于向量或列表派生
```cpp
template <typename T> class Queue: public List<T> { //原有接口一概沿用
public:
void enqueue( T const & e ) { insertAsLast( e ); } //入队
T dequeue() { return remove( first() ); } //出队
T & front() { return first()->data; } //队首
}; //以列表首/末端为队列头/尾——颠倒过来呢？
```
如此实现的队列接口，均只需$O(1)$时间。
=== 队列应用
*资源循环分配*：一组客户（client）共享同一资源时，如何兼顾公平与效率？比如，多个应用程序共享CPU，实验室成员共享打印机
```cpp
RoundRobin //循环分配器
Queue Q( clients ); //共享资源的所有客户组成队列
while ( ! ServiceClosed() ) //在服务关闭之前，反复地
e = Q.dequeue(); //令队首的客户出队，并
serve( e ); Q.enqueue( e ); //接受服务，然后重新入队
```
=== 直方图内最大矩形
设 `H[0,n)` 是一个非负整数直方图
- 如何找到 `H[]` 中最大的正交矩形？
- 为了消除可能存在的歧义，例如，我们可以选择最左侧的矩形
我们考虑由`H[r]`支撑的最大矩形，满足：
$
&"maxRect"[r] = "H"[r] times (t(r) - s(r))\
&s(r) = max{ 0 <= k < r | "H"[k-1] < "H"[r] }\
&t(r) = min{ t < k <= n | "H"[r] < "H"[k] }
$
其中，$s(r)$是$r$左侧第一个小于$H[r]$的位置，$t(r)$是$r$右侧第一个小于$H[r]$的位置。
#figure(
image("fig\栈\14.png",width: 80%),
caption: "直方图内最大矩形",
)
==== Brute-force方法
按照刚才的分析，对每一个位置都计算最大支撑矩形，然后取最大值。这样的复杂度是$O(n^2)$。
==== 利用单调栈
我们希望可以对每个`r`快速找到`s[r]`和`t[r]`。
从前往后扫描，维护一个单调栈：
- 栈内元素单调递增
- 每次插入新元素的时候都会弹出栈内所有比它小的元素
```cpp
Rank* s = new Rank[n]; Stack<Rank> S;
for ( Rank r = 0; r < n; r++ ) //using SENTINEL
while ( !S.empty() && ( H[S.top()] >= H[r] ) ) S.pop(); //until H[top] < H[r]
s[r] = S.empty() ? 0 : 1 + S.top(); S.push(r); //S is always ASCENDING
while( !S.empty() ) S.pop();
```
#figure(
image("fig\栈\15.png",width: 80%),
caption: "直方图内最大矩形——寻找`s[r]`",
)
- `s[r]`中记录的是左侧第一个`H[k]`小于`H[r]`的`k`（有哨兵），这样就可以计算出`H[r]`支撑的最大矩形的左边界。
- 对于单调栈：
- 每个元素都会被压入栈一次，而每个元素也会在后序的某个时刻被弹出栈一次，所以总的时间复杂度是$O(n)$。
- 递增栈可以保证栈顶元素就是*前一个最小的元素*，即`s[r]`。
按相反的顺序扫描一遍，可以计算出`t[r]`。
==== 一次扫描
如果数据是在线的，就很难做到正反两次扫描。对于一次扫描：
```cpp
Stack<Rank> SR; __int64 maxRect = 0; //SR.2ndTop() == s(r)-1 & SR.top() == r
for ( Rank t = 0; t <= n; t++ ) //amortized-O(n)
while ( !SR.empty() && ( t == n || H[SR.top()] > H[t] ) )
Rank r = SR.pop(), s = SR.empty() ? 0 : SR.top() + 1;
maxRect = max( maxRect, H[r] * ( t - s ) );
if ( t < n ) SR.push( t );
return maxRect;
```
#figure(
image("fig\栈\16.png",width: 80%),
caption: "直方图内最大矩形——一次扫描",
)
- `SR`同样是一个递增栈，`SR.top()`是当前最小的元素，`SR.2ndTop()`是次小的元素。
- 存先前最大的矩形，每次碰到有更小的数就到了右边界，然后计算面积，再与之前的最大值比较。
== Steap + Queap
=== Steap = Stack + Heap = `push` + `pop` + `getMax`
希望每次可以在$O(1)$时间内找到最大值，可以再开一个并列的堆来维护最大值。
#figure(
image("fig\栈\17.png",width: 80%),
caption: "Steap",
)
`P`中每个元素，都是`S`中对应后缀里的最大者：
```cpp
Steap::getMax() { return P.top(); }
Steap::pop() { P.pop(); return S.pop(); } //O(1)
Steap::push(e) { P.push( max( e, P.top() ) ); S.push(e); } //O(1)
```
通过看`P`的记录值，可以知道`S`中的最大值。
也可以用下面采用的指针+计数的方法：`P'`中存入指针与计数器，每次操作修改计数，加入指针，或者计数器变为0删除指针
#figure(
image("fig\栈\18.png",width: 80%),
caption: "Steap",
)
=== Queap = Queue + Heap = `enqueue` + `dequeue` + `getMax`
一样的方法，但是要注意出入口的操作：
```cpp
Queap::dequeue() { P.dequeue(); return Q.dequeue(); } //O(1)
Queap::enqueue(e) {
Q.enqueue(e); P.enqueue(e);
for ( x = P.rear(); x && (x->key <= e); x = x->pred ) //最坏情况O(n)
x->key = e;
}
```
#figure(
image("fig\栈\19.png",width: 80%),
caption: "Queap",
)
可以按照同样的方式化简成指针+计数的方法。
#figure(
image("fig\栈\20.png",width: 80%),
caption: "Queap",
)
== 双栈当队
Queue = Stack x 2
#figure(
image("fig\栈\21.png",width: 40%),
caption: "双栈当队",
)
但是区别是，每次`dequeue`的时候，要把`R`中的元素全部倒入`F`中。
```cpp
def Q.enqueue(e)
R.push(e);
def Q.dequeue() // 0 < Q.size()
if ( F.empty() )
while ( !R.empty() )
F.push( R.pop() );
return F.pop();
```
这样单步可能出现$O(n)$的情况。
现在来看分摊下来的复杂度：
==== Amortization By Accounting
#figure(
image("fig\栈\22.png",width: 50%),
caption: "Amortization By Accounting",
)
分析每个元素经历的操作次数。在整个过程中，每个元素至多经历1次`R`的`push`，1次`R`的`pop`，1次`F`的`push`，1次`F`的`pop`，所以每个元素至多经历4次操作。这样下来，每个元素的分摊复杂度是$O(1)$。
==== Amortization By Aggregate
考虑$d$次`dequeue()`和$e$次`enqueue()`已经做完了，一定有$d <= e$。所有的时间成本是$4d+3(e-d)=3e+d$。
这样下来，每个元素的分摊复杂度是$O(1)$。
==== Amortization By Potential
设第$k$次操作的势能
$
Phi_k = |F_k| - |R_k|
$
又考虑每次操作的分摊成本（Amortized Cost）
$
A_k = T_k+Delta Phi_k = T_k+ Phi_k - Phi_(k-1) eq.triple 2
$
其中$T_k$是实际成本（Actual Cost）。
从而可以得到：
$
&2n eq.triple sum_(k=1)^n A_k = sum_(k=1)^n T_k + Phi_n - Phi_0 = T(n) + Phi_n - Phi_0 > T(n) - n\
&T(n) < 3n = O(n)
$
所以每个元素的分摊复杂度是$O(1)$。 |
|
https://github.com/rabotaem-incorporated/calculus-notes-2course | https://raw.githubusercontent.com/rabotaem-incorporated/calculus-notes-2course/master/sections/06-fourier-series/03-trigonometrical-fourier-series.typ | typst | #import "../../utils/core.typ": *
== Тригонометрические ряды Фурье
#ticket[Тригонометрические многочлены и ряды. Коэффициенты Фурье сходящихся тригонометрических рядов.]
#def[
_Тригонометрическим многочленом_ назовем сумму вида
$
a_0/2 + sum_(k = 1)^n (a_k cos (k x) + b_k sin (k x)).
$
Его степень $n$, если $abs(a_n) + abs(b_n) != 0$.
]
#def[
_Комплексная форма тригонометрического многочлена_ --- сумма вида
$
sum_(k = -n)^n c_k e^(i k x).
$
Его степень $n$, если $abs(c_n) + abs(c_(-n)) != 0$.
]
#notice[
Это разные формы записи:
$
a_0/2 + sum_(k = 1)^n (a_k cos (k x) + b_k sin (k x)) =
a_0/2 + sum_(k = 1)^n (a_k (e^(i k x) + e^(-i k x))/2 + b_k (e^(i k x) - e^(-i k x))/(2i)).
$
Положим $c_0 = a_0/2$, $c_k = (a_k - b_k i) / 2$ при $k >= 1$, $c_k = (a_k + b_k i)/2$ при $k <= -1$.
]
#def[
_Тригонометрический ряд_ --- ряд вида
$
a_0/2 + sum_(k = 1)^oo (a_k cos (k x) + b_k sin (k x)).
$
или, в комплексной форме,
$
sum_(k = -oo)^oo c_k e^(i k x).
$
Сходимость ряда в комплексной форме означает существование предела $lim_(n -> oo) sum_(k = -n)^n c_k e^(i k x)$.
]
#lemma[
Пусть тригонометрический ряд сходится к $f$ по норме $L^1 [-pi, pi]$. Тогда
$
a_n = 1/(pi) &integral_(-pi)^pi f(x) cos(n x) dif x,\
b_n = 1/(pi) &integral_(-pi)^pi f(x) sin(n x) dif x,\
c_n = 1/(2pi) &integral_(-pi)^pi f(x) e^(-i n x) dif x.
$
]
#proof[
Рассмотрим
$
abs(
integral_(-pi)^pi f(x) cos (k x) dif x -
integral_(-pi)^pi (a_0/2 + sum_(j = 1)^n (a_j cos (j x) + b_j sin (j x))) cos (k x) dif x
) newline(<=)
integral_(-pi)^pi abs(f(x) - (a_0/2 + sum_(j = 1)^n (a_j cos (j x) + b_j sin (j x)))) underbrace(abs(cos (k x)), <= 1) dif x newline(<=)
norm(f - (a_0/2 + sum ...))_(L^1[-pi, pi]) --> 0.
$
С другой стороны,
$
abs(
integral_(-pi)^pi f(x) cos (k x) dif x -
integral_(-pi)^pi (a_0/2 + sum_(j = 1)^n (a_j cos (j x) + b_j sin (j x))) cos (k x) dif x
) newline(=)
abs(
integral_(-pi)^pi f(x) cos (k x) dif x -
pi a_k
).
$
при $n >= k$.
Значит
$
a_k = 1/pi integral_(-pi)^pi f(x) cos (k x) dif x.
$
]
#def[
$
a_k (f) := 1/pi &integral_(-pi)^pi f(x) cos (k x) dif x,\
b_k (f) := 1/pi &integral_(-pi)^pi f(x) sin (k x) dif x,\
c_k (f) := 1/(2pi) &integral_(-pi)^pi f(x) e^(-i k x) dif x
$
называются _коэффициентами Фурье_ функции $f$.
Дальше, если мы будем писать в утверждениях теоремы эти коэффициенты, то подразумевается, что $f in L^1 [-pi, pi]$.
]
#notice[
Если функция четная, то $b_k = 0$, если нечетная, то $a_k = 0$. Действительно, в первом случае в интеграле для $b_k$ стоит нечетная функция, и интеграл просто равен $0$. Аналогично для $a_k$.
]
#notice[
Ограничив тригонометрические функции под интегралом единицей, можно грубо оценить коэффициенты:
$
abs(a_n (f)) < norm(f)_1/pi, quad abs(b_n (f)) < norm(f)_1/pi.\
abs(c_k (f)) < norm(f)_1/(2pi).
$
]
#ticket[Представление $a_n cos n x + b_n sin n x$ в виде свертки. Л<NAME>–Лебега.]
#denote[
Обозначим
$
A_k (f, x) := cases(
(a_0 (f))/2\, "при" k = 0,
a_k (f) cos (k x) + b_k (f) sin (k x)\, "при" k > 0,
)
$
Ряд Фурье тогда можно записать как
$
sum_(k = 0)^oo A_k (f, x).
$
]
#notice[
$A_0 (f, x) = 1/(2pi) integral_(-pi)^pi f(x - t) dif t$.
Это верно, так как $f$ -- это сумма каких-то синусов и косинусов, которые $2pi$-периодичны и по периоду дают интеграл $0$, и константы $a_0/2$, а значит интеграл будет какой нужно. Для $k$-го слагаемого формула такая:
$
A_k (f, x) = &1/pi integral_(-pi)^pi f(x - t) cos (k t) dif t newline(=)
&1/pi integral_(-pi)^(pi) f(t) cos (k (x - t)) dif t newline(=)
& 1/pi integral_(-pi)^pi (f(t) cos (k t) cos (k x) + f(t) sin (k t) sin (k x)) dif t.
$
В этих формулах аргумент может вылезти за пределы $[-pi, pi]$. Чтобы больше не мучиться с этим, положим $f$ периодической с периодом $2pi$. В любом случае, раньше мы рассматривали $f: [-pi, pi] --> CC$, замкнув ее до периодической функции, мы ничего не потеряли. Ну, кроме, возможно, точки на границе отрезка, но на нее плевать: так как мы рассматриваем классы эквивалентности с точностью до равенства почти везде, можем положить значение там чем угодно.
]
#denote[
За $C_(2pi)$ обозначим непрерывные $2pi$-периодические функции.
]
#notice(name: "результаты о сходимости")[
- *Дюбуа-Реймон*: существует $f in C_(2pi)$ такая, что ее ряд Фурье расходится в некоторой точке.
- *Лебег*: существует $f in C_(2pi)$ такая, что ее ряд Фурье сходится во всех точках, но нет равномерной сходимости.
- *Колмогоров*: существует $f in L^1 [-pi, pi]$ такая, что ее ряд Фурье расходится во всех точках (!).
- *Карлесон*: для любой $f in L^2 [-pi, pi]$, ее ряд Фурье сходится почти везде.
- *Рисс*: при $1 < p < +oo$, для любой функции $f in L^p [-pi, pi]$ ее ряд Фурье сходится по норме в $L^p [-pi, pi]$.
]
#lemma(name: "Римана-Лебега")[
Если $E subset RR$ измеримое, $lambda in RR$, $f in L^1 (E)$, то
1. $
integral_E f (t) e^(i lambda t) dif t &--> 0 "при" lambda --> plus.minus oo,\
integral_E f (t) cos(lambda t) dif t &--> 0 "при" lambda --> plus.minus oo,\
integral_E f (t) sin(lambda t) dif t &--> 0 "при" lambda --> plus.minus oo.
$
2. Если $f in L^1 [-pi, pi]$, то
$
a_k (f) &--> 0 "при" k --> oo,\
b_k (f) &--> 0 "при" k --> oo,\
c_k (f) &--> 0 "при" k --> oo.
$
]
#proof[
Продолжим $f$ нулем. Теперь $f in L^1 (RR)$.
$
integral_RR f(t) e^(i lambda t) dif t =^(t = h + u)_((h in RR))
integral_RR f(h + u) e^(i lambda h) e^(i lambda u) dif u =
e^(i lambda h) integral_RR f(h + u) e^(i lambda u) dif u.
$
Равенство выше верно для любого $h$. Рассмотрим $h = pi/lambda$:
$
e^(i lambda h) integral_RR f(h + u) e^(i lambda u) dif u =
-integral_RR f(pi/lambda + u) e^(i lambda u) dif u.
$
Значит
$
2 integral_RR f(t) e^(i lambda t) dif t =
integral_RR f(t) e^(i lambda t) dif t - integral_RR f(pi/lambda + t) e^(i lambda t) dif t.
$
Вешаем модуль:
$
2 abs(integral_RR f(t) e^(i lambda t) dif t) =
abs(integral_RR f(t) e^(i lambda t) dif t - integral_RR f(pi/lambda + t) e^(i lambda t) dif t) newline(<=)
integral_RR abs(f(t) - f(t + pi/lambda)) dif t = norm(f - f_(pi/lambda))_1 --> 0
$
по теореме о непрерывности сдвига.
]
#ticket[Оценки коэффициентов Фурье для равномерно непрерывных, липшицевых и дифференцируемых функций.]
#remind[
Модуль непрерывности
$
w_f (delta) = sup { abs(f(x) - f(y)) : abs(x - y) <= delta }.
$
Если $f$ непрерывна на компакте, то $w_f (delta) --> 0$ при $delta -> 0+$. В частности, это верно для $f in C_(2pi)$.
]
#remind[
$f$ --- _липшицева_ с константой $M$, или $f in Lip_alpha M$ если $abs(f(x) - f(y)) <= M abs(x - y)^alpha$ для любых $x, y in RR$. Говорят $f in Lip_alpha$ (без указания константы), если $f in Lip_alpha M$ для некоторого $M$.
]
#notice[
$w_f (h) <= M h^alpha$ если $f in Lip_alpha M$.
]
#th[
$
abs(a_n (f)) &<= w_f (pi/n),\
abs(b_n (f)) &<= w_f (pi/n),\
abs(c_n (f)) &<= (w_f (pi/n))/2.
$
В частности, если $f in Lip_alpha M$, то $abs(a_n (f)), abs(b_n (f)), 2 abs(c_n (f)) <= M (pi/n)^alpha$.
]
#proof[
$
c_n (f) =
1/(2pi) integral_(-pi)^pi f(t) e^(-i n t) dif t =^(t = u + pi/n)
1/(2pi) integral_(-pi - pi/n)^(pi-pi/n) f(u + pi/n) e^(-i n u) e^(-i pi) dif u newline(=)
-1/(2pi) integral_(-pi)^pi f(u + pi/n) e^(-i n u) dif u ==>
2 c_n (f) = 1/(2pi) integral_(-pi)^pi (f(t) - f(t + pi/n)) e^(-i n t) dif t newline(==>)
abs(2 c_n (f)) <= 1/(2pi) integral_(-pi)^pi underbrace(abs(f(t) - f(t + pi/n)), <= w_f (pi/n)) dif t <= w_f (pi/n).
$
$
a_n (f) = 2 Re c_n (f) = 1/(2pi) integral_(-pi)^pi (f(t) - f(t + pi/n)) cos (n t) dif t ==> abs(a_n (f)) <= w_f (pi/n)
$
Аналогично с $b_n (f)$.
]
#lemma[
Если $f in C_(2pi)^1$, то
$
c_n (f') &= i n dot c_n (f),\
b_n (f') &= -n dot a_n (f),\
a_n (f') &= n dot b_n (f).
$
]
#proof[
Для остальных коэффициентов аналогично.
$
a_n (f') = 1/pi integral_(-pi)^pi f' (t) cos (n t) dif t =
1/pi (
lr(f(t) cos(n t) |)_(t = -pi)^(t = pi) +
integral_(-pi)^pi f(t) n sin (n t) dif t
)
newline(=)
n/pi integral_(-pi)^pi f(t) sin (n t) dif t = n b_n (f).
$
]
#follow[
Если $f in C_(2pi)^r$ и $f^((r)) in Lip_alpha M$, и $0 < alpha <= 1$, то
$
abs(a_n (f)), abs(b_n (f)), 2 abs(c_n (f)) <= M (pi/n)^alpha dot 1/n^r.
$
В частности, если $f$ дважды непрерывно дифференцируема, то ряд Фурье абсолютно сходится.
]
#proof[
$
abs(c_n (f)) = abs(c_n (f'))/n = ... = abs(c_n (f^((r))))/n^r <= 1/n^r dot M(pi/n)^alpha.
$
]
#ticket[Ядро Дирихле. Свойства. Три формулы для частичных сумм ряда Фурье. Следствие.]
#def[
_Ядро Дирихле_ --- тригонометрический многочлен
$
D_n (t) = 1/2 + sum_(k = 1)^n cos (k t).
$
]
#props[
1. $D_n$ --- четная, $2pi$-периодическая функция.
2. $D_n (0) = n + 1/2$.
3. $integral_(-pi)^pi D_n (t) dif t = pi$, $integral_0^pi D_n (t) dif t = pi/2$.
4. При $t != 2pi m$, $D_n (t) = (sin(n + 1/2) t)/(2 sin t/2)$.
]
#proof[
1. Очевидно.
2. Очевидно.
3. Очевидно, +четность.
4.
$
2 sin (t/2) D_n (t) = sin t/2 + sum_(k = 1)^n underbrace(2 cos(k t) dot sin(t/2), sin(k + 1/2)t - sin (k - 1/2)t) = sin (n + 1/2) t.
$
]
#denote[
Пусть $S_n (f, x)$ --- частичная сумма ряда Фурье функции $f$ в точке $x$,
$
S_n (f, x) = (a_0 (f))/2 + sum_(k=1)^n (a_k (f) cos (k x) + b_k (f) sin (k x)) = sum_(k = 0)^n A_k (f, x).
$
]
#lemma[
$
S_n (f, x) = 1/pi integral_(-pi)^pi f(x plus.minus t) D_n (t) dif t = 1/pi integral_0^pi (f(x + t) + f(x - t)) D_n (t) dif t.
$
]
#proof[
Знаем
$
A_k (f, x) = cases(
1/(2 pi) integral_(-pi)^pi f(x - t) dif t\, "при" k = 0,
1/pi integral_(-pi)^pi f(x - t) cos (k t) dif t\, "при" k > 0.
)
$
Складываем,
$
S_n (f, x) = sum_(k = 0)^n A_k (f, x) = 1/pi integral_(-pi)^pi f(x - t) underbrace((1/2 + sum_(k = 1)^n cos (k t)), D_n (t)) dif t.
$
Получили формулу для плюса. Для минуса аналогично (или выводится из этой формулы). Из четности получаем второе равенство.
]
#follow[
Если $f in L^1 [-pi, pi]$, $delta > 0$, то
$
S_n (f, x) = 1/pi integral_0^delta (f(x + t) + f(x - t)) D_n (t) dif t + o(1).
$
]
#proof[
Знаем
$
S_n (f, x) = 1/pi integral_0^pi (f(x + t) + f(x - t)) D_n (t) dif t = 1/pi (integral_0^delta ... + integral_delta^pi ...).
$
Надо доказать, что $integral_delta^pi ... --> 0$. Действительно,
$
integral_delta^pi (sin (n + 1/2) t)/(2 sin t/2) (f(x + t) + f(x - t)) dif t -->_(n-->oo) 0
$
по лемме Римана-Лебега.
]
#ticket[Принцип локализации. <NAME>. Следствия признака Дини.]
#th(name: "принцип локализации")[
Пусть $f, g in L^1 [-pi, pi]$ и $f$ совпадает с $g$ в $(x - delta, x + delta)$. Тогда ряды Фурье для функций $f$ и $g$ в точке $x$ ведут себя одинаково. Более того, $S_n (f, x) - S_n (g, x) -->_(n -> oo) 0$.
]
#proof[
$
S_n (f, x) &= 1/pi integral_0^delta D_n (f(x + t) + f(x - t)) dif t + o(1), \
S_n (g, x) &= 1/pi integral_0^delta D_n (g(x + t) + g(x - t)) dif t + o(1).
$
Вычтем:
$
S_n (f, x) - S_n (g, x) = 1/pi integral_0^delta D_n (t) underbrace((f(x + t) - g(x + t) + f(x - t) - g(x - t)), 0) dif t + o(1).
$
Сумма под интегралом равна нулю, так как $f = g$ в окрестности $x$. Значит предел равен нулю.
]
#lemma[
$f in L^1 [-pi, pi]$, $0 < delta < pi$. Тогда интегралы
$
integral_0^delta abs(f(t))/t dif t quad "и" quad integral_0^pi abs(f(t))/(2 sin t/2) dif t
$
ведут себя одинаково.
]
#proof[
$integral_delta^pi abs(f(t))/t dif t$ сходится, так как $abs(f(t))/t <= abs(f(t))/delta$. Надо понять, что $integral_0^pi abs(f(t))/t dif t$ и $integral_0^pi abs(f(t))/(2sin t/2) dif t$ ведут себя одинаково. Посмотрим на $t in (0, pi)$. На нем синус можно подпереть снизу и сверху: $t/2 dot 2/pi <= sin t/2 <= t/2$. Значит можно оценить функции под интегралами друг через друга, с какими-то константами:
$
pi/2 abs(f(t))/t >= abs(f(t))/(2 sin t/2) >= abs(f(t))/t.
$
Значит если один сходится, то другой тоже точно сходится.
]
#denote[
$
f(x_0 + 0) &:= lim_(x -> x_0+) f(x),\
f(x_0 - 0) &:= lim_(x -> x_0-) f(x).
$
]
#def[
$x_0$ --- регулярная точка функции $f$, если
$
f(x_0) = (f(x_0 + 0) + f(x_0 - 0))/2.
$
]
#notice[
Все точки непрерывности --- регулярные.
]
#def[
$x_0$ --- точка непрерывности или разрыва первого рода (то есть разрыва, в котором есть левый и правый предел). Положим
$
f'_+ (x_0) &:= lim_(h -> 0+) (f(x_0 + h) - f(x_0 + 0))/h,\
f'_- (x_0) &:= lim_(h -> 0-) (f(x_0 + h) - f(x_0 - 0))/h,\
$
]
#notice[
- Для дифференцируемой в $x_0$ функции, это обычная производная.
- Для функции непрерывной в $x_0$ это левая и правая производные.
]
#denote[
$f_x^* (t) = f(x + t) + f(x - t) - f(x + 0) - f(x - 0)$.
В регулярной точке, это просто $f(x + t) + f(x - t) - 2f(x)$.
]
#th(name: "<NAME>")[
$f in L^1 [-pi, pi]$, $x_0 in (-pi, pi)$ --- точка непрерывности или разрыва первого рода $f$, $0 < delta < pi$. Если
$
integral_0^delta abs(f_(x_0)^* (t))/t dif t
$
сходится, то ряд Фурье функции $f$ в точке $x_0$ сходится к $(f(x_0 + 0) + f(x_0 - 0))/2$.
]
#proof[
Рассмотрим
$
S_n (f, x_0) - (f(x_0 + 0) + f(x_0 - 0))/2 newline(=)
1/pi integral_0^pi D_n (t) (f(x_0 + t) + f(x_0 - t)) dif t -
1/pi integral_0^pi D_n (t) (f(x_0 + 0) + f(x_0 - 0)) dif t.
$
$S_n$ мы выражать умеем, а вторая шутка получилась такой, потому что мы просто ее креативно записали. $f(x_0 + 0) + f(x_0 - 0)$ это константа, ее можно вынести из интеграла, а интеграл ядра Дирихле --- это $pi/2$. Поэтому все сходится. Перепишем через наши обозначения, и распишем ядро Дирихле:
$
1/pi integral_0^pi D_n (t) (f(x_0 + t) + f(x_0 - t)) dif t -
1/pi integral_0^pi D_n (t) (f(x_0 + 0) + f(x_0 - 0)) dif t newline(=)
1/pi integral_0^pi D_n (t) f_(x_0)^* (t) dif t =
1/(2pi) integral_0^pi underbrace((f_(x_0)^* (t))/(sin t/2)) sin ((n + 1/2) t) dif t.
$
Теперь по лемме Римана-Лебега, это стремится к нулю, если штука над фигурной скобкой суммируема. То есть, если вот такой интеграл сходится:
$
integral_0^pi abs(f_(x_0)^* (t))/(sin t/2) dif t.
$
По предыдущей лемме, это равносильно тому, что сходится
$
integral_0^delta abs(f_(x_0)^* (t))/t dif t.
$
Это написано в условии. Доказали.
]
#follow(plural: true)[
1. Если $x_0$ --- регулярная точка суммируемой $f$ (или, в частности, точка непрерывности), и $integral_0^delta abs(f^*_(x_0) (t))/t dif t < +oo$, то ряд Фурье в $x_0$ сходится к $f(x_0)$.
2. Пусть $f in L^1 [-pi, pi]$, $x_0$ --- точка непрерывности или разрыва первого рода и существуют конечные $f'_plus.minus (x_0)$. Тогда ряд Фурье в $x_0$ сходится к $(f(x_0 + 0) + f(x_0 - 0))/2$.
3. Если $f in L^1 [-pi, pi]$ и кусочно дифференцируема, то во всех точках $x in (-pi, pi)$ ряд Фурье сходится к $(f(x + 0) + f(x - 0))/2$. А в точке $pi$, к $(f(pi - 0) + f(-pi + 0))/2$. В частности, если функция непрерывна, то ряд Фурье сходится к $f$ на $(-pi, pi)$.
]
#proof[
1. Просто частный случай теоремы.
2. $
integral_0^delta abs(f^*_x_0 (t))/t dif t <= integral_0^delta (abs(f(x_0 + t) - f(x_0 + 0))/t + abs(f(x_0 - t) - f(x_0 - 0))/t) dif t.
$
Тогда для некоторого $delta$ подынтегральная функция просто ограничена. Значит интеграл сходится. По признаку Дини ряд Фурье сходится к $(f(x_0 + 0) + f(x_0 - 0))/2$.
3. По предыдущему следствию.
]
#ticket[Ряд Фурье для функции $(pi-x)/2$.]
#example[
Пусть $f(x) = (pi-x)/2$ при $0 <= x < 2pi$, и переодически продолженная. В музыке такая функция называется Negative Ramp или Sawtooth. Это важно.
#TODO[график]
Посчитаем коэффициенты Фурье. Косинусные, очевидно, равны нулю (функция нечетная). Для синусных:
$
b_n =
1/pi integral_0^(2pi) (pi - x)/2 sin (n x) dif x =
-1/(2pi) integral_0^(2pi) x sin (n x) dif x newline(=)
-1/(2pi) (- lr(x (cos (n x))/n |)_0^(2pi) + integral_0^(2pi) (cos (n x))/n dif x) = 1/n.
$
Значит ряд Фурье это
$
sum_(n = 1)^oo (sin (n x))/n.
$
По следствию 3,
$
sum_(n = 1)^oo (sin (n x))/n = f(x)
$
при $x != 2pi m$.
Еще из этого ряда очевидно следуют:
$
sum_(n = 1)^oo (sin (n x))/n = (pi - x)/2 "при" 0 < x < 2pi,\
sum_(n = 1)^oo (sin (2 n x))/n = pi/2 - x "при" 0 < x < pi,\
sum_(n = 1)^oo (sin (2 n x))/(2n) = pi/4 - x/2 "при" 0 < x < pi.
$
Можем найти знакочередующийся ряд для $x$:
$
sum_(n = 1)^oo (-1)^n (sin (n x))/n = 2(pi/4 - x/2) - (pi - x)/2 = -x/2.
$
Значит
$
2 sum_(n = 1)^oo (-1)^(n + 1) (sin (n x))/n = x
$
при $0 < x < pi$, а из нечетности получается, что и при $-pi < x < pi$.
Это гениальное разложение $x$ в ряд иногда бывает полезно, так как, продолжив его периодически, получится что-то похожее на дробную часть. Это, например, можно использовать в формуле Эйлера-Маклорена.
]
#ticket[Ряд Фурье для функции $sign$. Эффект Гиббса.]
#example(name: "эффект Гиббса")[
$
f(x) = sign x = cases(
1\, "при" x > 0,
0\, "при" x = 0,
-1\, "при" x < 0.
)
$
Продолжим ее по периоду на $(-pi, pi)$. Найдем ряд Фурье. Косинусные коэффициенты нулевые. Для синусных:
$
b_n = 1/pi integral_(-pi)^pi f(x) sin (n x) dif x = 2/pi integral_0^pi sin (n x) dif x = 2/pi ( lr(-(cos (n x))/n|)_0^pi ) = 2/pi (1/n - (-1)^n/n)
$
Значит $b_(2n) = 0$, $b_(2n + 1) = 4/(pi(2n + 1))$. Ряд Фурье:
$
4/pi sum_(n = 1)^oo (sin ((2n - 1)x))/(2n - 1) = sign x "при" -pi < x < pi "(в нуле тоже, т.к. регулярная точка)."
$
#TODO[картинки этой красоты]
Нетрудно заметить, что около точки разрыва наблюдается всплеск значений частичных сумм. Посмотрим на его величину. Берем производную частичной суммы:
$
S'_n (x) = 4/pi sum_(k = 1)^n cos(2k - 1) x = 2/pi (sin (2n x))/(sin x) ==> S'_n (pi/(2n)) = 0.
$
Минимальный положительный корень производной --- $pi/(2n)$, то есть как раз этот всплеск. Теперь посмотрим на значения там:
$
S_n (pi/(2n)) =
integral_0^(pi/(2n)) S'_n (x) dif x =
2/pi integral_0^(pi/(2n)) (sin (2n x))/(sin x) dif x =^(y = 2n x)
2/pi integral_0^pi (sin (y))/(2n sin(y/(2n))) dif y -->^* 2/pi integral_0^pi (sin y)/y dif y.
$
Переход к пределу под $*$ можно делать, потому что у нас есть суммируемая мажоранта --- 1 (проверьте сами). Этот интеграл равен примерно $1.178...$ Получается, что такой всплеск, величиной примерно в 18% (то есть 9%, если считать что разрыв у нас величины 2 в примере, а не 1), всегда возникает в частичных суммах.
]
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https://github.com/polarkac/MTG-Stories | https://raw.githubusercontent.com/polarkac/MTG-Stories/master/stories/042%20-%20Strixhaven%3A%20School%20of%20Mages/005_The%20Chains%20That%20Bind.typ | typst | #import "@local/mtgstory:0.2.0": conf
#show: doc => conf(
"The Chains That Bind",
set_name: "Strixhaven: School of Mages",
story_date: datetime(day: 31, month: 03, year: 2021),
author: "<NAME>",
doc
)
"I don't know why I'm here," said Maraff, taking another sip of tea. "I don't need tutoring, and definitely not from another student—no offense."
"None taken," said Dina, her eyes trained on the notes left by <NAME>: #emph[Despite being a Quandrix hopeful, Maraff shows an uncommon affinity for summoning. Pity that his poor attitude makes him prone to mistakes. ] She looked up at the sound of Maraff's empty cup clinking on the saucer and reached over to her teapot, warming on the waning embers of the fire. Normally, fires wouldn't have been possible in the Sedgemoor bayou due to the dampness, but <NAME> had enchanted this space to be an ersatz office for Dina's tutor duties. It suited Dina. She preferred the buzz and bubble of the bayou to a stodgy lecture hall in Widdershins.
#figure(image("005_The Chains That Bind/01.jpg", width: 100%), caption: [Dina, Soul Steeper | Art by: <NAME>], supplement: none, numbering: none)
"More tea?" Dina offered.
Maraff held out his cup. "Thank you," he said, taking a swig after it was filled. "It's possible that Professor Tivash has a vendetta against me. I'm definitely his best student. Why else has he not placed me into his advanced classes? Dealing with other first-years is like being in a room full of babies."
#emph[Needs focus] , read Tivash's final note. #emph[Requires proper motivation to maximize potential.]
Dina refreshed Maraff's cup again.
"You have real talent as a counselor," said Maraff, eagerly downing the amber brew. "Magic isn't for everyone, and my keen instincts tell me you're better off pursuing other avenues."
Dina topped off Maraff's cup one last time.
#emph[This is fine] , she thought.
Approximately three and a half minutes later, Maraff was on the ground showing no signs of his earlier braggadocio. "I'm dying!" he wailed.
"Don't be silly," said Dina, standing over him as he scrounged for ingredients. "Spiders coming out your ears is hardly deadly." She thought about it for a second. "Unless they're venomous. Are they venomous?"
"Aren't you supposed to know?!" Maraff squealed.
"I'm fairly sure they're not," she said. "Fairly~anyway, you remember what you're looking for?"
"Mugwort and lanny fern root?"
"Very good!" said Dina. She stepped back to allow Maraff some space. Despite his infantile sobbing, she was sure that, at the very least, he wasn't going to forget the antidote for attercop charm any time soon. "While you're doing that, I'll schedule our next session. Next week, same time?"
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Dina ran her hands across the smooth walls of Widdershins Hall as she walked through its corridors. The main hall for each Strixhaven college endeavored to embody the college's mission, and in this, Widdershins succeeded wildly. At least, that's what most students at Witherbloom College were led to believe. Life and death. Growth, rot, and rebirth. Dina wondered how many Witherbloom students were aware that the trees housing their classrooms and sleeping quarters were not only alive but listening as well.
Dina entered the laboratory where the deans of Witherbloom College, Professors Lisette and Valentin, gazed into a crucible being heated by a floating blue flame.
"It's not working like you said it would," spat Valentin. He spun around in his characteristic huff and paced to the back of the room.
"Give it time," said Lisette. Her voice flowed slowly, like honey.
Valentin clacked the sharp ends of his fingers together. "How much time am I expected to give?"
"Enough time—oh, hello, Dina."
"My session with Maraff is done. Is Professor Tivash in?"
"Intercollegiate meeting," Lisette said. "Why he insists on attending those is beyond me."
Valentin twirled on his heel, returned to the crucible, and grunted after looking into it again. He glanced over to Dina but didn't address her. "Tivash likes the refreshments, Lisette. Lime cakes, elderberry pies."
"I'm sure Gyome can arrange to make anything he wants in the kitchen."
"Yes, but you see, Tivash adores being doted on," Valentin explained. "These treats are waiting there for him, as if by the grace of a benevolent universe. Small things quiet small minds."
"You can leave his notebook with us," said Lisette. "We'll get it back to him."
Dina placed Tivash's book onto the central table, sneaking a look at the silvery liquid churning and frothing in the crucible. Lisette added a pinch of volcanic ash, causing the mixture to hiss and change color to a deep orange. In other circumstances, Dina would have asked them to explain the spell they were casting. But not right then.
She had other business right then.
"Okay," said Dina, "I'll be going now."
"Off to the Prismari party?" Lisette called out. "All the professors are going, too. If you're not in a hurry, we can go together."
"Hmph," said Valentin.
"Most of the professors," said Lisette.
Dina looked out the window into the courtyard below. Students gathered together under the archways formed by the hall's massive roots, dressed in their most garish Witherbloom garments: some masked behind gauzy veils that swayed like spiderwebs when they talked, others festooned with pouches and belts holding spell components.
Standing out were the dryads, who bore a special love of this pageantry. In their Vastlands home, they had no need for clothing and, at Strixhaven, remained dressed only out of a sense of propriety. However, these kinds of social affairs gave them license to indulge in the novelty of fashion. It was customary to see dryads traipsing and prancing about, adorned with exotic textiles paying tribute to the groves and dales where they were born.
Dina pulled her plain brown cloak around her shoulders.
"No, thank you," she said. "I have work to do."
"Work? This late?" Lisette said, frowning. "You should spend time with your friends."
Ever since she'd brought Dina to Strixhaven two years ago, Lisette had been on a nonstop quest to make introductions with anyone who remotely shared Dina's interests in collecting spores, molds, and fungi (there weren't that many, and most of them wanted to be alone, too). This mission had expanded to anyone who breathed and could speak.
"Do you give all your charges such awful advice?" interrupted Valentin. "Young Dina shows drive, unlike some of the more unfortunate members of our studentry."
"Having friends is awful advice?" Lisette said. "Even you have friends!"
"Oh? Who?"
"Me!"
Valentin rumpled his brow and cocked his head in thought. "Well, I'm terribly sorry for giving you the wrong idea. I beg your forgiveness."
Lisette shook her head. "Dina, go have some fun."
#v(0.35em)
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#v(0.35em)
Dina considered that trudging across Sedgemoor into the forlorn Detention Bog probably wouldn't count as "fun" to Dean Lisette. Then again, there was nothing about attending a party at Prismari College that struck Dina as enjoyable. Lisette couldn't seem to understand that all the opportunities were there if Dina had actually wanted to commiserate with other students. Libation-filled nights at the Bow's End were always available for those who didn't mind waking up in the morning with the consequences of questionable decision-making. And for last-minute cram sessions, there were all-nighters at Firejolt Café with other try-hards.
Dina understood that Lisette felt responsible for her. She'd told her as much whenever they sat down for their weekly tea. But maybe Dina just didn't want to do those things. And maybe there were tasks that held more importance.
"Good evening," said Dina, laying her hand on the Asenath tree. It had been one month since she'd first discovered this particular tree, one month since she'd started on her own secret project. Its spindly branches overlooked a lazy creek, and its broad, hollow trunk ballooned out to make a perfect, if cramped, workshop. The tree's location deep within the bog ensured that her work would remain secret for as long as possible. The entire area had been enchanted to block scrying into or out of it—all the better to prevent students from using the time to chat with friends rather than think about their mistakes. Even so, Dina was hasty in stepping inside and resetting the glamer that obscured its opening.
"What do you do for fun?" she said to the tree as she sat down.
The tree didn't respond. They seldom do.
Dina cast a simple ghostlight spell, illuminating the spell reagents arranged in a circle around her. In the center sat an old tome, its cover made from thin metallic plates scalloped like a knight's pauldron. Delicate chains bound the supple vellum pages together into a work whose craftsmanship was unequaled by any set of hands on Arcavios.
It is said that the Strixhaven Biblioplex is the most complete archive of magic in the Multiverse. All manner of spells, from the lowliest hedge wizard's anti-itch cantrip to a demon's ritual for harnessing the power of a dying sun, are recorded and stored somewhere under the library's vaulted arches. No one save for Strixhaven's Founder Dragons, and perhaps the Oracle of Arcavios herself, knew exactly how the Biblioplex carried out its function. Nevertheless, most patrons understood that a sought-after grimoire was more likely to hunt them down than the other way around.
On the day that Dina discovered this particular book on the shelf, it seemed to beckon to her, begging her to read its contents. She did, drawn at first by her curiosity and then by the gravity of what she'd stumbled upon. Part manual, part journal, it captured the meditations of an unnamed mage fascinated by life, death, and the realms locked between them.
She opened the book to its final page.
#emph[I have trod upon the skulls of mighty lords; commanded boundless armies who obey without fail. Yet no conquest can turn the tide against my own desire for what I want—what I have always wanted. Not the mere escaping of death, nor the mere facsimile, but true life from lifelessness. That is the ultimate proof of power, the most definite testament to godhood. I have been told by those who deemed themselves wise that the most anticipated ends are sweet only so long as they remain unattainable.]
#emph[I will prove them wrong.]
These words prefaced an incantation meant to bridge the transition between living realms and the void, a place of ineffable darkness where, according to the book, the souls of the hopeless dwelled.
One by one, Dina read off spell components, pulling the corresponding ingredient from the circle and placing it into a bowl. Some, like luna moss, had been easy enough to obtain in the bayou. Others, such as a knuckle bone from a woolly sloar, required Dina to access the personal laboratories of Witherbloom's professors. This wasn't difficult, especially with Lisette and Valentin so wrapped up in their own projects. They never noticed their ingredients being skimmed away. A pinch of this, a slice of that.
#figure(image("005_The Chains That Bind/02.jpg", width: 100%), caption: [Art by: <NAME>], supplement: none, numbering: none)
"The root of the esis tree," she whispered, her finger at the bottom of the ingredient list. No plant on Arcavios bore the name #emph[e] #emph[sis] , nor did any leaf she knew of resemble the delicate, feather-like shape drawn on the page.
For weeks, Dina searched fruitlessly. Perhaps esis was an archaic name for another species of plant. Or the drawing was not as accurate as it could have been. These inquests all led to dead ends, forcing her to concede that there were no esis trees on Arcavios. What about obtaining it from places outside Arcavios? Dina shifted her research to arcane rituals that theoretically could enable travel from one plane to another—from Arcavios to a place where esis groves were plentiful. Without fail, these spells were almost impossible to understand, far above her ability to craft, and promised painful fates worse than death.
Her search had stalled, and it remained that way until that very day, in her potions class just before her session with Maraff. While Professor Onyx droned on about the distinctions between atramentous and achromic elixirs, Dina's eye spied something notable about the terrarium at the back of the room. Whether by an aspect of the light or a preternatural instinct, Dina was drawn to the clump of small ferns in the far corner. Among them was a single seedling whose ghostly white leaves matched that of the esis tree. When class released, she flew into action, extracting a sliver of root amidst the hubbub of students gossiping over that night's social gatherings.
Sitting in her workshop, Dina gazed at the piece of esis root in her palm. It was barely larger than a human fingernail, pale white, and still supple. #emph[Such a small thing] , she thought, then dropped it into the bowl with the rest of the ingredients. All that remained was binding the spell. Picking up her knife, she pricked her fingertip and squeezed a single drop of blood into the mixture. A few minutes spent pulverizing the ingredients produced a poultice that glowed like faint moonlight.
Carrying the book in one hand and the bowl in the other, Dina emerged and proceeded to her next destination, her ghostlight spell dutifully lighting the way. The evening had brought the bog to life. The acrid smell of soaked bark had grown bold. Things, just out of eyesight, slithered through mud pools. The shiver of wet leaves overhead told her she was being watched from the branches above.
She recalled nights like this when she was younger—quietly glorious but tinged with an impending sense of doom. When the Brittleblight came for her glade, like it had done for many across Arcavios, few noticed its effects. Those who made the glade their home began to fall prey to a subtle yet persistent melancholy. Over years, its grip quietly tightened, stealing dreams and replacing them with despair. As minds were overtaken by misery, bodies followed. Animals lay down and never rose again. Dryads grew fragile and decayed into husks.
At the very end, there was no grass.
No flowers.
The birds did not bring their sweet songs.
Insects had stopped skittering.
All color had turned to gray; everything was silent.
Despite the efforts of scholars across Arcavios, no one knew the genesis of the disease or how it found its way into a habitat. Lisette was one such scholar, and it was she who had arrived at Dina's glade to rescue her before the sickness could take a permanent hold. But even Lisette's formidable expertise couldn't save the glade itself. Now Dina potentially had the ability to change that, though it wouldn't be easy.
Dina followed the creek to a den of twigs and mud where a family of pests made their home. Most Witherbloom students merely tolerated the pests. They couldn't avoid them completely—pests were an incredible source for magical energy. But the little wart-ridden creatures were not the most pleasant to be around. They were cold and slimy and flagrantly violated decorum around manners and personal hygiene. Dina didn't mind any of that.
"Hello Bastion, Vedredi, Kiara, and Nenioc," she said, greeting the pests rolling in the mud alongside the water's edge. "How are you today?" The pests, much like trees, rarely answered direct questions. But they did flop around, splashing mud onto Dina's cloak. "I'm here to ask you for a favor," she said. "I need you to take a short trip for me." There was a tug of anxiety as she applied her poultice to the pests—ten in all—who gathered around her. They trusted her, perhaps loved her in their own way. She stroked Nenioc, named for her glade sister who had passed years before. The pest burped and licked Dina's hand. "If I succeed, you'll be back here. Like you never left."
#figure(image("005_The Chains That Bind/03.jpg", width: 100%), caption: [Art by: <NAME>], supplement: none, numbering: none)
She placed the spellbook on the ground, and on each pest, she traced a spiral, the symbol of all life radiating from a unified point. Then she began to recite the words. The first few syllables were easy enough to announce. The subsequent words, however, brought with them a sensation like a dull mallet tapping on the inside of her skull. Dina persisted, focusing on a sensation that brought her joy—the feel of the rough bark of her father tree, the first being who greeted her after she was born.
If her experiment proved a success, she'd be able to go back to where her glade had been and bring it back. Bring them back. All the plants, animals, and dryads, just as she remembered. #emph[L] #emph[ife from lifelessness.]
A snap broke her concentration. Across the clearing, a dead tree fell with a crash, its trunk bisected cleanly by~something. Dina closed the tome, snuffed out her light, and ducked down in the mud close to the water's edge. There was no moon out that night, and the starlight could only barely penetrate the bog's haze.
No swamp creature could have done that precise damage to the tree trunk. It had to be someone from Strixhaven.
"#emph[Dissatisfied?] " a voice shouted. "Do you even know the meaning of that word?" A second later, a sleek, black projectile hit the ground in front of her. #emph[Ink magic?] she thought. Another shadowy bolt came out of the night and splashed into the mud precariously close to the water's edge where the pests were blissfully playing. It was absolutely ink magic, the signature spell style of Silverquill College. But what was someone from Silverquill doing out in Detention Bog? The answer was obvious: it was a student, one who was being punished.
"You weren't even there! Where the hell were you?"
Inky coils reached out from the darkness like twin claws, gripping a pair of high tree branches and ripping them down to the ground. This time the trees did speak. Their howls filled Dina's mind. #emph[What did we do? Why is this happening? ] Their wails of pain spurred her to action. She crawled out of hiding and cast her ghostlight hoping that the sight of another student would give the intruder pause.
Unfortunately, her sudden appearance had the opposite effect.
"Who's there?" the voice screamed, and a moment later, a wave of inky force was rolling toward Dina. Instinctively, she chanted the syllables of the summer charm, a spell that originated with the dryads, but one which all nature-oriented mages have since included into their repertoires. It was enough to shield her from the brunt of the wave, but its sheer strength still knocked her onto her back. Footsteps rushed toward the spot where Dina lay. A moment later, a pair of hands pulled her back to her feet. A young man dressed in the black and white garb of a Silverquill student stood in front of her, a look of shock on his face.
"I~I didn't see you."
"That's because it's dark," said Dina. "Human eyes don't adjust well to the lack of light."
"No, I mean~"
His voice trailed off, and his eyes strayed from Dina to a point behind her.
The pests! Dina's heart dropped. #emph[If they're hurt] ~Dina prepared for the grisly scene and turned to look. But instead of dead pests, sitting on the ground was a jet-black sphere of ink magic quivering as if alive. Prominences of green mist leapt from point to point on its surface.
"What magic is this?" the young man asked in a whisper.
Dina didn't answer. She watched as the sphere shuddered and then sprouted tendrils that burrowed into the soft ground of the bog. The dirt under her feet started to shift and roil like miniature fingers clawing the bottoms of her boots.
"We can't stay here," she said.
"You haven't answered my question!"
Without another word, she took the young man's wrist, pulled as hard as she could, and ran away from the site, dragging him behind her. His answers could wait until later, not that she had any. The ritual had to be performed delicately and with precision, and now it had been corrupted. The trees bellowed with thunderous shrieks. #emph[The void! Where have you sent us? So much pain. . .]
Their anguish brought Dina to her knees. This time, it was the young man picking her up and pulling her along until they came across a thicket where they took shelter.
All around them was the sound of tree limbs thrashing.
"Now answer my question," he said.
Up close, Dina recognized the young man as the son of <NAME>, the more vocal and charismatic of Silverquill's deans. They had the same steely, resolute countenance when they talked. Dina had seen it many times (from the back rows, of course) when <NAME> would give his fiery speeches on commitment and duty at all-college assemblies.
"Your name is Killian," she said. "Your father—"
"Don't talk about my father," he snapped, then softened his expression. "We have other things to deal with right now, starting with the truth. What was that back there?"
There was no use in hiding things. Dina produced the spellbook from her satchel.
Killian cracked the book open and leafed through its pages. "Forbidden magic," he said.
"I know," said Dina. "That's why I was hiding it out here, where no one was supposed to be."
"That doesn't change a thing."
"Except you destroying my one chance—"
"At what?" he said. "What were you trying to do?"
Dina stopped short of saying it: #emph[To save everything I ever loved in this world] . It was the kind of statement that sounded either megalomaniacal or at least deeply ridiculous, even if it was the truth. So she sidestepped his question.
"Wait, do you hear that?" said Dina.
Killian stopped and listened. "No."
"Exactly. We should go back and look."
Emerging from the trees, Dina and Killian traced their steps back to where the pest den had been, this time using a radiant orb conjured by Killian as a light source. Though only a short time had passed, the effect of Dina's spell was clear. Deep gashes marked tree trunks and the soft ground, as if a great beast had raked its talons across the landscape. The trees around the area had been severed at the stump or uprooted entirely. There were no signs of the pests, and the only remnants of their den were splinters floating on the surface of the creek.
"We have to go," said Dina. "<NAME> is at Widdershins. He can help us."
Killian shook his head. "I'm trapped here all night." He turned his right arm over to show Dina the Silverquill sigil on his wrist. It was a detention token, a brand that prevented students from simply eschewing their mandatory stays in Detention Bog. If they tried to escape, the token would react with the landscape to force the student back toward the bog's center. "That's what I get for letting a Prismari player steal my inkling from right under my nose. I cost my team that point, and Silverquill lost the Mage Tower match. That's my father for you."
"He gave you detention for a game?"
"No, he gave me a detention for not #emph[applying myself] ," he said. "You should go back. I can handle myself."
"I'm not leaving you out here alone."
"Then help me fix your mistake."
"#emph[Our] mistake," said Dina. "Remember that part with yelling and the careless spellcasting?"
"Fine," Killian said. He pointed to a patch of ground at the far end of the clearing. A fresh trail strewn with battered branches had been blazed through the bog. "It's moving. I'll lead the way."
"You do know that if something attacks us from the front, you'll likely be hit first," said Dina.
"Sure, but—"
"So, it's not in your best interest to be in front of me, nor is it in my best interest to have the light source so far ahead. What if I get ambushed from behind?" She motioned to the width of the trail. "We can walk side by side. Doesn't that make more sense?"
"I was just trying~never mind."
Spellbook in hand, Dina skimmed pages as she walked. The ritual was clear in its intent. As pests were repositories for magical energy, her professors conjectured that their essences were as primordial as elementals, that they may have been related to every living thing on Arcavios. One of the simplest spells taught to all Witherbloom students drew forth the magical essence of a pest, converting it, body and soul, into pure magic. The ritual from the book promised a conduit to harness this magic and convert it back into its original living state.
#emph[Back here. Like you never left.]
"Find anything?" asked Killian.
"No," said Dina. There were no unbindings, no counters included with any of the spells inside. "It's almost like the mage has been trying to do the same thing again and again."
"Raise the dead?"
"Restore the living."
"I wonder who they lost," said Killian.
"Who did you lose?"
"How did you~am I really that transparent?" Killian hung his head and smiled at her behind long strands of hair. "My mother died when I was very young. But I can't even say I lost her. I hardly remember her." He swept his hair back onto his head and continued to walk down the path.
Dina knew better than to take his nonchalance at face value. She knew what it was to lose those she loved, and moreover to have that ache of the #emph[never knowing] . It was a profound awareness of how empty you would always be, like a whirlpool draining into a bottomless chasm. No width of smile or depth of laugh could hide that wound from those who also bore it.
"I didn't know my mother, either," Dina said, catching up. "Everyone from my glade is gone."
"Your entire family?"
"Dryads don't have families," Dina explained. "At the end of her life, a dryad finds a tree that is similarly close to its end. She rests at its foot, allowing the earth to reclaim her body, and, eventually, a new dryad emerges from the tree knowing nothing but her name—the same one as her mother's. We don't have parents like you, but we still have community—our glade sisters and all the plants and animals."
"But they're all gone."
"Yes. When the blight comes, few are spared."
They continued to follow the trail as it widened into another clearing. As soon as they stepped foot into it, a low growl emanated from a patch of bushes a short distance away.
"Is that it?" said Killian, his hands ready to direct an inky bolt toward a threat.
"No," said Dina. She sniffed the air. "It's a vineclinger."
"What? How do you know?"
"<NAME>. It's what they eat. It gives them their smell."
Killian breathed in. "Is that what that stink is?"
Lumbering out from the bushes was a hulking creature whose features, other than its powerful arms and large black claws, were obscured by tufts of long, stringy hair. As soon as it spotted them, it tried to roar, but its bellow came out as a pained gurgle.
"It's hurt," said Dina, pointing to patches of blood on its hair. "We need to help it."
"That's a wild animal!"
"I know." Though she'd wanted to approach the vineclinger in peace, Killian did have a point. Its gait was unsteady, and its movements were sluggish. Any sudden movements would rattle it. Even a weakened vineclinger could break every bone in hers or Killian's body with a single swipe. "Back me up?"
Killian nodded.
"It's okay," Dina whispered, walking forward slowly. "Let me help." She placed her palm onto the beast and chanted an incantation to quell the magic invading the vineclinger's body. But the corruption was too strong for her to uproot. Dina doubled her effort to eject the infection, but this only caused the vineclinger's massive arm to tense, eliciting a howl of pain. It swung out at Dina with its claws extended.
Acting quickly, Killian pulled her away with one arm and with his other arm peppered the vineclinger's face with barbs of ink magic. It wailed, stumbled backward, and fell onto its side, lying motionless save for its labored breaths. Killian helped Dina up, and together, they approached the beast. Black wisps of Killian's magic wafted off the vineclinger's body.
Dina knelt down and brushed away clumps of bloody hair from the vineclinger's face. It whined and moved its eyes to follow her movements. "I need to know what you saw," she said to the beast.
"Is it~?" Killian started to ask.
"My magic isn't strong enough to heal it," Dina said quietly. She placed the back of her hand to the vineclinger's forehead. Communing with flora came naturally to dryads—that's why they made perfect nature wizards. But establishing rapport with animals was much harder. Dina began to concentrate by imagining that she was floating down a long, dark tunnel. Upon reaching the end, she found herself looking down onto the clearing from the treetops—the world through the vineclinger's eyes. An abrupt snap of a twig caused her vision to refocus onto a creature creeping into the clearing below. It moved like a great wurm, gouging a path in the soft ground. As it moved, it took earth, rotten vegetation, and half-devoured carrion into itself to grow in size, strength, and speed.
Dina could only watch as the vineclinger bounded from branch to branch to confront the creature. Once on the ground, the vineclinger sprinted toward it and sunk teeth and talon into its body. Dina tasted the dirt on her tongue, felt fragments of bone crack between her teeth.
The intruder's counterattack was swift. From its body, long black tendrils emerged to impale the vineclinger and batter it against the trees. Dina experienced every shred of physical pain that the vineclinger had endured, its confusion at being tossed around like a leaf in a gale. Ultimately, the creature discarded the vineclinger in the brush, content to proceed on its way.
Dina let go of the vineclinger, her whole body aching from phantom fractures and lacerations. "It's headed northeast," she said, steadying herself. "Toward Sedgemoor."
"Toward school? Maybe it's drawn to magical energy?"
"Or it's looking for a purpose," said Dina. "It was just born, and it doesn't know why it's here or what it has to do."
"Like a giant murdering baby?"
"#emph[Our] giant murdering baby."
Killian sent his radiant orb farther down the trail, and they followed along. Dina couldn't get the vineclinger's memories out of her head. If that thing escaped the bog, countless students would be in danger, not to mention the wildlife that had already been imperiled. Yet, the experiment had been a success of a sort. Was that creature not a new life from the aether? Could it be anything but a sign that these magics held promise for true resurrection? How much good could the dryads of her glade bring back to Arcavios? How much wisdom could they reclaim from the abyss and bring back to the people?
And who would she be willing to sacrifice to see them return?
Killian's hand clutched onto hers, breaking her fugue. "C'mon! I think I see it!"
Dina looked ahead. In the far distance, Killian's orb had indeed illuminated a colossal shape that had wrapped itself around a patch of tall ancient Sylvatica trees. Though it was dark, she could have sworn that its silhouette looked twice the size that it had been when it fought with the vineclinger. Why had it stopped and settled in this part of the bog? Did it know that they were coming for it?
Had it been waiting for them?
Killian snuffed out his light spell and pulled Dina off the trail and behind a stack of felled trees. "We can't just run in there," he said. "Wait—that black orb that we first saw. That thing's body is made from the swamp, but its heart—"
"Your magic," said Dina.
"And yours, too," said Killian. "If we could just access its heart again, we could break the spell, counteract a piece of it, causing the whole thing to fall apart!" He thought for another moment. "I think I might be able to cancel out the ink magic, but I'd have to be right next to the orb for it to work. Could we burn the body away?"
"No, the bog is too damp," said Dina. "But I have a plan."
Killian smiled. "Care to share?"
"With you?" asked Dina. "Oh. That would probably be a good idea, right?"
#v(0.35em)
#line(length: 100%, stroke: rgb(90%, 90%, 90%))
#v(0.35em)
The second to last thing Dina said before she and Killian parted ways was "Eat these," as she pressed a handful of dried tea leaves into his palm. "You'll be able to see better in the dark."
Killian crunched them up in his mouth and swallowed them. A moment later, his eyes took on a faint blue hue. He blinked and looked around him in astonishment.
"This is amazing! Why didn't we use this before now?"
"Lionspaw has side effects on humans," said Dina.
"Such as?"
"You should stay close to the privy tomorrow."
"Oh."
"The next day, too."
And then came the last thing she'd say to him before they enacted their respective parts of the plan.
"Don't die, okay?" Dina told Killian.
"I won't. I like my odds."
Things like "the odds" didn't seem to slow Killian down in the slightest. He was impulsive and reckless, traits that Dina had always considered negative. At the same time, she wondered what it was like to be able to say something with that sort of confidence. Whether it be blind, foolish, or deserved, that poise was a trait that Dina had never possessed but had always wanted—for nothing else than to convince herself that she was doing the right thing.
Now she was by herself once more, stepping through thistle patches to circle around the abomination. Somewhere on the other side of the grove, Killian was settling into a good vantage point to wait until it was time to play his part. The stench of rot filled Dina's nostrils. Being this close to the monster's body was like being buried under layers and layers of dead vegetation. She didn't dare touch it directly. Prematurely provoking it from its sluggish state could have proven fatal. Instead, Dina sunk her hand into the dirt a few steps away from the creature and began reciting one of the first spells she learned at Strixhaven.
#emph[Nature] , Lisette had explained, #emph[is drawn to balance. Magic is simply a way to slightly alter this balance without destroying the elements you're working with. The key is to start small. A mountain can rest on a single pebble. An ocean begins as a drop of rain.]
Dina breathed in, and with every breath, she imagined her mind extending outward to the smallest elements of water and earth, plant and bone—all the things that the creature's body was made of. She imagined splinters curling around each other and seizing taut, bits of earth glomming onto each other and holding fast like granite.
#emph[Beware of taking too much on] , warned Lisette.#emph[ Nothing is without cost.]
In class, Dina had been able to turn a handful of dirt into a sculpture of her favorite flower, the mantis orchid. That feat had required several pests to empower her spell. But now she was without that extra supply of magical energy, forcing her to use the next best power source—herself. She continued chanting, forcing the words out through gritted teeth. Every part of her body erupted in a torrent of pinpricks like thousands of nettle stings underneath her skin.
The creature began to move. It attempted to unmoor itself from the trees, only for sections of its body to break off and shatter when they hit the ground. Black tentacles sprung out from these deep gashes, but they were notably sluggish, sloughing off chunks of rotting vegetation with every movement. As long as Dina could maintain her spell, the creature would be slow and brittle, a perfect target for Killian's part of the plan. She peered past the dark mass in front of her to spot her companion. No sign of him yet. Suddenly, a pair of irregular appendages sprouted from the thing's body and started to probe the gaps between trees. With enough time, it would eventually find her. That is, if her own spell didn't kill her first.
"I don't #emph[apply myself] , huh?" With Killian's yell came two sickle-shaped blades of pure ink magic slicing into the body of the creature. Debris sprayed off its body. "Maybe you just can't accept who I am!" Two more bolts sailed out from the darkness to cleave off more of the creature. Their plan was working! All he had to do was work his way to the monster's core. But he had to be quick. Dina's chest felt like it was being pierced by a thousand flaming swords.
"You're so self-righteous!" Killian leapt up onto a fallen log and let loose another bolt of ink magic, this one taking the shape of a hammer which he hurled directly at the monster. More of its body broke off and shattered. "You're always willing to tell others that they're not worthy, not right for #emph[your] school!" He flipped off the log. "This is not #emph[your] school! This is #emph[our] school!" Killian spun around, conjuring an inky blade extending from his arm and bringing it down onto the creature.
Dina had never been to a Mage Tower game. Did all the players move as fluidly as Killian did? His actions formed an exquisite pattern, a dance as dazzling as it was forceful. Unfortunately, Killian's final maneuver had brought him too close to the creature, close enough for it to shift its mass and rake him across the chest with a pair of shadowy claws.
"Killian!" screamed Dina as she watched him crumple to the ground. She broke her spell and ran to Killian's side, dodging a flurry of blows from the monster. Dina dragged him away from the creature to the foot of the nearest tree and spoke an overgrowth enchantment aloud to compel the tree's roots to wrap around him. Then she stood up and turned to face down this adversary of her own making. The creature's body shuddered as it shook off the effects of Dina's petrification charm. It reared far above her, showcasing an immense maw of splintered bone on its underside.
And then, like a great tidal wave, the creature crashed down upon her.
#v(0.35em)
#line(length: 100%, stroke: rgb(90%, 90%, 90%))
#v(0.35em)
Dina stood amidst the tall reeds that tickled her nose. Water caressed her feet up to her ankles, and the cool mud snuggled her toes. The scent of sweet citrus permeated the air, prompting her to take a deep breath.
#emph[Home.]
"You've always loved strawberry season," she heard someone say. To Dina's left, from beyond the treeline, stepped forth a figure that was both alien and intimately familiar all at once—a tall beautiful dryad who almost seemed to flow through the air. The tips of the branches crowning her head were black and cracked. Her skin had turned from green to a lurid assortment of russets, ambers, and mottled grays. "You recognize this place," she said, stroking the tree next to her.
There was no way Dina couldn't recognize it. This was her glade, and more specifically, the tree she crawled out of when she was born. All the details were as she remembered. Perfectly so.
Too perfect.
"Are we really here?" said Dina.
"Does it matter, love?" said the dryad. "This is what you've desired, is it not?"
"It is," said Dina. "Everything as it was before the Brittleblight. I want~"
"Me," said the dryad, sitting down at the foot of the tree. "Once you start asking for the improbable, the impossible doesn't seem so out of the question."
"Do you know how long I've wanted to talk to you?" said Dina. "How long I've looked?"
"Yes. In the wrong places, and for answers you know already."
"That's not true! I want to know why I am the only one left! Why me over all the others? There needs to be a reason!"
"A reason?" said the dryad. "You mean proof that you play some pivotal role in the schemes of an unseen architect? I wish I had an easy answer, if only to give you peace."
"But why else am I still alive if not to bring the others back?" said Dina. "I've found a way!"
"Have you?" the dryad said. "And how do you know that they want that?"
"I~"
Dina searched for a rebuttal but found herself without words. For so long, she'd held on to her fading memories of home and later coupled them with the determination to rescue all that she'd lost. Clinging to that wish had been enough to help save her own life. In time, it defined what she stood for, who she was. But what if it was wrong—a violation not only against nature itself but also the very ones she wanted to save? "Then what am I supposed to do?"
"You can help those who need it right now." The dryad looked to her left, and Dina followed suit. There, entangled in a cage of roots, was Killian, his face wracked with pain. "Does he mean something to you?"
"We've only just met," said Dina. "He's~my friend."
"A nice place to start. Of course, there is a matter of your present situation." The dryad leaned her head on the tree trunk and closed her eyes. "It's time to be whole again, my love."
Dina understood. She shut her own eyes and projected her mind outward as far as she could, past the boundaries of this memory and into the black heart of the creature she had birthed into the world. Envisioning her own body floating in this void, Dina focused on the single drop of her own blood that had bound the spell together. She let herself be pulled toward it until the drop was in front of her, suspended in the air. She reached out and touched it with her fingertip, the sensation of sharp teeth creeping up her hand. Suddenly, her entire arm felt like it had been plunged into a sea of ice. The chill raced up her neck to her face and into her nose, eyes, and mouth.
Then she was falling. Falling endlessly. Falling forever.
#v(0.35em)
#line(length: 100%, stroke: rgb(90%, 90%, 90%))
#v(0.35em)
Dina gasped for air and flailed her arms out at the dark shapes cast upon the wall. Grasping her bedcovers, she took stock of her surroundings. Gone were the environs of Detention Bog, replaced by the soft golden light radiating from a lantern set on a bedside table. Dina recognized this long room as the infirmary in Widdershins Hall. Alongside Lisette, she'd attended to bedridden students as part of her lessons on advanced healing. Sitting on a chair a short distance away from the bed was <NAME>, who stared at Dina from under the hood of his cowl.
"I was too hasty in complimenting you earlier," he said.
"Where~Killian—"
"Is recovering in his own room," said Valentin.
"How did I get here?"
"The boy is tenacious, dragging you all the way from the bog with a festering wound. Not to mention a particularly nasty case of lionspaw poisoning."
"What about the bog?"
"You're referring to the forces you've been meddling with?" he said. "Rest assured, if there were still a threat to students there, you wouldn't be here right now. You would be dead, as would young Mister Lu."
Valentin knew everything. And surely Killian would have been obliged to tell the Silverquill deans all that had gone on in the bog from his point of view. Dina, on the other hand, was sure that her time at Strixhaven had come to an end. She knew why she had made the choices that she made. She just wished there had been a different outcome. Then again, perhaps that was the only way she would have learned to let the past rest. A cost paid.
"I know you're disappointed," said Dina. "I didn't mean—"
Valentin sighed. "Disappointed? In truth, I'm very unsurprised. None of you students ever mean for things to go badly, especially when they do."
"As soon as I'm able, I'll take my things and leave." Dina leaned on the side table to get out of bed, but pain shot through her body, forcing her back down.
"You do know that this is an institution of learning, eh?" said Valentin. "I trust that you have learned something this night—that #emph[you] are the student, and #emph[we] are the instructors. #emph[We] painstakingly assemble lessons, and #emph[you] follow them to the letter. Venturing outside of that dynamic is~fraught. Such a lesson will be valuable in your future coursework."
"So~I can stay?"
"Hmph," he grunted. "Above all else, Strixhaven is a place for new beginnings. Often that comes in the form of second chances. None of us are faultless, <NAME>." He paused and clacked his fingers together. "And I am among the last who deserves to chastise others for their missteps."
#figure(image("005_The Chains That Bind/04.jpg", width: 100%), caption: [Art by: <NAME>], supplement: none, numbering: none)
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#line(length: 100%, stroke: rgb(90%, 90%, 90%))
#v(0.35em)
Professor <NAME> blew air at the flame, causing it to dance. At the beginning of the night, the candle on her desk had stood tall and solid. But by the time it had melted down into a nub, she had only graded a handful of her students' exams. How long had it been since she herself was subject to the judgment of an instructor? <NAME> had been a strict mentor, one widely recognized for her prowess in the healing arts. And what did that get her? A husband who left her. Children who shunned her. A swift end at the hands of a patient charged to her care. And worst of all, being utterly forgotten by everyone save the person who hated her most. Onyx dipped her quill into a jar of ink and proceeded to cross out a whole page of the exam in front of her. In the margin, she wrote one word: #emph[Pathetic] .
Barging through her classroom door came Lisette, fellow Strixhaven professor and dean of Witherbloom College. She marched up to Onyx's desk and dropped a heavy tome onto its surface.
"I believe this is yours," said Lisette, her eyes lit with fury.
Onyx gasped at what she saw before her. It's not that she thought the volume would elude her forever. She had all the time in the Multiverse to scour the Biblioplex's shelves. Rather, she hadn't expected it to come into her possession in such a convenient manner. Yet, there it was—one of the reasons why she was at Strixhaven wasting effort on ungrateful brats who already thought themselves wizards of esteemed repute.
She didn't want to alert Lisette to her excitement. It was, after all, best to stay calm and collected, especially in the face of a potential enemy. Anyone—a friend, a family member—could swiftly become an adversary. Onyx had learned that too well and too often.
"Your collegiality is appreciated," said Onyx, a slight smile on her face.
"I know who you are—what you are," Lisette threatened. "And I'll die before I stop trying to get you as far away from this school as I can."
<NAME> sat back and danced her fingers across the book's cover. "That can be arranged, Professor."
Without another word, Lisette stormed out, leaving Onyx alone with her prize. She flipped through the book, occasionally pausing and reading over the contents to reminisce. She remembered the names of those who volunteered as her test subjects—if not in life, then assuredly in death.
Onyx stopped on the final page and read over the spell. It, like all the others, had been a failure. #emph[Life from lifelessness. ] With her fingertip, she traced the outline of the esis leaf, caressing its edges like the cheek of a long-lost love. A black rot spread outward from where she touched it, consuming all the pages in the book, leaving nothing but the chains that had bound them.
|
|
https://github.com/liuguangxi/erdos | https://raw.githubusercontent.com/liuguangxi/erdos/master/Problems/typstdoc/figures/p156.typ | typst | #import "@preview/cetz:0.2.1"
#cetz.canvas({
import cetz.draw: *
let stroke-color = rgb("#03A9F4").darken(50%)
let fill-color = rgb("#03A9F4").darken(30%)
let a = 0.85
set-style(stroke: stroke-color + 1.5pt, fill: fill-color)
rect((0, 0), (10.5-0.15, 7-0.15), fill: none)
rect((0.5, 0.5), (rel: (a, a)))
rect((1.5, 0.5), (rel: (a, a)))
rect((2.5, 0.5), (rel: (a, a)))
rect((1.5, 1.5), (rel: (a, a)))
rect((2.5, 1.5), (rel: (a, a)))
rect((2.5, 2.5), (rel: (a, a)))
rect((4, 0.5), (rel: (a, a)))
rect((5, 0.5), (rel: (a, a)))
rect((5, 1.5), (rel: (a, a)))
rect((5, 2.5), (rel: (a, a)))
rect((5, 3.5), (rel: (a, a)))
rect((5, 4.5), (rel: (a, a)))
rect((6.5, 0.5), (rel: (a, a)))
rect((7.5, 0.5), (rel: (a, a)))
rect((6.5, 1.5), (rel: (a, a)))
rect((7.5, 1.5), (rel: (a, a)))
rect((7.5, 2.5), (rel: (a, a)))
rect((7.5, 3.5), (rel: (a, a)))
rect((9, 0.5), (rel: (a, a)))
rect((9, 1.5), (rel: (a, a)))
rect((9, 2.5), (rel: (a, a)))
rect((9, 3.5), (rel: (a, a)))
rect((9, 4.5), (rel: (a, a)))
rect((9, 5.5), (rel: (a, a)))
content(((10.5-0.15)/2, -0.5), [For N = #text(fill: red)[6]])
})
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https://github.com/Myriad-Dreamin/typst.ts | https://raw.githubusercontent.com/Myriad-Dreamin/typst.ts/main/fuzzers/corpora/visualize/line_00.typ | typst | Apache License 2.0 |
#import "/contrib/templates/std-tests/preset.typ": *
#show: test-page
#set page(height: 60pt)
#box({
set line(stroke: 0.75pt)
place(line(end: (0.4em, 0pt)))
place(line(start: (0pt, 0.4em), end: (0pt, 0pt)))
line(end: (0.6em, 0.6em))
}) Hello #box(line(length: 1cm))!
#line(end: (70%, 50%))
|
https://github.com/TypstApp-team/typst | https://raw.githubusercontent.com/TypstApp-team/typst/master/tests/typ/compiler/methods.typ | typst | Apache License 2.0 | // Test method calls.
// Ref: false
---
// Test whitespace around dot.
#test( "Hi there" . split() , ("Hi", "there"))
---
// Test mutating indexed value.
#{
let matrix = (((1,), (2,)), ((3,), (4,)))
matrix.at(1).at(0).push(5)
test(matrix, (((1,), (2,)), ((3, 5), (4,))))
}
---
// Test multiline chain in code block.
#{
let rewritten = "Hello. This is a sentence. And one more."
.split(".")
.map(s => s.trim())
.filter(s => s != "")
.map(s => s + "!")
.join("\n ")
test(rewritten, "Hello!\n This is a sentence!\n And one more!")
}
---
// Test .at() default values for content.
#test(auto, [a].at("doesn't exist", default: auto))
---
// Error: 2:10-2:13 type array has no method `fun`
#let numbers = ()
#numbers.fun()
---
// Error: 2:2-2:43 cannot mutate a temporary value
#let numbers = (1, 2, 3)
#numbers.map(v => v / 2).sorted().map(str).remove(4)
---
// Error: 2:3-2:19 cannot mutate a temporary value
#let numbers = (1, 2, 3)
#(numbers.sorted() = 1)
---
// Error: 2-5 cannot mutate a constant: box
#box.push(1)
---
// Test content fields method.
#test([a].fields(), (text: "a"))
#test([a *b*].fields(), (children: ([a], [ ], strong[b])))
---
// Test length unit conversions.
#test((500.934pt).pt(), 500.934)
#test((3.3453cm).cm(), 3.3453)
#test((4.3452mm).mm(), 4.3452)
#test((5.345in).inches(), 5.345)
#test((500.333666999pt).pt(), 500.333666999)
#test((3.5234354cm).cm(), 3.5234354)
#test((4.12345678mm).mm(), 4.12345678)
#test((5.333666999in).inches(), 5.333666999)
#test((4.123456789123456mm).mm(), 4.123456789123456)
#test((254cm).mm(), 2540.0)
#test(calc.round((254cm).inches(), digits: 2), 100.0)
#test((2540mm).cm(), 254.0)
#test(calc.round((2540mm).inches(), digits: 2), 100.0)
#test((100in).pt(), 7200.0)
#test(calc.round((100in).cm(), digits: 2), 254.0)
#test(calc.round((100in).mm(), digits: 2), 2540.0)
#test(5em.abs.cm(), 0.0)
#test((5em + 6in).abs.inches(), 6.0)
---
// Error: 2-21 cannot convert a length with non-zero em units (`−6pt + 10.5em`) to pt
// Hint: 2-21 use `length.abs.pt()` instead to ignore its em component
#(10.5em - 6pt).pt()
---
// Error: 2-12 cannot convert a length with non-zero em units (`3em`) to cm
// Hint: 2-12 use `length.abs.cm()` instead to ignore its em component
#(3em).cm()
---
// Error: 2-20 cannot convert a length with non-zero em units (`−226.77pt + 93em`) to mm
// Hint: 2-20 use `length.abs.mm()` instead to ignore its em component
#(93em - 80mm).mm()
---
// Error: 2-24 cannot convert a length with non-zero em units (`432pt + 4.5em`) to inches
// Hint: 2-24 use `length.abs.inches()` instead to ignore its em component
#(4.5em + 6in).inches()
---
// Test color kind method.
#test(rgb(1, 2, 3, 4).space(), rgb)
#test(cmyk(4%, 5%, 6%, 7%).space(), cmyk)
#test(luma(40).space(), luma)
#test(rgb(1, 2, 3, 4).space() != luma, true)
---
// Test color '.components()' without conversions
#test-repr(rgb(1, 2, 3, 4).components(), (0.39%, 0.78%, 1.18%, 1.57%))
#test-repr(luma(40).components(), (15.69%, ))
#test-repr(cmyk(4%, 5%, 6%, 7%).components(), (4%, 5%, 6%, 7%))
#test-repr(oklab(10%, 0.2, 0.3).components(), (10%, 0.2, 0.3, 100%))
#test-repr(oklch(10%, 0.2, 90deg).components(), (10%, 0.2, 90deg, 100%))
#test-repr(color.linear-rgb(10%, 20%, 30%).components(), (10%, 20%, 30%, 100%))
#test-repr(color.hsv(10deg, 20%, 30%).components(), (10deg, 20%, 30%, 100%))
#test-repr(color.hsl(10deg, 20%, 30%).components(), (10deg, 20%, 30%, 100%))
---
// Test color conversions.
#test(rgb(1, 2, 3).to-hex(), "#010203")
#test(rgb(1, 2, 3, 4).to-hex(), "#01020304")
#test(luma(40).to-hex(), "#282828")
#test-repr(cmyk(4%, 5%, 6%, 7%).to-hex(), "#e4e1df")
#test-repr(rgb(cmyk(4%, 5%, 6%, 7%)).components(), (89.28%, 88.35%, 87.42%, 100%))
#test-repr(rgb(luma(40%)).components(false), (40%, 40%, 40%))
#test-repr(cmyk(luma(40)).components(), (11.76%, 10.67%, 10.51%, 14.12%))
#test-repr(cmyk(rgb(1, 2, 3)), cmyk(66.67%, 33.33%, 0%, 98.82%))
#test-repr(luma(rgb(1, 2, 3)), luma(0.73%))
#test-repr(color.hsl(luma(40)), color.hsl(0deg, 0%, 15.69%))
#test-repr(color.hsv(luma(40)), color.hsv(0deg, 0%, 15.69%))
#test-repr(color.linear-rgb(luma(40)), color.linear-rgb(2.12%, 2.12%, 2.12%))
#test-repr(color.linear-rgb(rgb(1, 2, 3)), color.linear-rgb(0.03%, 0.06%, 0.09%))
#test-repr(color.hsl(rgb(1, 2, 3)), color.hsl(-150deg, 50%, 0.78%))
#test-repr(color.hsv(rgb(1, 2, 3)), color.hsv(-150deg, 66.67%, 1.18%))
#test-repr(oklab(luma(40)).components(), (27.68%, 0.0, 0.0, 100%))
#test-repr(oklab(rgb(1, 2, 3)).components(), (8.23%, -0.004, -0.007, 100%))
#test-repr(oklch(oklab(40%, 0.2, 0.2)).components(), (40%, 0.283, 45deg, 100%))
#test-repr(oklch(luma(40)).components(), (27.68%, 0.0, 72.49deg, 100%))
#test-repr(oklch(rgb(1, 2, 3)).components(), (8.23%, 0.008, 240.75deg, 100%))
---
// Test gradient functions.
#test(gradient.linear(red, green, blue).kind(), gradient.linear)
#test(gradient.linear(red, green, blue).stops(), ((red, 0%), (green, 50%), (blue, 100%)))
#test(gradient.linear(red, green, blue, space: rgb).sample(0%), red)
#test(gradient.linear(red, green, blue, space: rgb).sample(25%), rgb("#97873b"))
#test(gradient.linear(red, green, blue, space: rgb).sample(50%), green)
#test(gradient.linear(red, green, blue, space: rgb).sample(75%), rgb("#17a08c"))
#test(gradient.linear(red, green, blue, space: rgb).sample(100%), blue)
#test(gradient.linear(red, green, space: rgb).space(), rgb)
#test(gradient.linear(red, green, space: oklab).space(), oklab)
#test(gradient.linear(red, green, space: oklch).space(), oklch)
#test(gradient.linear(red, green, space: cmyk).space(), cmyk)
#test(gradient.linear(red, green, space: luma).space(), luma)
#test(gradient.linear(red, green, space: color.linear-rgb).space(), color.linear-rgb)
#test(gradient.linear(red, green, space: color.hsl).space(), color.hsl)
#test(gradient.linear(red, green, space: color.hsv).space(), color.hsv)
#test(gradient.linear(red, green, relative: "self").relative(), "self")
#test(gradient.linear(red, green, relative: "parent").relative(), "parent")
#test(gradient.linear(red, green).relative(), auto)
#test(gradient.linear(red, green).angle(), 0deg)
#test(gradient.linear(red, green, dir: ltr).angle(), 0deg)
#test(gradient.linear(red, green, dir: rtl).angle(), 180deg)
#test(gradient.linear(red, green, dir: ttb).angle(), 90deg)
#test(gradient.linear(red, green, dir: btt).angle(), 270deg)
#test(
gradient.linear(red, green, blue).repeat(2).stops(),
((red, 0%), (green, 25%), (blue, 50%), (red, 50%), (green, 75%), (blue, 100%))
)
#test(
gradient.linear(red, green, blue).repeat(2, mirror: true).stops(),
((red, 0%), (green, 25%), (blue, 50%), (green, 75%), (red, 100%))
)
---
// Test alignment methods.
#test(start.axis(), "horizontal")
#test(end.axis(), "horizontal")
#test(left.axis(), "horizontal")
#test(right.axis(), "horizontal")
#test(center.axis(), "horizontal")
#test(top.axis(), "vertical")
#test(bottom.axis(), "vertical")
#test(horizon.axis(), "vertical")
#test(start.inv(), end)
#test(end.inv(), start)
#test(left.inv(), right)
#test(right.inv(), left)
#test(center.inv(), center)
#test(top.inv(), bottom)
#test(bottom.inv(), top)
#test(horizon.inv(), horizon)
---
// Test 2d alignment methods.
#test((start + top).inv(), (end + bottom))
#test((end + top).inv(), (start + bottom))
#test((left + top).inv(), (right + bottom))
#test((right + top).inv(), (left + bottom))
#test((center + top).inv(), (center + bottom))
#test((start + bottom).inv(), (end + top))
#test((end + bottom).inv(), (start + top))
#test((left + bottom).inv(), (right + top))
#test((right + bottom).inv(), (left + top))
#test((center + bottom).inv(), (center + top))
#test((start + horizon).inv(), (end + horizon))
#test((end + horizon).inv(), (start + horizon))
#test((left + horizon).inv(), (right + horizon))
#test((right + horizon).inv(), (left + horizon))
#test((center + horizon).inv(), (center + horizon))
#test((top + start).inv(), (end + bottom))
#test((bottom + end).inv(), (start + top))
#test((horizon + center).inv(), (center + horizon))
---
// Test direction methods.
#test(ltr.axis(), "horizontal")
#test(rtl.axis(), "horizontal")
#test(ttb.axis(), "vertical")
#test(btt.axis(), "vertical")
#test(ltr.start(), left)
#test(rtl.start(), right)
#test(ttb.start(), top)
#test(btt.start(), bottom)
#test(ltr.end(), right)
#test(rtl.end(), left)
#test(ttb.end(), bottom)
#test(btt.end(), top)
#test(ltr.inv(), rtl)
#test(rtl.inv(), ltr)
#test(ttb.inv(), btt)
#test(btt.inv(), ttb)
---
// Test angle methods.
#test(1rad.rad(), 1.0)
#test(1.23rad.rad(), 1.23)
#test(0deg.rad(), 0.0)
#test(2deg.deg(), 2.0)
#test(2.94deg.deg(), 2.94)
#test(0rad.deg(), 0.0)
---
// Test date methods.
#test(datetime(day: 1, month: 1, year: 2000).ordinal(), 1);
#test(datetime(day: 1, month: 3, year: 2000).ordinal(), 31 + 29 + 1);
#test(datetime(day: 31, month: 12, year: 2000).ordinal(), 366);
#test(datetime(day: 1, month: 3, year: 2001).ordinal(), 31 + 28 + 1);
#test(datetime(day: 31, month: 12, year: 2001).ordinal(), 365);
|
https://github.com/lxl66566/my-college-files | https://raw.githubusercontent.com/lxl66566/my-college-files/main/信息科学与工程学院/机器视觉实践/报告/7/7.typ | typst | The Unlicense | #import "../template.typ": *
#show: project.with(
title: "7",
authors: ("absolutex",),
)
= 机器视觉实践 七
== 实验目的
结肠镜图像局部分割
+ 编程实现结肠镜图像局部分割
+ 要求用曲线分割出息肉的区域
== 实验代码
一般的图像处理应该很难做到这一点，所以直接使用大模型。
模型是 kaggle 上的 Automatic Polyp Detection in Colonoscopic Frames，使用 U-Net: Convolutional Networks for Biomedical Image Segmentation 训练，数据集为 CVC-ClinicDB。最终模型大小 130MB。
此处代码是加载模型并进行预测的代码。
#include_code("../src/polyp/__init__.py")
== 实验结果与心得
#figure(
image("res.png", width: 100%),
caption: [效果图],
)
所有息肉均分辨无误。 |
https://github.com/jgm/typst-hs | https://raw.githubusercontent.com/jgm/typst-hs/main/test/typ/compiler/shorthand-02.typ | typst | Other | - En dash: --
- Em dash: ---
|
https://github.com/RaphGL/ElectronicsFromBasics | https://raw.githubusercontent.com/RaphGL/ElectronicsFromBasics/main/DC/chap2/6_nonlinear_conduction.typ | typst | Other | #import "../../core/core.typ"
=== Nonlinear conduction
#quote(
attribution: [<NAME>, Astrophysicist],
block: true,
)[
Advances are made by answering questions. Discoveries are made by questioning answers.
]
Ohm's Law is a simple and powerful mathematical tool for helping us analyze electric circuits, but it has limitations, and we must understand these limitations in order to properly apply it to real circuits. For most conductors, resistance is a rather stable property, largely unaffected by voltage or current. For this reason we can regard the resistance of many circuit components as a constant, with voltage and current being directly related to each other.
For instance, our previous circuit example with the 3 $Omega$ lamp, we calculated current through the circuit by dividing voltage by resistance ($I = E/R$). With an 18 volt battery, our circuit current was 6 amps. Doubling the battery voltage to 36 volts resulted in a doubled current of 12 amps. All of this makes sense, of course, so long as the lamp continues to provide exactly the same amount of friction (resistance) to the flow of electrons through it: 3 $Omega$.
#image("static/6-circuit.png")
However, reality is not always this simple. One of the phenomena explored in a later chapter is that of conductor resistance changing with temperature. In an incandescent lamp (the kind employing the principle of electric current heating a thin filament of wire to the point that it glows white-hot), the resistance of the filament wire will increase dramatically as it warms from room temperature to operating temperature. If we were to increase the supply voltage in a real lamp circuit, the resulting increase in current would cause the filament to increase temperature, which would in turn increase its resistance, thus preventing further increases in current without further increases in battery voltage. Consequently, voltage and current do not follow the simple equation $I=E/R$ (with R assumed to be equal to 3 $Omega$) because an incandescent lamp's filament resistance does not remain stable for different currents.
The phenomenon of resistance changing with variations in temperature is one shared by almost all metals, of which most wires are made. For most applications, these changes in resistance are small enough to be ignored. In the application of metal lamp filaments, the change happens to be quite large.
This is just one example of "nonlinearity" in electric circuits. It is by no means the only example. A "linear" function in mathematics is one that tracks a straight line when plotted on a graph. The simplified version of the lamp circuit with a constant filament resistance of 3 $Omega$ generates a plot like this:
The straight-line plot of current over voltage indicates that resistance is a stable, unchanging value for a wide range of circuit voltages and currents. In an "ideal" situation, this is the case. Resistors, which are manufactured to provide a definite, stable value of resistance, behave very much like the plot of values seen above. A mathematician would call their behavior "linear."
A more realistic analysis of a lamp circuit, however, over several different values of battery voltage would generate a plot of this shape:
#image("static/6-voltage-current-relationship.png")
The plot is no longer a straight line. It rises sharply on the left, as voltage increases from zero to a low level. As it progresses to the right we see the line flattening out, the circuit requiring greater and greater increases in voltage to achieve equal increases in current.
If we try to apply Ohm's Law to find the resistance of this lamp circuit with the voltage and current values plotted above, we arrive at several different values. We could say that the resistance here is nonlinear, increasing with increasing current and voltage. The nonlinearity is caused by the effects of high temperature on the metal wire of the lamp filament.
Another example of nonlinear current conduction is through gases such as air. At standard temperatures and pressures, air is an effective insulator. However, if the voltage between two conductors separated by an air gap is increased greatly enough, the air molecules between the gap will become "ionized," having their electrons stripped off by the force of the high voltage between the wires. Once ionized, air (and other gases) become good conductors of electricity, allowing electron flow where none could exist prior to ionization. If we were to plot current over voltage on a graph as we did with the lamp circuit, the effect of ionization would be clearly seen as nonlinear:
#image("static/6-ionization-potential-graph.png")
The graph shown is approximate for a small air gap (less than one inch). A larger air gap would yield a higher ionization potential, but the shape of the $I / E$ curve would be very similar: practically no current until the ionization potential was reached, then substantial conduction after that.
Incidentally, this is the reason lightning bolts exist as momentary surges rather than continuous flows of electrons. The voltage built up between the earth and clouds (or between different sets of clouds) must increase to the point where it overcomes the ionization potential of the air gap before the air ionizes enough to support a substantial flow of electrons. Once it does, the current will continue to conduct through the ionized air until the static charge between the two points depletes. Once the charge depletes enough so that the voltage falls below another threshold point, the air de-ionizes and returns to its normal state of extremely high resistance.
Many solid insulating materials exhibit similar resistance properties: extremely high resistance to electron flow below some critical threshold voltage, then a much lower resistance at voltages beyond that threshold. Once a solid insulating material has been compromised by high-voltage breakdown, as it is called, it often does not return to its former insulating state, unlike most gases. It may insulate once again at low voltages, but its breakdown threshold voltage will have been decreased to some lower level, which may allow breakdown to occur more easily in the future. This is a common mode of failure in high-voltage wiring: insulation damage due to breakdown. Such failures may be detected through the use of special resistance meters employing high voltage (1000 volts or more).
There are circuit components specifically engineered to provide nonlinear resistance curves, one of them being the varistor. Commonly manufactured from compounds such as zinc oxide or silicon carbide, these devices maintain high resistance across their terminals until a certain "firing" or "breakdown" voltage (equivalent to the "ionization potential" of an air gap) is reached, at which point their resistance decreases dramatically. Unlike the breakdown of an insulator, varistor breakdown is repeatable: that is, it is designed to withstand repeated breakdowns without failure. A picture of a varistor is shown here:
#image("static/6-varistor-example.jpg")
There are also special gas-filled tubes designed to do much the same thing, exploiting the very same principle at work in the ionization of air by a lightning bolt.
Other electrical components exhibit even stranger current/voltage curves than this. Some devices actually experience a decrease in current as the applied voltage increases. Because the slope of the current/voltage for this phenomenon is negative (angling down instead of up as it progresses from left to right), it is known as negative resistance.
#image("static/6-neg-resistance-graph.png")
Most notably, high-vacuum electron tubes known as tetrodes and semiconductor diodes known as Esaki or tunnel diodes exhibit negative resistance for certain ranges of applied voltage.
Ohm's Law is not very useful for analyzing the behavior of components like these where resistance varies with voltage and current. Some have even suggested that "Ohm's Law" should be demoted from the status of a "Law" because it is not universal. It might be more accurate to call the equation $R=E/I$ a definition of resistance, befitting of a certain class of materials under a narrow range of conditions.
For the benefit of the student, however, we will assume that resistances specified in example circuits are stable over a wide range of conditions unless otherwise specified. I just wanted to expose you to a little bit of the complexity of the real world, lest I give you the false impression that the whole of electrical phenomena could be summarized in a few simple equations.
#core.review[
- The resistance of most conductive materials is stable over a wide range of conditions, but this is not true of all materials.
- Any function that can be plotted on a graph as a straight line is called a linear function. For circuits with stable resistances, the plot of current over voltage is linear (I=E/R).
- In circuits where resistance varies with changes in either voltage or current, the plot of current over voltage will be nonlinear (not a straight line).
- A varistor is a component that changes resistance with the amount of voltage impressed across it. With little voltage across it, its resistance is high. Then, at a certain "breakdown" or "firing" voltage, its resistance decreases dramatically.
- Negative resistance is where the current through a component actually decreases as the applied voltage across it is increased. Some electron tubes and semiconductor diodes (most notably, the tetrode tube and the Esaki, or tunnel diode, respectively) exhibit negative resistance over a certain range of voltages.core.review[
]
|
https://github.com/morrisLuke/typst_quarto_barebones_report_template | https://raw.githubusercontent.com/morrisLuke/typst_quarto_barebones_report_template/main/typst-template.typ | typst | #let psc-report(
title: "title",
body,
) = {
set text(
font: "Arial",
size: 12pt,
)
set page(
"us-letter",
margin: (left: 1in, right: 1in, top: 1.25in, bottom: 1in),
header: align(center + bottom, image("assets/logo-rectangle.png", height: 70% )),
footer: align(
grid(
columns: (20%, 60%, 20%),
align(top, text(fill: rgb("000000"), size: 12pt, counter(page).display("1"))),
align(center + top, text(fill: rgb("000000"), size: 12pt, "\"Acceptance is just one click away\"")),
align(right + top, image("assets/logo-square.png", height: 60%)),
)
)
)
body
} |
|
https://github.com/jgm/typst-hs | https://raw.githubusercontent.com/jgm/typst-hs/main/test/typ/text/linebreak-05.typ | typst | Other | // Test consecutive breaks.
Two consecutive \ \ breaks and three \ \ more.
|
https://github.com/BeiyanYunyi/Architectural-Technology-and-Art-Paper | https://raw.githubusercontent.com/BeiyanYunyi/Architectural-Technology-and-Art-Paper/main/nju-thesis/templates/bachelor-abstract.typ | typst | MIT License | #import "@preview/t4t:0.3.2": is
#import "../utils/style.typ": 字号, 字体
#import "../utils/indent.typ": fake-par
#import "../utils/double-underline.typ": double-underline
#import "../utils/invisible-heading.typ": invisible-heading
// 本科生中文摘要页
#let bachelor-abstract(
// documentclass 传入的参数
anonymous: false,
twoside: false,
fonts: (:),
info: (:),
// 其他参数
keywords: (),
outline-title: "中文摘要",
outlined: true,
anonymous-info-keys: ("author", "supervisor", "supervisor-ii"),
leading: 1.08em,
spacing: 1.08em,
body,
) = {
// 1. 默认参数
fonts = 字体 + fonts
info = (
title: ("基于 Typst 的", "南京大学学位论文"),
author: "张三",
department: "某学院",
major: "某专业",
) + info
// 2. 对参数进行处理
// 2.1 如果是字符串，则使用换行符将标题分隔为列表
if (is.str(info.title)) {
info.title = info.title.split("\n")
}
// 3. 内置辅助函数
let info-value(key, body) = {
if (not anonymous or (key not in anonymous-info-keys)) {
body
}
}
// 4. 正式渲染
pagebreak(weak: true, to: if twoside { "odd" })
[
#set text(font: fonts.楷体, size: 字号.小四)
#set par(leading: leading, justify: true)
#show par: set block(spacing: spacing)
// 标记一个不可见的标题用于目录生成
// #invisible-heading(level: 1, outlined: outlined, outline-title)
// 标题
#align(center)[
#set text(size: 字号.三号, weight: "bold", font: fonts.黑体 )
#info-value("title", (("",)+ info.title).sum())
#v(字号.五号)
]
// 作者
#align(center)[
#set text(size: 字号.四号, font: fonts.宋体)
#info-value("author", info.author)
]
// 学院
#align(center)[
#set text(size: 字号.小五, font: fonts.宋体)
南京信息工程大学#info-value("department", info.department), 江苏 南京, 210044
]
#[
#set text(size: 字号.五号, font: fonts.黑体, weight: "bold")
摘要：
#set text(size: 字号.五号, font: fonts.楷体, weight: "regular")
#body
]
#[
#set text(size: 字号.五号, font: fonts.黑体, weight: "bold")
*关键词*：
#set text(size: 字号.五号, font: fonts.楷体, weight: "regular")
#(("",)+ keywords.intersperse("；")).sum()
]
]
} |
https://github.com/Myriad-Dreamin/typst.ts | https://raw.githubusercontent.com/Myriad-Dreamin/typst.ts/main/fuzzers/corpora/text/em_00.typ | typst | Apache License 2.0 |
#import "/contrib/templates/std-tests/preset.typ": *
#show: test-page
#set text(size: 5pt)
A // 5pt
#[
#set text(size: 2em)
B // 10pt
#[
#set text(size: 1.5em + 1pt)
C // 16pt
#text(size: 2em)[D] // 32pt
E // 16pt
]
F // 10pt
]
G // 5pt
|
https://github.com/jgm/typst-hs | https://raw.githubusercontent.com/jgm/typst-hs/main/test/typ/compiler/block-04.typ | typst | Other | // Block in expression does create a scope.
#let a = {
let b = 1
b
}
#test(a, 1)
// Error: 3-4 unknown variable: b
#{b}
|
https://github.com/RanolP/resume | https://raw.githubusercontent.com/RanolP/resume/main/resume.typ | typst | #import "modules/util.typ": *
#import "modules/activity.typ": *
#import "modules/components.typ": *
#import "modules/github.typ": *
#import "modules/solved-ac.typ": *
#import "metadata.typ": metadata
#set page(
paper: "a4",
margin: (top: 1.5cm, left: 1.5cm, right: 1.5cm, bottom: 1.8cm),
header: context {
if here().page() != 1 {
pad(left: -0.4cm)[
#text(
fill: color.rgb("#575049"),
)[
#text(weight: 700)[#metadata.name.nickname / #metadata.name.real-korean]
---
#text(weight: 600, tracking: 1pt)[#metadata.role]
\@
#text(weight: 600, tracking: 0.5pt)[#metadata.location]
]
]
}
},
footer-descent: 0pt,
footer: [
#pad(left: -0.4cm, top: 0.6cm, bottom: -0.01cm)[
#text(size: 10pt, fill: color.rgb("#575049"))[
상기 이력은
#datetime.today().display("[year]년 [month]월 [day]일")
기준입니다
]
]
#align(right)[
#pad(
top: -1cm,
right: -0.5cm,
)[
#square(
size: 24pt,
fill: color.rgb("#000000"),
stroke: none,
radius: (top-left: 25%, top-right: 25%, bottom-left: 25%, bottom-right: 25%),
)[
#place(horizon + center)[
#text(fill: color.rgb("#ffffff"), weight: 900, number-width: "tabular")[
#context {
counter(page).display("1")
}
]
]
]
]
]
],
)
#set text(font: "Pretendard", features: ("ss06",), fallback: true)
#show heading: set text(size: 16pt)
= #text(size: 32pt)[#metadata.name.nickname / #metadata.name.real-korean#super[#upper[#metadata.name.real-english]]]
#text(size: 12pt)[
#text(weight: 900, tracking: 2pt)[#metadata.role]
#text(weight: 600)[\@]
#text(weight: 700, tracking: 1pt)[#metadata.location]
]
#{
set text(size: 10pt)
grid(
columns: (1fr, 1.5fr),
grid(
columns: (auto, 1fr),
column-gutter: 16pt,
row-gutter: 8pt,
[#icon("lucide/mail") *전자 우편#super[Mailbox]*], link("mailto:" + metadata.email)[#metadata.email],
[#icon("lucide/phone") *전화#super[Phone]*], link("tel:" + metadata.phone.join())[#metadata.phone.join(" ")],
),
grid(
columns: (auto, 1fr),
column-gutter: 16pt,
row-gutter: 8pt,
[#icon("devicon/github") *GitHub*],
link("https://github.com/" + metadata.social.github)[\@#metadata.social.github],
[#icon("logos/twitter") *Twitter*],
link("https://twitter.com/" + metadata.social.twitter)[\@#metadata.social.twitter],
[#icon-solved-ac() *solved.ac*],
link("https://solved.ac/profile/" + metadata.social.solved-ac)[
#solved-ac-profile(metadata.social.solved-ac)
],
),
)
}
#text(size: 14pt, weight: 400)[
#set par(leading: 8pt)
#text(size: 8pt, weight: 900, top-edge: -0pt, bottom-edge: 0pt)[
자기소개 #sym.dash.em #text(tracking: 2pt)[INTRODUCTION]
] \
#metadata.bio.ko.title \ #text(size: 10pt)[#metadata.bio.ko.body]
]
#line(length: 100%, stroke: 0.75pt)
== 기술#super[Skills]
#box(inset: (left: 8pt, top: 4pt))[
#align(center)[
#for row in (
(
tech-list.typescript--short,
tech-list.javascript--short,
tech-list.css,
tech-list.react-and-react-native,
tech-list.nextjs,
tech-list.solidjs,
tech-list.tailwindcss,
tech-list.unocss,
tech-list.eslint,
),
(
tech-list.rust,
tech-list.kotlin,
tech-list.swift,
tech-list.bash,
tech-list.gradle,
tech-list.git,
tech-list.github,
tech-list.github-actions,
),
) {
set text(size: 8pt)
enumerate(
row.map(tech => (icon(tech.icon, size: 16pt, bottom: 0pt), tech.label)),
)
}
]
]
#workExpList(
header: [
== 경력#super[Work Experiences]
],
(
workExpEntry(
from: datetime(year: 2023, month: 3, day: 20),
to: datetime.today(),
role: "프론트엔드 엔지니어",
organization: "주식회사 라프텔(Laftel)",
homepage: link("https://laftel.oopy.io")[laftel.oopy.io],
)[
애니메이션 OTT 서비스 라프텔에서 React와 React Native를 활용한 웹/앱 개발을 맡았습니다. \
수행한 주요 업무는 다음과 같습니다.
- Firebase를 활용한 A/B 테스트
- react-email과 tailwindcss를 활용한 이메일 템플릿 생성 및 관리, CI 연동 작업
- Next.js ISR을 활용한 Notion Database 기반 회사 블로그 구현
- AVFoundation 및 exoplayer (media3)를 활용한 react-native용 다운로드 모듈 개선
],
),
)
#activityList(
header: [
== 기타 활동#super[Other Activities]
],
(
activityEntry(
from: datetime(year: 2023, month: 11, day: 17),
title: belonging([해커톤 멘토 $and$ 심사위원], [쿠씨톤]),
)[
#link("https://kucc.co.kr/")[#text(
fill: color.rgb("#1c7ed6"),
)[#underline[KUCC]#sub[Korea University Computer Club]]]에서 주최한 2023년 쿠씨톤에서 해커톤
멘토 및 심사위원을 맡아 Django, React, Pygame 등을 사용하는 멘티들을 서포트하고, 작품을 심사했습니다.
],
activityEntry(
from: datetime(year: 2022, month: 9, day: 20),
title: "NYPC 2022 특별상",
)[],
),
)
#activityList(
header: [
== 프로젝트#super[Projects]
],
(
activityEntry(
from: datetime(year: 2023, month: 10, day: 29),
title: pad(top: -1em / 4)[
#gh-repo("psl-lang/psl") #h(1fr) #tech-chips.rust
],
)[ 알고리즘 문제 해결에 활용하기 좋은 프로그래밍 언어를 설계하고 만들었습니다. 간단한 입출력과 사칙 연산, 반복문 및 조건문을 사용할 수
있습니다. 컴파일 결과물로 읽기 쉬운 C 코드를 생성합니다. ],
activityEntry(
from: datetime(year: 2022, month: 8, day: 21),
title: pad(top: -1em / 4)[
#gh-repo("RanolP/crowdin-strife") #h(1fr) #tech-chips.rust #tech-chips.mysql
],
)[ Minecraft 번역 커뮤니티 사용자들이 기존 번역 및 외전 게임 텍스트를 쉽게 찾아볼 수 있도록 봇을 제작했습니다 ],
activityEntry(
from: datetime(year: 2022, month: 1, day: 9),
title: pad(top: -1em / 4)[
#gh-repo("RanolP/measurrred") #h(1fr) #tech-chips.rust
],
)[
WinAPI를 활용해 작업 표시줄에 CPU 사용량, 남은 배터리 등의 정보를 커스텀 위젯으로 보여줄 수 있는 프로그램을
만들었습니다
],
activityEntry(
from: datetime(year: 2021, month: 12, day: 10),
title: pad(top: -1em / 4)[
#gh-repo("RanolP/bojodog") #h(1fr) #tech-chips.typescript #tech-chips.webpack
],
)[ VS Code 안에서 백준 온라인 저지 문제를 확인할 수 있는 간단한 VS Code 확장을 만들었습니다 ],
activityEntry(
from: datetime(year: 2021, month: 11, day: 27),
title: pad(top: -1em / 4)[
#gh-repo("RanolP/bojoke") #h(1fr) #tech-chips.typescript #tech-chips.vite
],
)[ prosemirror를 활용해 백준 온라인 저지의 양식으로 문제 본문을 편집할 수 있는 WYSIWYG 에디터를 구현했습니다 ],
activityEntry(
from: datetime(year: 2021, month: 1, day: 4),
title: pad(top: -1em / 4)[
#gh-repo("RanolP/rano-lang") #h(1fr) #tech-chips.rust #tech-chips.wasm
],
)[ WebAssembly로 컴파일되는 작은 프로그래밍 언어를 만들어 함수 선언 및 호출, if ~ else 문 등을 구현했습니다. ],
activityEntry(
from: datetime(year: 2020, month: 10, day: 9),
title: pad(top: -1em / 4)[
#gh-repo("RanolP/dalmoori-font") #h(1fr) #tech-chips.typescript
],
)[ 한글날을 기념해 현대 한글 11,172자를 전부 지원하는 8 $times$ 8 도트풍 한글 글꼴 '달무리'를 만들었습니다. 현재 산돌 무료
폰트 중 하나로 등재되어 있습니다. ],
activityEntry(
from: datetime(year: 2020, month: 6, day: 21),
title: pad(top: -1em / 4)[
#gh-repo("solvedac/unofficial-documentation") #h(1fr) #tech-chips.openapi
],
)[ 알고리즘 문제풀이 커뮤니티, #link(
"https://solved.ac/",
)[#icon-solved-ac() #underline[#text(fill: color.rgb("#1c7ed6"))[solved.ac]]]의
API를 비공식적으로 OpenAPI 규격에 맞게 문서화했습니다 ],
activityEntry(
from: datetime(year: 2020, month: 5, day: 13),
title: pad(top: -1em / 4)[
#link("https://github.com/hanzzok")[#icon("devicon/github", bottom: -1em / 6) hanzzok]
#h(1fr)
#tech-chips.rust #tech-chips.wasm #tech-chips.typescript #tech-chips.nextjs
],
)[ Markdown의 대안으로 쓸 수 있는 마크업 언어를 설계해 HTML로 컴파일하는 Rust 구현체를 작성했습니다. 이후, 해당 구현을
WebAssembly로 컴파일해 웹페이지에서 실행하는 놀이터를 만들었습니다. ],
activityEntry(
from: datetime(year: 2020, month: 4, day: 8),
title: pad(top: -1em / 4)[
#gh-repo("RanolP/boj") #h(1fr) #tech-chips.typescript #tech-chips.playwright
],
)[ 백준 온라인 저지에 문제를 제출하고, 성공 여부를 바탕으로 특정일에 푼 문제 및 사용 언어 통계들을 제공하는 툴체인을 개발했습니다 ],
),
)
== 오픈소스 기여#super[Open Source Contributions]
#for (url,) in metadata.oss-contribs {
gh-pull-req(url)
}
#{
let pulls = metadata.oss-contribs.map(((url,)) => gh-pull(url))
let groups = pulls.map(pull => pull.nameWithOwner).dedup()
for group in groups.filter(group => group != none) {
[
- #gh-repo(group)
#for pull in pulls.filter(pull => pull.nameWithOwner == group) {
[
- #gh-pull-rich(pull)
]
}
]
}
}
|
|
https://github.com/lucannez64/Notes | https://raw.githubusercontent.com/lucannez64/Notes/master/Capture/Quotes.typ | typst | #import "template.typ": *
// Take a look at the file `template.typ` in the file panel
// to customize this template and discover how it works.
#show: project.with(
title: "Quotes",
authors: (
"<NAME>",
),
date: "14 Octobre, 2023",
)
#set heading(numbering: "1.1.")
#emph[Le moi est un autre qui se fait passer pour moi] <NAME>
|
|
https://github.com/jneug/typst-ccicons | https://raw.githubusercontent.com/jneug/typst-ccicons/main/README.md | markdown | MIT License | <div align="center">
<h1>ccicons (v1.0.0)</h1>
Creative Commons icons for your Typst documents</div>
----
> [!NOTE]
> `ccicons` is an adaption of the [ccicons package](https://ctan.org/pkg/ccicons) for LaTeX by [<NAME>](https://github.com/ummels).
## Getting Started
> [!IMPORTANT]
> As of now, the package is not published in the Typst Universe, but should be in the next few days.
Import the package into your document:
```typ
#import "@preview/ccicons:1.0.0": *
```
Start using license icons:
```typst
#cc-by-nc-sa
```
See the [the manual](docs/ccicons-manual.pdf) for more details and an overview all available Creative Commons icons.
# License
Please note that all icons that can be typeset using this package are trademarks of Creative Commons and are subject to the Creative Commons trademark policy (see http://creativecommons.org/policies).
The symbols in this font have been obtained from https://creativecommons.org/mission/downloads/ and released by Creative Commons under a Creative Commons Attribution 4.0 International license: https://creativecommons.org/licenses/by/4.0/
|
https://github.com/hei-templates/hevs-typsttemplate-thesis | https://raw.githubusercontent.com/hei-templates/hevs-typsttemplate-thesis/main/02-main/00-acknowledgements.typ | typst | MIT License | #pagebreak()
#heading(numbering:none)[Acknowledgements] <sec:ack>
#lorem(50)
#lorem(50)
|
https://github.com/savonarola/emqx-slides | https://raw.githubusercontent.com/savonarola/emqx-slides/main/main.typ | typst | #import "emqx-slides.typ": emqx-slides, frame
#show: emqx-slides.with(
font-family: none,
title: "EMQX Super new feature",
subtitle: "Doing this and that",
date: "2024",
authors: ("<NAME>", "EMQX Team"),
layout: "medium",
ratio: 4/3,
title-color: none,
)
== Slide 1 #lorem(10)
XXXX
- Bullet 1
- Bullet 2
- Bullet 3
- Sub-bullet 1
- Sub-bullet 2
- Sub-bullet 3
Content
== Slide 2
#frame(
title: "Slide 2 frame",
[Some content]
)
#frame(
[Some othe content]
)
#lorem(100)
|
|
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/datify/0.1.1/datify.typ | typst | Apache License 2.0 | #let dayNames = toml("dayName.toml")
#let monthNames = toml("monthName.toml")
#let firstLetterToUpper(string) = (
string.replace(regex("^\w"), m=>{upper(m.text)})
)
#let dayName(weekday, lang: "en", upper: false) = (
let weekdayToStr = str(weekday),
if upper == true {
return firstLetterToUpper(dayNames.at(lang).at(weekdayToStr))
} else {
return dayNames.at(lang).at(weekdayToStr)
}
)
#let monthName(month, lang: "en", upper: false) = (
let monthToStr = str(month),
if upper == true {
return firstLetterToUpper(monthNames.at(lang).at(monthToStr))
} else {
return monthNames.at(lang).at(monthToStr)
}
)
#let writtenDate(date, lang: "en") = (
return [#dayName(date.weekday, lang: lang) #date.day #monthName(date.month, lang: lang) #date.year]
)
|
https://github.com/lucifer1004/leetcode.typ | https://raw.githubusercontent.com/lucifer1004/leetcode.typ/main/solutions/s0014.typ | typst | #import "../helpers.typ": *
#let longest-common-prefix-ref(strs) = {
let strs = strs.map(x => x.clusters())
let i = 0
let n = strs.len()
let ans = ("",) // We put an empty string here to avoid returning none
while i >= 0 {
for j in range(n) {
if strs.at(j).len() <= i or strs.at(j).at(i) != strs.at(0).at(i) {
i = -1
break
}
}
if i != -1 {
ans.push(strs.at(0).at(i))
i += 1
}
}
ans.join()
}
|
|
https://github.com/RhenzoHideki/com1 | https://raw.githubusercontent.com/RhenzoHideki/com1/main/Relatorio-03/Relatorio-03.typ | typst | #import "@preview/klaro-ifsc-sj:0.1.0": report
#show: doc => report(
title: "Relatório 03",
subtitle: " Sistemas de comunicação I (COM029007)",
// Se apenas um autor colocar , no final para indicar que é um array
authors:("<NAME>",),
date: "17 de março de 2024",
doc,
)
= Introdução
Este relatório apresenta as atividades realizadas em MATLAB para simular um modulador/demodulador de fase e quadratura (IQ). Além disso, são resumidas as seções 5.1, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9 e 5.10 do livro "Software Defined Radio Using MATLAB & Simulink and the RTL-SDR", que abordam conceitos fundamentais para a compreensão e implementação dessa técnica
= Conteúdo teórico
== 5.1 Real and Complex Signals — it’s all Sines and Cosines
Esta seção explora a representação de sinais reais e complexos na engenharia de sinais, utilizando a fórmula de Euler para simplificar matematicamente a manipulação de sinais em termos de exponenciais complexas. A representação complexa dos sinais facilita a análise matemática, mesmo operando com sinais reais no mundo físico.
== 5.4 Quadrature Modulation and Demodulation (QAM)
Introduz o conceito de modulação em quadratura e demonstra sua implementação no RTL-SDR. Explica a motivação por trás do uso da modulação em quadratura para melhorar a eficiência espectral e destaca o processo de recuperação de sinais de banda base a partir do sinal recebido.
== 5.5 Quadrature Amplitude Modulation using Complex Notation
Descreve a modulação de amplitude em quadratura (QAM) usando notação complexa, simplificando a representação e manipulação de sinais QAM. Apresenta um exemplo prático de modulação de sinais para transmissão.
== 5.6 Quadrature Amplitude Demodulation using Complex Notation
Explora o processo de demodulação de amplitude em quadratura usando notação complexa, evidenciando como a notação complexa facilita a extração de sinais de banda base do sinal recebido.
== 5.7 Spectral Representation for Complex Demodulation
Examina a representação espectral de sinais complexos e sua aplicação na demodulação, detalhando a transformação espectral de sinais modulados em frequência para sua baseband complexa.
== 5.8 Frequency Offset Error and Correction at the Receiver
Discute o erro de deslocamento de frequência no receptor e métodos para corrigi-lo, especialmente em relação ao uso do RTL-SDR.
== 5.9 Frequency Correction using a Complex Exponential
Descreve um método de correção de frequência usando uma exponencial complexa, apresentando uma técnica para ajustar a frequência de sinais recebidos por meio da multiplicação por uma exponencial complexa.
== 5.10 RTL-SDR Quadrature / Complex Architecture
Conecta os conceitos de modulação complexa e demodulação com a arquitetura do RTL-SDR, explicando como os princípios de modulação e demodulação em quadratura são implementados nessa arquitetura.
#pagebreak()
= Desenvolvimento
A atividade em MATLAB que simula um modulador/demodulador de fase e quadratura com aúdio seguiu com este código:
```MATLAB
pkg load signal;
clear all;
close all;
clc;
[sinal1, Fs] = audioread('audio-1.wav');
fcc = 10e3;
Ac = 1 ;
duracao = length(sinal1)/Fs;
Ts = 1/Fs;
t = [0:Ts:duracao-Ts];
[sinal2, Fs] = audioread('audio-2.wav');
sinal1 = transpose(sinal1);
sinal2 = transpose(sinal2);
sinal2 = sinal2(1:length(sinal1));
c1_t = Ac*cos(2*pi*fcc*t);
c2_t = -Ac*sin(2*pi*fcc*t);
sinal1_f = fftshift(fft(sinal1)/length(sinal1));
sinal2_f = fftshift(fft(sinal2)/length(sinal2));
s1_t = sinal1 .* c1_t;
s2_t = sinal2 .* c2_t;
passo_f = 1/duracao;
f = [-Fs/2:passo_f:Fs/2 - passo_f];
s1_f = fftshift(fft(s1_t)/length(s1_t));
s2_f = fftshift(fft(s2_t)/length(s2_t));
y_t = s1_t + s2_t;
y_f = fftshift(fft(y_t)/length(y_t));
audiowrite('audio-y.wav',y_t,Fs);
sa_t = y_t .* c1_t;
sb_t = y_t .* c2_t;
sa_f = fftshift(fft(sa_t)/length(sa_t));
sb_f = fftshift(fft(sb_t)/length(sb_t));
filtro_pb = [zeros(1, (length(f) - 2*Fs)/2 ) ones(1,2*Fs) zeros(1, (length(f) - 2*Fs)/2)];
ya_f = sa_f .* filtro_pb;
yb_f = sb_f .* filtro_pb;
ya_t = ifft(ifftshift(ya_f)) * length(sa_f);
yb_t = ifft(ifftshift(yb_f)) * length(sa_f);
audiowrite('audio-a.wav',ya_t,Fs);
audiowrite('audio-b.wav',yb_t,Fs);
figure(1)
subplot(211);
plot(t,sinal1);
title("Sinal 1 - original");
subplot(212);
plot(t,sinal2);
title("Sinal 2 - original");
figure(2)
subplot(411);
plot(f,abs(sinal1_f));
title("Sinal 1 - original");
subplot(412);
plot(f,abs(s1_f));
title("Sinal 1 - Deslocado (Modulando)");
subplot(413);
plot(f,abs(sinal2_f));
title("Sinal 2 - original");
subplot(414);
plot(f,abs(s2_f));
title("Sinal 2 - Deslocado (Modulando");
figure(3)
subplot(211)
plot(t,y_t);
title("Sinal Resultante - Dominio do tempo");
subplot(212)
plot(f,abs(y_f));
title("Sinal Resultante - Dominio da frequência");
figure(4)
subplot(211);
plot(f,abs(sa_f));
title("Sinal 1 - Deslocado (Demodulando)");
subplot(212);
plot(f,abs(sb_f));
title("Sinal 2 - Deslocado (Demodulando)");
figure(5)
subplot(411);
plot(f,abs(sinal1_f));
title("Sinal 1 - original");
subplot(412);
plot(f,abs(ya_f));
title("Sinal 1 - Pós demodulado");
subplot(413);
plot(f,abs(sinal2_f));
title("Sinal 2 - original");
subplot(414);
plot(f,abs(yb_f));
title("Sinal 2 - Pós demodulado");
```
Este código gerou os resultados a seguir.
#figure(
image("./Figuras/sinaisOriginais.png",width:100%),
caption: [
Sinais gerados pelos audios \ Fonte: Elaborada pelo autor
],
supplement: "Figura"
);
Na figura 1 mostra 2 sinais são sinais gerados por 2 aúdios diferentes. Estes estão sendo mostrados no dominio do tempo.
#figure(
image("./Figuras/modulandoSinais.png",width:100%),
caption: [
Sinais gerados sendo modulados \ Fonte: Elaborada pelo autor
],
supplement: "Figura"
);
Na figura 2 é apresentado os 2 sinais de aúdio , porém agora no dominio da frequência , junto aos sinais originais também são mostrados os sinais modulados
#figure(
image("./Figuras/difentesDominiosModulado.png",width:100%),
caption: [
Sinais somados nos diferentes Dominios \ Fonte: Elaborada pelo autor
],
supplement: "Figura"
);
Na figura 3 é mostrado o sinal resultante da soma dos 2 sinais , está sendo apresentada em ammbos os dominios
#figure(
image("./Figuras/demodulandoSemFiltro.png",width:100%),
caption: [
Sinais sendo demodulado sem o filtro \ Fonte: Elaborada pelo autor
],
supplement: "Figura"
);
Descolando os sinais para fazer a demodulação dos sinais
#figure(
image("./Figuras/demodulandoComFiltro.png",width:100%),
caption: [
Sinais demodulado filtrado \ Fonte: Elaborada pelo autor
],
supplement: "Figura"
);
Sinais recuperados , fazendo a demodulação
= Conclusão
O trabalho realizado demonstrou a importância dos conceitos abordados nas seções do livro para a implementação do modulador/demodulador de fase e quadratura (IQ) no MATLAB. A compreensão desses conceitos é fundamental para o desenvolvimento de sistemas de comunicação eficientes e de alta qualidade. |
|
https://github.com/soul667/typst | https://raw.githubusercontent.com/soul667/typst/main/PPT/MATLAB/touying/docs/i18n/zh/docusaurus-plugin-content-docs/current/utilities/oop.md | markdown | ---
sidebar_position: 1
---
# 面向对象编程
Touying 提供了一些便利的工具函数，便于进行面向对象编程。
---
```typst
#let empty-object = (methods: (:))
```
一个空类。
---
```typst
#let call-or-display(self, it) = {
if type(it) == function {
return it(self)
} else {
return it
}
}
```
调用或原样输出。
---
```typst
#let methods(self) = { .. }
```
用于为方法绑定 self 并返回，十分常用。
|
|
https://github.com/VisualFP/docs | https://raw.githubusercontent.com/VisualFP/docs/main/SA/design_concept/content/design/design.typ | typst | #import "../../../style.typ": *
#part("Design")
This part describes the requirements, the design proposals, the design evaluation process, and the detailed final design for VisualFP.
#include_section("design_concept/content/design/functional_requirements.typ")
#include_section("design_concept/content/design/non_functional_requirements.typ")
#include_section("design_concept/content/design/design_iteration_1.typ")
#include_section("design_concept/content/design/design_iteration_2.typ")
|
|
https://github.com/matchy233/typst-chi-cv-template | https://raw.githubusercontent.com/matchy233/typst-chi-cv-template/main/CHANGELOG.md | markdown | MIT License | # [v1.1](https://github.com/matchy233/typst-chi-cv-template/releases/tag/1.1)
## Added
- Impelement `#personal-info` function, which accepts the following inputs and generates a line of personal info with icon separated by vertical line symbols accordingly
- `email`, `phone`, `github`,` linkedin` and `website`, with predefined styles
- `<name of icon>: <link>`, for example: `#personal-info(x-twitter: "https://x.com/iskyzh")` will generate an icon link like the figure below:
- a dictionary with keys: link, text, icon, solid, which will generate an icon link accordingly
- Make page margin and padding around cventry blocks adjustable
- Also alllow adjusting cventry block padding individually
<!-- ## Removed -->
## Changed
- Use `typst-fontawesome` package
- Make second level heading font size larger (12pt $\to$ 14pt)
<!-- ## Migration Guide from v0.1.X -->
---
# [v1.0.0](https://github.com/matchy233/typst-chi-cv-template/releases/tag/v1.0)
Initial Release
|
https://github.com/johannesbrandenburger/typst-build-server | https://raw.githubusercontent.com/johannesbrandenburger/typst-build-server/main/example-project/main.typ | typst | #let data = json("data.json")
#let name = data.name
= Hello, #name!
== Example Image
#figure(
image(
"img/resume-generator.png",
width: 10cm
)
) |
|
https://github.com/yhtq/Notes | https://raw.githubusercontent.com/yhtq/Notes/main/抽象代数/作业/hw6.typ | typst | #import "../../template.typ": *
// Take a look at the file `template.typ` in the file panel
// to customize this template and discover how it works.
#show: note.with(
title: "作业6",
author: "YHTQ ",
date: none,
logo: none,
withOutlined: false
)
= P64
== 5.
#answer[
显然 $6 = 2 * 3$，由 $p q$ 阶群至多只有两种知 $6$ 阶群要么是 $ZZ_6$，要么是 $S_3$
]
== 6.
#answer[
$|S_4| = 4! = 24 = 2^3 * 3$
显然 ${e, (123),(132)}$ 是一个 $3$ 阶子群。
对于 $8$ 阶子群，考虑 $D_8$ 到 $S_4$ 某个子群的同构，容易取得：
$
generatedBy((1234)\, (12)(34))
$（注意到 $ord((1234)) = 4,ord((12)(34))=2, (1234)(12)(34) = (31) = (12)(34)(2143)$）
将成为 $S_4$ 的一个 $8$ 阶子群。
]
== 12.
#answer[
$56 = 2^3 * 7$
由 $7| n_7 - 1$ 及 $n_7 | 8$ 知 $n_7 = 8$ 或 $1$\
由 $2 | n_2 - 1$ 及 $n_2 | 7$ 知 $n_2 = 7$ 或 $1$\
只需证明不可能 $n_7 = 8, n_2 = 7$：
事实上，由于 $n_7$ 中有 $6$ 个 $7$ 阶元，且每个 $7$ 阶元子群除单位元外不交，因此总共给出 $6 * 8 = 48$ 个 $7$ 阶元，其余元素仅剩 $8$ 个，显然不可能有 $7$ 个 $8$ 阶子群。
]
== 19.
#answer[
任取 $x in G$
注意到由 $N$ 是正规子群：
$
x P Inv(x) <= N
$
进而 $x P Inv(x)$ 也是 $N$ 的 #Sylow($p$) 子群，因此存在 $n in N$，使得：
$
x P Inv(x) = n P Inv(n)
$
这表明 $Inv(n) x in N_G (P)$，也即 $x in N N_G (P)$，证毕
]
== 20.
设 $|G| = 2^k m$，其中 $m$ 为奇数。
考虑 $G$ 到 $H <= S_(|G|)$ 的同构 $phi$，只需证明 $H$ 中有奇置换。
事实上，取 $G$ 中 Sylow-2 子群的生成元 $x$，$phi(x)$ 将成为 $2^k$ 个元素：$e, x, x^2, ..., x^(2^k-1)$ 上的轮换，因此它是奇置换，证毕。
=== 21.
#answer[
首先计算 $|G|$。考虑逐行填充元素，第一行可以是除零向量外任意向量，共有：
$
p^n - 1
$
种选法。
第二行需要排除第一行的倍数，因此有：
$
p^n - p
$
种选法。
第三行需要排除前两行的线性组合，注意到它们的线性组合互不相同，因此共有：
$
p^n - p^2
$
种选法。
以此类推，$|G| = (p^n - 1)(p^n - p)(p^n - p^2)...(p^n - p^(n-1))$
因此它的 #Sylow($p$) 子群的阶为：
$
p^0 * p^1 * ... * p^(n-1) = p^(n(n-1)/2)
$
注意到 $G$ 中所有主对角线为 $1$ 的上三角矩阵构成 $G$ 的群，且其阶恰为上式，因此它就是题目所求 $G$ 的 #Sylow($p$) 子群
]
= 补充题
== 1.
#answer[
$|S_5| = 120 = 2^3 * 3 * 5$
由 $5 | n_5 - 1$ 及 $n_5 | 24$ 知 $n_5 = 1, 6$\
另一方面，由于 $S_5$ 没有除 $A_5$ 外的非平凡正规子群，因此 $n_5 = 6$
显然：
$
generatedBy((12345))
$
就是一个满足要求的 $5$ 阶子群
]
== 2.
#answer[
注意到对任意 $P$ 为 $G$ 的 #Sylow($p$) 子群，均有：
$
exists x: N <= x P Inv(x) <=> Inv(x) N x <= P <=> N <= P
$
]
== 3.
#answer[
由同构定理：
$
(|P N|)/(|P|) = (|N|)/(|N sect P|)
$
设 $|G| = p^k m, |N| = p^r n$，其中 $m, n$ 均不含 $p$，则有：
$
|P N| |P sect N| = p^k p^r n
$
但另一方面，$|P N|$ 中 $p$ 的指数不超过 $k$，$|P sect N|$ 中不超过 $r$，由上式知两者必须都取等，因此两子群都是 #Sylow($p$) 子群。
]
== 4.
#answer[
注意到 $H$ 也是 $K$ 的 $Sylow(p)$ 子群，且 $normalSub(p, K)$，因此它将成为 $K$ 中唯一的 $Sylow(p)$ 子群。
另一方面，对任意 $x in N_G (K)$，将有：
$
x K Inv(x) = K
$
因此：
$
H <= K => x H Inv(x) <= x K Inv(x) = K => x H Inv(x) = K
$
这表明 $x H Inv(x)$ 也是 $K$ 中的 $Sylow(p)$ 子群，因此：
$
x H Inv(x) = H => x in K
$
进而 $L subset K$，而 $K subset L$ 是显然的，因此 $K = L$，证毕。
]
== 5.
#answer[
由于 $G$ 中至少有两个 $Sylow(p)$ 子群，取另一个 $Sylow(p)$ 子群为 $K'$，显然 $K' sect K$ 不是 $K$ 的 $Sylow(p)$ 子群，否则将有：
$
|K' sect K| = |K| = |K'| => K' = K
$
]
== 6.
#answer[
（1）：设 $72$ 阶群 $G$ 是单群
$
72 = 2^3 * 3^2\
2 | n_2 -1, n_2 | 9 => n_2 = 1, 3, 9\
3 | n_3 - 1, n_3 | 8 => n_3 = 1, 4\
$
从而 $n_3 = 4$\
考虑 $G$ 在所有 $4$ 个 $3$ 阶子群上的共轭作用，这将自然诱导出 $phi: G -> S_4$ 为同态，由于 $G$ 是单群，因此 $ker(phi) = {e}, G$，而 $|S_4| = 24 < 72$，因此 $ker(phi) = G$，但这与该作用是传递的显然矛盾，因此 $G$ 不可能是单群。
（2）：设 $180$ 阶群 $G$ 是单群
$
180 = 2^2 * 3^2 * 5\
2 | n_2 -1, n_2 | 45 => n_2 = 1, 3, 5, 9, 15, 45\
3 | n_3 - 1, n_3 | 20 => n_3 = 1, 4, 10\
5 | n_5 - 1, n_5 | 36 => n_5 = 1, 6\
$
仿照之前，考虑 $G$ 在所有 $6$ 个 $5$ 阶子群上的共轭作用，这将自然诱导出 $phi: G -> S_6$ 为同态，并有 $phi$ 为单射，因此 $G$ 同构于 $S_6$ 的某个 $180$ 阶子群 $H$。注意到 $H sect A_6 <= H$，因此考虑：
- $H sect A_6 = H => H <= A_6$
又 $180 = |H| = 1/2 |A_6| = 360$，从而 $H$ 将成为 $A_6$ 的指数为 $2$ 的正规子群，这与 $A_6$ 是单群矛盾
- $H sect A_6 != H$
此时符号函数 $sgn|_H$ 将给出 $H -> {1, -1}$ 的非平凡同态（显然不是单同态），进而 $ker(sgn)$ 是 $H$ 的非平凡正规子群，与 $H$ 是单群矛盾
]
== 7.
#answer[
#lemma[][
若 $G$ 存在 $p, q$ 或 $r$ 阶正规子群，则结论成立。
]
#proof[
- 若 $r$ 阶正规子群存在，结论是显然的。
- 若 $p$ 阶正规子群 $P$ 存在：
考虑 $quotient(G, P)$，容易发现 $|quotient(G, P)| = q r$，进而 $quotient(G, P)$ 中将唯一存在 $r$ 阶正规子群 $R'$
另一方面，对 $G$ 中任意 $r$ 阶子群 $R$，令 $pi: G -> quotient(G, P)$ 是自然同态，则由 $|pi(R)| | r, pi(R)$ 要么是平凡群，要么是 $R'$。
- 由于 $R sect P = {1}$，前者显然是不可能的
- 后者意味着若 $R_1, R_2$ 都是 $r$ 阶群，则：
$
R_1 <= ker(pi) R_2 = P R_2
$
（注意到由 $P$ 正规，$P R_2$ 是子群）\
然而由 $|P R_2| = p r$ 知 $P R_2$ 中的 $r$ 阶子群唯一，这就表明 $R_1 = R_2$
- 若 $q$ 阶正规子群存在，结论类似成立（注意到上面的证明没有用到 $p, q$ 之间的大小关系）
]
由 $n_r | p q$ 知 $n_r = 1, p, q, p q$\
又 $r | n_r - 1$，因此显然 $n_r$ 不能为 $p, q$，只能为 $1, p q$。
由 $n_p | q r$ 知 $n_p = 1, q, r, q r$\
又 $p | n_p - 1$，因此 $n_p != q$，故 $n_p = 1, r, q r$
若 $n_p, n_q, n_r$ 中有一个为 $1$，则由引理结论成立。
如若不然：
+ 此时 $n_r = p q$，这将给出 $p q (r - 1) = p q r - p q$ 个 $r$ 阶元素
+ $n_p = r, q r > q$，这将给出多于 $q(p-1) = p q - q$ 个 $p$ 阶元素
+ 群中剩余元素将小于 $q$ 个，此时 $n_q$ 只能为 $1$，矛盾！
]
== 8.
#answer[
设:
$
D_n = generatedBy(r\, s | r^n = s^2 = 1\, s r = r^(-1) s)
$
由于 $ord(r) = n$，因此 $r$ 应为一个长度为 $n$ 的轮换，显然 $D_n <= A_n$ 需要 $n$ 为奇数。
无妨设 $r = (123...n)$，则 $Inv(r) = (n (n-1) ... 321)$
由于 $s$ 是二阶元，它应该是若干不相交对换的乘积。无妨设 $s(1) = n$，则 $s$ 只能为 $(1 space n)(2 space n-1)(3 space n-2)...$，共计 $(n-1)/2$ 个对换。又 $s in A_n$，将有 $(n-1)/2$ 是偶数，也即：
$
4 | n - 1
$
根据以上构造，这就是充要条件。
对于命题 2，注意到 $2 p$ 阶子群只能为 $ZZ_(2p)$ 或 $D_p$，之前已经证明 $A_p$ 不含 $D_p$，显然 $A_p$ 也不含 $ZZ_(2 p)$ ，因此 $A_p$ 不含 $2 p$ 阶子群。
] |
|
https://github.com/alberto-lazari/cv | https://raw.githubusercontent.com/alberto-lazari/cv/main/modules_en/certifications.typ | typst | #import "/common.typ": *
= Certifications
#honor(
date: [January 2023],
title: [English B2 - Speaking],
issuer: [University of Padua],
)
#honor(
date: [July 2022],
title: [Laurea in Informatica],
issuer: [University of Padua],
)
#honor(
date: [September 2019],
title: [English B2 - Reading and Listening],
issuer: [University of Padua],
)
|
|
https://github.com/thimotedupuch/Template_Rapport_ISMIN_Typst | https://raw.githubusercontent.com/thimotedupuch/Template_Rapport_ISMIN_Typst/main/main.typ | typst | #set page(margin: 0%)
#set text(font: "New Computer Modern",lang: "fr")
#set heading(numbering:"I.1.")
// Permet de générer le rendu des blocs de code
#show raw: x=>rect(
radius: 5pt,
fill:luma(245),
stroke:0.7pt+black,
width: 100%,
text(font: "Cascadia Code",weight: "medium",size:8pt,x)
)
#let violet_emse = rgb(87,42,134)
#rect(width: 100%,fill: violet_emse)[
#v(2%)
#align(center)[
#image("Nouv_logo_emse_Blanc.svg",width: 50%)
]
#v(2%)
]
#v(15%)
#align(center)[#box(width: 80%)[
#line(length: 100%)
#text(size : 25pt)[*Titre du projet*]
#line(length: 100%)
#text(size:15pt)[
#table(
align: left,
stroke: none, column-gutter: 15pt,
columns: 2, // nombre de personnes dans le projet
[*NomA PrenomA*],[*NomB PrenomB*],
[#underline[<EMAIL>]],[#underline[<EMAIL>]]
)
]
#text(size:18pt)[*31 février 2056*] // changer la date
]]
#align(bottom)[
#box(width: 100%)[
#image("slogan.png",width: 40%)
]]
#align(bottom + center)[
#rect(width: 100%,fill: violet_emse)[
#v(3%)
]
]
#pagebreak()
#set page(margin: auto,numbering: "1")
#set par(justify: true)
// Configuration de l'en-tête de page
#set page(header: [
#smallcaps[Titre du projet] // à modifier
#line(length: 100%,stroke: 0.5pt)
])
#outline() // c'est la table des matières
// #pagebreak() // Pour passer à la page suivante
= Introduction
La fonction "lorem" permet de générer du texte pour remplir un paragraphe : #lorem(53) // En pratique elle ne sert à rien
= Développement
Pour faire un tableau basique :
#align(center)[
#table(columns: 3,
[*aaaaaa*],[*bbbbbbbb*],[*cccccccccc*],
[ddddddd],[eeeee],[ffffffff],
[],[],[],
[],[],[],
[],[],[],
)]
== Sous partie
On peut aussi écrire des bouts de code :
```python
import numpy as np
def FahrenheitToCelsius(T):
# celsius = (fahrenheit - 32) / 1.8
return (T-32)/1.8
```
En SQL,
```sql
SELECT
first_name,
last_name
FROM employees
WHERE first_name = 'Luca';
```
La plupart des langages sont pris en charge par le thème de couleurs :
```julia
using Plots
x = range(0, 10, length=100)
y = sin.(x)
plot(x, y)
```
etc...
=== Sous-sous partie
= Conclusion
|
|
https://github.com/gabrielluizep/klaro-ifsc-sj | https://raw.githubusercontent.com/gabrielluizep/klaro-ifsc-sj/main/template/main.typ | typst | MIT License | #import "@preview/klaro-ifsc-sj:0.1.0": report
#show: doc => report(
title: "Typst IFSC-SJ",
subtitle: "Um template para o Typst voltado para",
// Se apenas um autor colocar , no final para indicar que é um array
authors: ("<NAME>",),
date: "13 de Setembro de 2023",
doc,
)
= Soft
== Close
=== Closest
@hard #lorem(80)
== Softest
#lorem(80)
== Softest
#lorem(80)
= Hard <hard>
#lorem(80)
== Hardest
#lorem(80) |
https://github.com/lxl66566/my-college-files | https://raw.githubusercontent.com/lxl66566/my-college-files/main/信息科学与工程学院/信息论与编码/第二章作业.typ | typst | The Unlicense | #import "../template.typ": *
#import "@preview/tablem:0.1.0": tablem
#import "@preview/mitex:0.2.4": *
#import "@preview/cetz:0.2.2"
#show: project.with(
title: "2",
authors: ("absolutex",),
)
#set par(first-line-indent: 0em) // 不换行
#show heading: it => {
set text(font: 字体.黑体)
if it.level == 1 {
pagebreak(weak: true)
align(center)[#text(size: 字号.小二, it.body)]
} else if it.level == 2 {
// 不标序号
text(size: 字号.四号, it.body)
} else if it.level == 3 {
text(size: 字号.小四, it)
} else {
text(size: 字号.五号, it)
}
}
= 第二章作业
== 2.12
a. $H(X)=-2/3 log 2/3 - 1/3 log 1/3 = 0.918 "bits" = H(Y)$
b. #mi[`H(X|Y)=\frac{1}{3}H(X|Y=0)+\frac{2}{3}H(X|Y=1)=0.667\text{ bits }=H(Y|X)`]
c. #mi[`H(X,Y)=3\times\frac{1}{3}\log3=1.585 \mathrm{bits}`]
d. #mi[`H(Y)-H(Y|X)=0.251 \mathrm{bits}`]
e. #mi[`I(X;Y)=H(Y)-H(Y|X)=0.251&\text{ bits.}`]
f. #cetz.canvas({
import cetz.draw: *
circle((3, 0),radius: (3,3), stroke: blue)
circle((6.5, 0),radius: (3,3), stroke: blue)
content((2,0), [$H(X|Y)$])
content((5,0), [$I(X;Y)$])
content((8,0), [$H(Y|X)$])
content((5,3.2), [$H(X,Y)$])
content((2,-3), [$H(X)$])
content((7.5,-3), [$H(Y)$])
})
== 2.18
世界职业棒球锦标赛。世界职业棒球锦标赛为7场系列赛制，只要其中一队赢得4场，比赛就结束。设随机变量X代表在棒球锦标赛中，A队和B队较量的结果。例如，X的取值可能为AAAA，BABABAB，BBBAAAA。设Y代表比赛的场数，取值范围为4～7。假定A队和B队是同等水平的，且每场比赛相互独立。试计算$H(X)$,$H(Y)$,$H(Y|X)$及$H(X|Y)$.
#tablem[
| 场数 | 4 | 5 | 6 | 7 |
| ------ | ----- | ---- | --- | --- |
| 概率 | $2/2^4 = 1/8$ | $8/2^5 = 1/4$ | $20/2^6 = 5/16$ | $40/2^7 = 5/16$ |
]
#mi[`
H(X)= \sum p(x)log\frac{1}{p(x)} \\
=2(1/16)\log16+8(1/32)\log32+20(1/64)\log64+40(1/128)\log128 \\
= 5.8125
`]
#mi[`
H(Y)=\sum p(y)log\frac{1}{p(y)} \\
= 1/8\log8+1/4\log4+5/16\log(16/5)+5/16\log(16/5)\\
=1.924`]
$H(Y | X)=0$
#mi[`H(X|Y)=H(X)+H(Y|X)-H(Y)=3.889`]
== 2.32
a. 试求最小误差概率估计量$hat(X) (Y)$与相应的 $P_e$
$hat(X)(y) = cases(1\, & y=a,2\, & y=b, 3\, & y=c)$
$P_e = P(1,b)+ P(1,c)+ P(2,a)+ P(2,c)+ P(3,a)+ P(3,b)=1 / 2$
b. 估计出该习题的费诺不等式，并与(a)中求得的值比较。
$P_e>=((H(X|Y)-1) / (log |chi|))$
$H(X|Y)=H(1 / 2,1 / 4,1 / 4)=1.5 "bits"$
$P_e>= ((1.5-1) / (log 3))=0.316$
== 2.35
相对熵是不对称的。设随机变量X有三个可能的结果{a，b，c}。考虑该随机变量上的两个分布（右表）：计算$H(p)$,$H(q)$,$D(p||q)$和 $D(q||p)$,并验证在此情况下 $D(p||q)≠D(q||p)$。
#mi[`\begin{gathered}
H(p)=\frac{1}{2}\operatorname{log}2+\frac{1}{4}\operatorname{log}4+\frac{1}{4}\operatorname{log}4=1.5\mathrm{~bits.} \\
H(q)=\frac{1}{3}\operatorname{log}3+\frac{1}{3}\operatorname{log}3+\frac{1}{3}\operatorname{log}3=\operatorname{log}3=1.585\mathrm{~bits.} \\
D(p||q)=\frac{1}{2}\operatorname{log}\frac{3}{2}+\frac{1}{4}\operatorname{log}\frac{3}{4}+\frac{1}{4}\operatorname{log}\frac{3}{4}=\operatorname{log}(3)-1.5=1.585-1.5=0.085 \\
D(q||p)=\frac13\operatorname{log}\frac23+\frac13\operatorname{log}\frac43+\frac13\operatorname{log}\frac43=\frac53-\operatorname{log}(3)=1.667-1.585=0.082
\end{gathered}`] |
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/bookletic/0.1.0/README.md | markdown | Apache License 2.0 | # Bookletic :book:
Create beautiful booklets with ease.
The current version of this library (0.1.0) contains a single function to take in an array of content blocks and order them into a ready to print booklet, bulletin, etc. No need to fight with printer settings or document converters.
### Example Output
Here is an example of the output generated by the `sig` function (short for a book's signature) with default parameters and some sample content:
Here is an example with some customization applied:
## `sig` Function
The `sig` function is used to create a signature (booklet) layout from provided content. It takes various parameters to automatically configure the layout.
### Parameters
- `signature_paper`: The paper size for the booklet. Currently supports `"us-letter"` and `"us-legal"`.
- `page_margin_top`: The top margin for each page in the booklet.
- `page_margin_bottom`: The bottom margin for each page in the booklet.
- `page_margin_binding`: The binding margin for each page in the booklet.
- `page_margin_edge`: The edge margin for each page in the booklet.
- `page_border`: Takes a color space value to draw a border around each page. If set to none no border will be drawn.
- `draft`: A boolean value indicating whether to output an unordered draft or final layout.
- `pNum_pattern`: The pattern for page numbering (e.g., `"1"`, `"01"`, `"a"`, `"A"`).
- `pNum_placment`: The placement of page numbers on each page. Can be `top` or `bottom`.
- `pNum_align_horizontal`: The horizontal alignment of page numbers. Can be `left`, `center`, or `right`.
- `pNum_align_vertical`: The vertical alignment of page numbers. Can be `top`, `horizon`, or `bottom`.
- `pNum_size`: The size of the page numbers.
- `pNum_pad_horizontal`: The horizontal padding for the page numbers.
- `pNum_border`: The border color for the page numbers. If set to none no border will be drawn.
- `pad_content`: The padding around the page content.
- `contents`: The content to be laid out in the booklet. This should be an array of blocks.
### Usage
To use the `sig` function, simply call it with the desired parameters and provide the content to be laid out in the booklet:
```typst
#sig(
signature_paper: "us-letter",
contents: [
["Page 1 content"],
["Page 2 content"],
["Page 3 content"],
["Page 4 content"],
],
)
```
This will create a signature layout with the provided content, using the default values for the other parameters.
You can customize the layout by passing different values for the various parameters. For example:
```typst
#sig(
signature_paper: "us-legal",
page_margin_top: 0.5in,
page_margin_bottom: 0.5in,
page_margin_binding: 0.5in,
page_margin_edge: 0.5in,
page_border: none,
draft: true,
pNum_pattern: "-1-",
pNum_placment: bottom,
pNum_align_horizontal: right,
pNum_align_vertical: bottom,
pNum_size: 10pt,
pNum_pad_horizontal: 2pt,
pNum_border: rgb("#ff4136"),
pad_content: 10pt,
contents: [
["Page 1 content"],
["Page 2 content"],
["Page 3 content"],
["Page 4 content"],
],
)
```
This will create an unordered draft signature layout with US Legal paper size, larger margins, no page borders, page numbers at the bottom right corner with a red border, and more padding around the content.
### Notes
- The `sig` function is currently hardcoded to only handle two-page single-fold signatures. Other more complicated signatures may be supported in the future.
- Paper size is also currently hardcoded to only handle US Letter and US Legal.
- The function does not handle odd numbers of pages correctly yet. There is a TODO comment to implement this functionality.
- The `booklet` function is a placeholder for automatically break a single content block into pages dynamically. It is not implemented yet but will be added in coming versions.
### Collaboration
I would love to see this package eventually turn into a community effort. So any interest in collaboration is very welcome! However, at this point bookletic is still in its first iteration and can no doubt use a lot more field testing and improvements. If there is enough interest for collaboration, I will gladly create a public repository for bookletic. In the mean time, if you are interested you can ping me on the typst discord server with the username: `harrellbm`
|
https://github.com/Myriad-Dreamin/typst.ts | https://raw.githubusercontent.com/Myriad-Dreamin/typst.ts/main/fuzzers/corpora/math/linebreak_06.typ | typst | Apache License 2.0 |
#import "/contrib/templates/std-tests/preset.typ": *
#show: test-page
// Page breaks can happen after a relation even if there is no
// explicit space.
#let hrule(x) = box(line(length: x))
#hrule(90pt)$<;$\
#hrule(95pt)$<;$\
#hrule(90pt)$<)$\
#hrule(95pt)$<)$
|
https://github.com/rem3-1415926/Typst_Thesis_Template | https://raw.githubusercontent.com/rem3-1415926/Typst_Thesis_Template/main/template.typ | typst | MIT License |
#let thesis(
// Title of the thesis or work
thesis_title: "Some Thesis",
// A Short description below the title on the cover
sub_title: "Engineering an advanced innovation",
// Thesis author or authors. Use array syntax.
authors: ("Author1", ),
// Advisor or Professor. Use array syntax.
advisors: ("Prof. Dr. <NAME>", ),
// Co-Advisors (optional). Use array syntax.
co_advisors: (),
// Industry partner (optional). Use array syntax.
industry_partners: (),
// University. Use string syntax
university: "College of Winterhold",
// Paper size. Must not be capitalized.
paper: "a4",
// Margins. Header and footer will cut somewhat into them
margins: (
top: 3.0cm,
bottom: 2.5cm,
outside: 1.5cm,
inside: 2.5cm
),
// List of preferred fonts to use. First available will be taken.
fonts: (
"Grandview",
"Liberation Sans",
),
// Default text font size
font_size: 10pt,
// For general language settings (https://typst.app/docs/reference/text/text/#parameters-lang)
lang: "en",
// Optional, replaces the auto-generated if given
titlepage: none,
// Everything before the Table of Contents
frontmatter: [],
// Everything after main content
appendix: [],
// List of bibliography files, path relative to template. Use array syntax.
bib_files: (),
body
) = { // Layout etc ----------------------------------------------------------
set document(
title: thesis_title,
author: authors,
)
set par(justify: true)
set text(
font: fonts,
size: font_size,
lang: lang,
hyphenate: false,
)
let header = locate(loc => {
let currentpage = loc.page()
let target_page = -1
let next_heading = [
#let elems = query(
selector(heading.where(level: 1)).after(loc),
loc
)
#if elems != () {
target_page = elems.at(0).location().page()
elems.first().body
}
]
if (currentpage == target_page) { return } // No header on Title page
let last_heading = [
#let elems = query(
selector(heading.where(level: 1)).before(loc),
loc
)
#let elems2 = query(
selector(heading.where(level: 2)).before(loc),
loc
)
#if elems != () {
target_page = elems.at(-1).location().page()
if elems2 != () {
// par(justify:false)[#elems.last().body \ #elems2.last().body]
[#elems2.last().body]
} else {
[#elems.last().body]
}
}
]
grid(
columns: (1fr, 0.5fr, 1fr),
align(left)[
#if calc.even(currentpage) [_ #last_heading _] else [/*_ #thesis_title _*/]],
[],
align(right)[
#if calc.odd(currentpage) [_ #last_heading _] else [/*_ #thesis_title _*/]]
)
pad(y:-0.75em)[#line(length: 100%, stroke: 0.5pt)]
})
let footer = locate(loc => {
let currentpage = counter(page).at(loc).at(0)
let total_pages = counter(page).at(query(<document_end>, loc).at(0).location()).at(0)
let numbering = [#currentpage / #total_pages]
let txt_authors = [
#set par(justify: false)
#set text(hyphenate: false)
#for a in authors.slice(0,-1) [#a, ]
#authors.at(-1)
]
let date = [#datetime.today().display("[day]. [Month repr:long]. [year]")]
pad(y:-0.5em)[#line(length: 100%, stroke: 0.5pt)]
grid(
columns: (1fr, 1fr, 1fr),
align(left)[#if calc.odd(currentpage) [#numbering] else [/*#date*/_ #thesis_title _]],
align(center)[/*#txt_authors*/],
align(right)[#if calc.even(currentpage) [#numbering] else [/*#date*/_ #thesis_title _]],
)
})
let footer_front = locate(loc => {
let page_counter = counter(page).at(loc).at(0)
align(center)[#numbering("(I)", page_counter)]
})
set page(
paper: "a4",
binding: left,
margin: margins,
header: header,
header-ascent: 30%,
footer: footer,
footer-descent: 30%,
)
set heading(
supplement: "Chapter",
numbering: (..numbers) =>
if numbers.pos().len() <= 3 {
return numbering("1.", ..numbers)
}
)
show heading: it => block[
#if it.level == 1{
return{
// pagebreak is defined locally
text(size: 24pt)[#it]
pad(top: -0.5em, bottom: 1em)[#line(length: 100%, stroke: 2pt)]
}
}
#if it.level == 2{
return{ text(size: font_size*1.5)[#it] }
}
#if it.level == 3{
return{ text(size: font_size*1.25)[#it] }
}
#if it.level == 4{
return{ text(size: font_size*1.1)[_ #it _] }
} else {
it
}
]
show outline.entry.where(
level: 1
): it => {
v(12pt, weak: true)
strong(it)
}
set math.equation(numbering: "(1)")
show ref: it => {
let eq = math.equation
let el = it.element
if el != none and el.func() == eq {
// Override equation references.
[Eq.#numbering(
"(1)",
..counter(eq).at(el.location())
)]
} else {
// Other references as usual.
it
}
}
show link: it => text(style:"italic")[#underline[#it]]
// Title page -------------------------------------------------------------
if (titlepage != none) {
set page(header: none, footer: none)
titlepage
}
else {
set page(header: none, footer: none)
align(center + horizon)[
#set par(justify: false)
#text(3em)[*#thesis_title*]
#v(1.5em, weak: true)
#text(2em, sub_title)
]
align(left + bottom)[
#set text(size: 12pt)
*#if(authors.len() > 1) [Authors] else [Author]*
#v(0.6em, weak: true)
#for a in authors.slice(0,-1) [#a, ]
#authors.at(-1)
#v(0.6em, weak: true)
*#if(advisors.len() > 1) [Advisors] else [Advisor]*
#v(0.6em, weak: true)
#for a in advisors.slice(0,-1) [#a, ]
#advisors.at(-1)
#if(co_advisors != none){
if(co_advisors.len() > 0) [
#v(0.6em, weak: true)
*#if(co_advisors.len() > 1) [Co-Advisors] else [Co-Advisor]*
#v(0.6em, weak: true)
#for a in co_advisors.slice(0,-1) [#a, ]
#co_advisors.at(-1)
]}
#if(industry_partners != none){
if(industry_partners.len() > 0) [
#v(0.6em, weak: true)
*#if(industry_partners.len() > 1) [Industry Partners] else [Industry Partner]*
#v(0.6em, weak: true)
#for a in industry_partners.slice(0,-1) [#a, ]
#industry_partners.at(-1)
]}
#v(1.2em, weak: true)
#university
#v(0.6em, weak: true)
]
}
// Frontmatter ------------------------------------------------------------
[
#set page(footer: footer_front)
#counter(page).update(1)
#set heading(numbering:none, outlined: false, bookmarked: true)
// use odd side pagebreak for frontmatter
#show heading: it => block[
#if it.level == 1{
return{pagebreak(weak: true, to: "odd"); it}
} else {it}
]
#frontmatter
#outline(
depth: 2,
indent: true,
)
]
// Main content -----------------------------------------------------------
{
// use any side pagebreak for main content
show heading: it => block[
#if it.level == 1{
return{
pagebreak(weak: true)
it
}
} else {
it
}
]
counter(page).update(1)
body
// Bibliography
[= Bibliography]
bibliography(
title: none, // doesn't follow heading formatting
bib_files,
)
// v(15cm)
// lorem(300)
[#circle(radius: 0pt, stroke: none)
// void structures help with pagebreaks. Very interesting.
<bibliography_end>
#circle(radius: 0pt, stroke: none)
]
}
// Appendix ---------------------------------------------------------------
{
let app_entries = state("x", ())
[
#pagebreak(weak: true, to:"odd")
= Appendix
// #[#circle(radius: 0pt, stroke: none)]
#text(size: 12pt, weight: "bold")[
#locate(loc => {
let all_app_entries = app_entries.at(query(<document_end>, loc)
.first()
.location()
)
return for (i, ae) in all_app_entries.enumerate() [
#v(1em)
#grid(columns: (1fr, 5em),
[#numbering("A", i+1) #ae.at(0)],
align(right)[#ae.at(1)]
)
]
})
]
// apparently does not work:
// #outline(
// title: "Appendix Contents",
// target: heading.where(supplement: "Appendix ")
// )
]
counter(heading).update(0)
set heading(
supplement: "Appendix",
outlined: false,
bookmarked: true,
numbering: (..numbers) =>
if numbers.pos().len() <= 3 {
return numbering("A.1.", ..numbers)
},
)
show heading: it => block[
#if it.level == 1{
// use odd side pagebreak for main content.
// This is because pagebreak here kills manual pagebreaks needed for A3
return{[#pagebreak(weak: true, to: "odd") #it #locate(loc => {
let pn = counter(page).at(loc).at(0)
// add entry to Appendix outline
app_entries.update( x => {x.push((it.body, pn)); x})
})
]}
} else{
it
}
]
appendix
// void structure helps with this bug. (label otherwise on wrong page)
[#circle(radius: 0pt, stroke: none)<document_end>]
}
} |
https://github.com/mariuslb/thesis | https://raw.githubusercontent.com/mariuslb/thesis/main/abstract.typ | typst | Diese Bachelorarbeit analysiert den Energieverbrauch von Elektro- und Verbrennungsfahrzeugen unter Verwendung der ISO 23795-1:2022. Ziel der Arbeit ist es einerseits, die Effizienz und Nachhaltigkeit von Elektrofahrzeugen im Vergleich zu Verbrennungsmotoren zu untersuchen. Im Rahmen dieser Untersuchung wurden detaillierte Vergleichsfahrten durchgeführt und anhand deren Datensätze verschiedene statistische Modelle angewendet. Andererseits wird ebenso die Diskrepanz zwischen den WLTP-Normwerten und den realen Energieverbräuchen analysiert.Die Ergebnisse zeigen, dass Fahrten des Elektrofahrzeugs (Opel Mokka E) im Vergleich zum Verbrennerfahrzeug (VW Golf 8) eine höhere Energieeffizienz aufgrund ihres niedrigeren Verbrauchs aufweisen. Zudem wurden signifikante Unterschiede zwischen den WLTP-Normwerten und den unter realen Bedingungen gemessenen Verbräuchen festgestellt, was auf die Abweichungen zwischen standardisierten Testbedingungen und realen Fahrverhältnissen hinweist. |
|
https://github.com/darioglasl/Arbeiten-Vorlage-Typst | https://raw.githubusercontent.com/darioglasl/Arbeiten-Vorlage-Typst/main/Anhang/06_Jira/02_stories.typ | typst | === Open Stories <appendixOpenStories>
In den nachfolgenden Tabellen ist eine Übersicht zu finden, welche sortiert nach Epic ist.
#figure(
table(
columns: (auto, auto, auto, auto),
align: left,
[*Issue Key*], [*Summary*], [*Prio*], [*Epic*],
[DI-02],[Beispiel Story],[Lowest],[Beispiel Epic],
),
caption: "Übersicht der offenen Stories",
) |
|
https://github.com/sitandr/typst-examples-book | https://raw.githubusercontent.com/sitandr/typst-examples-book/main/src/basics/must_know/place.md | markdown | MIT License | # Placing, Moving, Scale & Hide
This is **a very important section** if you want to do arbitrary things with layout,
create custom elements and hacking a way around current Typst limitations.
TODO: WIP, add text and better examples
# Place
_Ignore layout_, just put some object somehow relative to parent and current position.
The placed object _will not_ affect layouting
> Link to [reference](https://typst.app/docs/reference/layout/place/)
```typ
#set page(height: 60pt)
Hello, world!
#place(
top + right, // place at the page right and top
square(
width: 20pt,
stroke: 2pt + blue
),
)
```
### Basic floating with place
```typ
#set page(height: 150pt)
#let note(where, body) = place(
center + where,
float: true,
clearance: 6pt,
rect(body),
)
#lorem(10)
#note(bottom)[Bottom 1]
#note(bottom)[Bottom 2]
#lorem(40)
#note(top)[Top]
#lorem(10)
```
### dx, dy
Manually change position by `(dx, dy)` relative to intended.
```typ
#set page(height: 100pt)
#for i in range(16) {
let amount = i * 4pt
place(center, dx: amount - 32pt, dy: amount)[A]
}
```
# Move
> Link to [reference](https://typst.app/docs/reference/layout/move/)
```typ
#rect(inset: 0pt, move(
dx: 6pt, dy: 6pt,
rect(
inset: 8pt,
fill: white,
stroke: black,
[Abra cadabra]
)
))
```
# Scale
Scale content _without affecting the layout_.
> Link to [reference](https://typst.app/docs/reference/layout/scale/)
```typ
#scale(x: -100%)[This is mirrored.]
```
```typ
A#box(scale(75%)[A])A \
B#box(scale(75%, origin: bottom + left)[B])B
```
# Hide
Don't show content, but leave empty space there.
> Link to [reference](https://typst.app/docs/reference/layout/hide/)
```typ
Hello Jane \
#hide[Hello] Joe
```
|
https://github.com/PgBiel/typst-tablex | https://raw.githubusercontent.com/PgBiel/typst-tablex/main/tablex-test.typ | typst | MIT License | #import "tablex.typ": *
*Test*
test
deeteeeeereeeedetteeeee
// vvvv causes the dreaded warning (alongside another table downwards)
#tablex(
columns: (auto, auto, auto), // rows: ((1em, 1em, 1em),) eeee
rows: (auto,),
column-gutter: 1fr,
row-gutter: none,
repeat-header: (3, 4),
header-hlines-have-priority: false,
align: (column, row) => {(top, center).at(calc-mod(row + column, 2))},
// fill: (column, row) => {(blue, red).at(calc-mod(row + column, 2))},
vlinex(), vlinex(), vlinex(), vlinex(),
hlinex(),
[*My*], colspanx(2)[*Headedr*], //
hlinex(start: 0, end: 1),
cellx(colspan: 2, rowspan: 2)[a], [b\ c],
hlinex(),
() , (), [cefdsrdeefffeerddeeeeeedeeeeeeerd],
hlinex(),
[a], [b], [xyz],
hlinex(end: 1),
[b],
hlinex(),
..range(0, 125).map(i => ([d], [#{i + 3}], [a],
hlinex())).flatten(),
[b], [c],
)
#tablex(
columns: 5,
rows: 1,
stroke: red + 2pt,
vlinex(), (), vlinex(), vlinex(), vlinex(), vlinex(),
hlinex(),
[abcdef], colspanx(3, rowspanx(2, [ee], fill: red), align: horizon), (), (), [c],
hlinex(stroke: blue),
[abcdef], (), (), (), [c],
hlinex(),
[aa], [b], [c], [b], cellx(inset: 2pt, align: center+horizon)[cdeecfeeeeeeeeeeeeeeeeeerdteeettetteeefdxeeeeeddeeeetec],
hlinex(),
// [abcdef], [a], [b],
// hlinex(),
)
#tablex(
columns: 4,
[a], [b], [c], [d],
hlinex(),
[a], colspanx(2, rowspanx(2)[b]), [d],
[a], (), (), [d],
[a], [b], [c], [d],
)
#tablex(
columns: (1fr, 1fr, 1fr, 1fr),
map-cells: cell => (..cell, content: cell.content + [adf]),
map-rows: (row, cells) => cells.map(c => if c == none { none } else { (..c, content: c.content + [#row]) }),
map-cols: (col, cells) => cells.map(c => if c == none { none } else { (..c, content: c.content + [#col]) }),
map-hlines: h => (..h, stroke: 5pt + (red, blue).at(calc-mod(h.y, 2))),
map-vlines: v => (..v, stroke: 5pt + (yellow, green.darken(50%)).at(calc-mod(v.x, 2))),
[a], [b], [c], [d],
hlinex(),
[a], colspanx(2, rowspanx(2)[b]), [d],
[a], (), (), [d],
[a], [b], [c], [de],
)
#tablex(
columns: (1em, 2em, auto, auto),
rows: (1em, 1em, auto),
[a], [b], [cd], [d],
hlinex(),
[a], colspanx(2, rowspanx(2)[bcccccccc\ c\ c\ c]), [d],
[a], (), (), [d],
[a], (x, y) => text(size: 7pt)[#(x, y)], [f], [dee],
[a], [b], [c], [dee],
)
eeeedreetetdeederfttddeerreddeeeteeeeeerettededteeedeceesdeedeeefteetdedeeesefdferreeedeefeettgederedaeeteeeeddrdfeeedeeffteeeeeeeeesedteteestderedeeeeefeeeeessdeeee
s
s
s
s
s
s
#tablex(
columns: (1em, 2em, auto, auto),
rows: (1em, 1em, auto),
gutter: 20pt,
align: center + horizon,
auto-lines: true,
map-hlines: h => (..h, stop-pre-gutter: default-if-auto(h.stop-pre-gutter, true)),
map-vlines: h => (..h, stop-pre-gutter: default-if-auto(h.stop-pre-gutter, true)),
[a], [b], [cd], [d],
hlinex(start: 0, end: 1),
hlinex(start: 4, end: 3),
hlinex(start: 1, end: none, gutter-restrict: top),
hlinex(start: 1, end: 2, stop-pre-gutter: false, gutter-restrict: bottom), hlinex(start: 2, end: 4, stop-pre-gutter: true, gutter-restrict: bottom),
[a],
vlinex(gutter-restrict: left),
vlinex(start: 0, end: 1, gutter-restrict: right),
vlinex(start: 3, end: 4, gutter-restrict: right),
vlinex(start: 4, end: 5, gutter-restrict: right),
vlinex(stop-pre-gutter: false, start: 1, end: 2, gutter-restrict: right),
vlinex(stop-pre-gutter: true, start: 2, end: 3, gutter-restrict: right),
colspanx(2, rowspanx(2)[bcccccccc\ c\ c\ c]), [d],
[a], (), (), [d],
[a], (x, y) => text(size: 7pt)[#(x, y)], [f], [dee],
[a], [b], [c], [dee],
)
== Examples from the docs
\
#tablex(
columns: 4,
align: center + horizon,
auto-vlines: false,
// indicate the first two rows are the header
// (in case we need to eventually
// enable repeating the header across pages)
header-rows: 2,
// color the last column's cells
// based on the written number
map-cells: cell => {
if cell.x == 3 and cell.y > 1 {
cell.content = {
let value = int(cell.content.text)
let text-color = if value < 10 {
red.lighten(30%)
} else if value < 15 {
yellow.darken(13%)
} else {
green
}
set text(text-color)
strong(cell.content)
}
}
cell
},
/* --- header --- */
rowspanx(2)[*Username*], colspanx(2)[*Data*], (), rowspanx(2)[*Score*],
(), [*Location*], [*Height*], (),
/* -------------- */
[John], [Second St.], [180 cm], [5],
[Wally], [Third Av.], [160 cm], [10],
[Jason], [Some St.], [150 cm], [15],
[Robert], [123 Av.], [190 cm], [20],
[Other], [Unknown St.], [170 cm], [25],
)
#tablex(
columns: (auto, 1em, 1fr, 1fr), // 3 columns
rows: auto, // at least 1 row of auto size,
fill: red,
align: center + horizon,
stroke: green,
[a], [b], [c], [d],
[e], [f], [g], [h],
[i], [j], [k], [l]
)
#repeat[a]
#place(bottom+right)[b]
#tablex(
columns: 3,
colspanx(2)[a], (), [b],
[c], rowspanx(2)[d], [ed],
[f], (), [g]
)
#tablex(
columns: 4,
auto-lines: false,
vlinex(), vlinex(), vlinex(), (), vlinex(),
colspanx(2)[a], (), [b], [J],
[c], rowspanx(2)[d], [e], [K],
[f], (), [g], [L],
)
#tablex(
columns: 4,
auto-vlines: false,
colspanx(2)[a], (), [b], [J],
[c], rowspanx(2)[d], [e], [K],
[f], (), [g], [L],
)
#block(breakable: false, gridx(
columns: 4,
(), (), vlinex(end: 2),
hlinex(stroke: yellow + 2pt),
colspanx(2)[a], (), [b], [J],
hlinex(start: 0, end: 1, stroke: yellow + 2pt),
hlinex(start: 1, end: 2, stroke: green + 2pt),
hlinex(start: 2, end: 3, stroke: red + 2pt),
hlinex(start: 3, end: 4, stroke: blue.lighten(50%) + 2pt),
[c], rowspanx(2)[d], [e], [K],
hlinex(start: 2),
[f], (), [g], [L],
))
#block(breakable: false, tablex(
columns: 3,
map-hlines: h => (..h, stroke: blue),
map-vlines: v => (..v, stroke: green + 2pt),
colspanx(2)[a], (), [b],
[c], rowspanx(2)[d], [ed],
[f], (), [g]
))
#block(breakable: false, tablex(
columns: 3,
fill: red,
align: right,
colspanx(2)[a], (), [beeee],
[c], rowspanx(2)[d], cellx(fill: blue, align: left)[e],
[f], (), [g],
// place this cell at the first column, seventh row
cellx(colspan: 3, align: center, x: 0, y: 6)[hi I'm down here]
))
#tablex(
columns: 4,
auto-vlines: true,
// make all cells italicized
map-cells: cell => {
(..cell, content: emph(cell.content))
},
// add some arbitrary content to entire rows
map-rows: (row, cells) => cells.map(c =>
if c == none {
c
} else {
(..c, content: [#c.content\ *R#row*])
}
),
// color cells based on their columns
// (using 'fill: (column, row) => color' also works
// for this particular purpose)
map-cols: (col, cells) => cells.map(c =>
if c == none {
c
} else {
(..c, fill: if col < 2 { blue } else { yellow })
}
),
colspanx(2)[a], (), [b], [J],
[c], rowspanx(2)[dd], [e], [K],
[f], (), [g], [L],
)
#tablex(
columns: 4,
fill: blue,
colspanx(2, rotate(30deg)[a]), rotate(30deg)[a], rotate(30deg)[a],rotate(30deg)[a],
)
#tablex(
columns: 4,
stroke: 5pt,
fill: blue,
(), vlinex(expand: (-2%, 4pt)),
[a], [b], [c], [d],
[e], [f], [g], [h]
)
#set page(width: 300pt)
#pagebreak()
#v(80%)
#tablex(
columns: 4,
align: center + horizon,
auto-vlines: false,
repeat-header: true,
header-rows: 2,
/* --- header --- */
rowspanx(2)[*Names*], colspanx(2)[*Properties*], (), rowspanx(2)[*Creators*],
(), [*Type*], [*Size*], (),
/* -------------- */
[Machine], [Steel], [5 $"cm"^3$], [John p& Kate],
[Frog], [Animal], [6 $"cm"^3$], [Robert],
[Frog], [Animal], [6 $"cm"^3$], [Robert],
[Frog], [Animal], [6 $"cm"^3$], [Robert],
[Frog], [Animal], [6 $"cm"^3$], [Robert],
[Frog], [Animal], [6 $"cm"^3$], [Robert],
[Frog], [Animal], [6 $"cm"^3$], [Robert],
[Frog], [Animal], [6 $"cm"^3$], [Rodbert],
)
#v(35em)
#set page(width: auto, height: auto)
*Auto page tests (infinite dimensions):*
#table(
columns: 3,
[a], [b], [c],
[d], [e], [f],
[g], [h], [i],
[f], [j], [e\ b\ c\ d],
)
#tablex(
columns: 3,
[a], [b], [c],
[d], [e], [f],
[g], [h], [i],
[f], [j], [e\ b\ c\ d],
)
#table(
columns: (99%, auto),
[a], [b],
[c], [d]
)
#tablex(
columns: (99%, auto),
[a], [b],
[c], [d]
)
#table(
columns: (auto, 1fr, 1fr),
[a], [b], [c],
[c], [d], [e]
)
#tablex(
columns: (auto, 1fr, 1fr),
[a], [b], [c],
[c], [d], [e]
)
#table(
columns: 4,
gutter: 10pt,
[a], [b], [c], [d],
[a], [b], [c], [d],
[a], [b], [c], [d],
[a], [b], [c], [d],
)
// vvv causes the dreaded warning (alongside the first table in the file)
#tablex(
columns: 4,
gutter: 10pt,
[a], [b], [c], [d],
[a], [b], [c], [d],
[a], [b], [c], [d],
[a], [b], [c], [d],
)
#set page(width: 300pt, height: 1000pt)
#tablex(
columns: (1fr, 1fr, 1fr),
[a], [b], [c]
)
#table(
columns: (1fr, 1fr, 1fr),
[a], [b], [c]
)
#tablex(
columns: (10%, 10%, 10%, 10%, 10%),
// map-hlines: h => (..h, stop-pre-gutter: default-if-auto(h.stop-pre-gutter, true)),
// map-vlines: v => (..v, stop-pre-gutter: default-if-auto(v.stop-pre-gutter, true)),
gutter: 15pt,
[a], [b], [c], [d], [e],
hlinex(stroke: blue),
[f], rowspanx(2, colspanx(2)[ggggoprdeetet\ eeeeeee]), (), [i], [j],
[k], (), (), [n], [o],
[p], [q], [r], [s], [t]
)
#tablex(
columns: (auto, 1fr),
rowspanx(2, [a\ a\ a\ a\ a]), "dfjasdfjdaskfjdsaklfj", "height should be correct here"
)
This table should be contained within the page's width:
#tablex(
columns: (auto, auto),
[#lorem(40)], [#lorem(100)]
)
Accept array of column alignments:
#block(breakable: false, tablex(
columns: 5,
align: (right + top, center + bottom, left + horizon),
[a], [b], [d], [e], [f],
[cccc], [cccfdd], [esdfsd], [ffeff\ erfad], [adspfp]
))
Empty array inherits from outside:
#block(breakable: false, tablex(
columns: 5,
align: (),
[a], [b], [d], [e], [f],
[cccc], [cccfdd], [esdfsd], [ffeff\ erfad], [adspfp]
))
Accept array for fill:
#tablex(
columns: 5,
fill: (red, blue, green),
[a], [b], [c], [d], [e],
[dddd], [eeee], [ffff], [ggggg], [hhhhhh]
)
Empty fill array is no-op:
#tablex(
columns: 5,
fill: (),
[a], [b], [c], [d], [e],
[dddd], [eeee], [ffff], [ggggg], [hhhhhh]
)
Align and fill function tests:
#tablex(
columns: 5,
align: (column, row) => (
(top, bottom).at(row)
+ (left, right).at(calc-mod(column, 2))
),
fill: (column, row) => (red, blue).at(row).lighten((50%, 10%).at(calc-mod(column, 2))),
[a\ b], [b], [c], [d], [e],
[dddd\ eapdsfp], [eeee\ eapdlf], [ffff], [ggggg], [hhhhhh]
)
Test division by zero bug:
#tablex(
columns: 3,
[Name],[Entität],[Eigenschaft],
[GammaTaurus],[ThisIsASuperlongSymbolicName which is similar important as Supercalifragilistic],[],
)
Test superfluous row bug:
#tablex(
columns: 3,
[a],
cellx(y: 2)[a]
)
Test gutter restrict top:
#tablex(
columns: 3,
auto-lines: false,
row-gutter: 5pt,
[a], [b], [c],
hlinex(gutter-restrict: top),
hlinex(gutter-restrict: bottom),
[d], [e], [f]
)
Test gutter restrict without gutter:
#tablex(
columns: 3,
auto-lines: false,
[a], [b], [c],
hlinex(gutter-restrict: top),
[e], [f], [g],
hlinex(gutter-restrict: bottom),
[d], vlinex(gutter-restrict: left), [e], vlinex(gutter-restrict: right), [f]
)
#pagebreak(weak: true)
#v(80%)
Test gutter split between pages:
#tablex(
columns: 3,
auto-vlines: false,
row-gutter: 5pt,
[a], [b], [c],
[a], [b], [c],
[a], [b], [c],
[a], [b], [c],
[a], [b], [c],
[a], [b], [c],
[a], [b], [c],
hlinex(stroke: blue),
[a], [b], [c],
[a], [b], [c],
)
Small gutter test:
#tablex(
columns: 4,
gutter: 10pt,
[a], [b], [c], [d],
[a], [b], [c], [d],
[a], [b], [c], [d],
[a], [b], [c], [d],
)
Test fractional columns in an auto-sized block:
#block(tablex(
columns: (auto, 1fr, 1fr),
[a], [b], [c],
[d], [e], [f],
[g], [h], [i]
))
*Using the examples from issue \#44:*
1.
#table(columns: 1fr, [1A. table])
#tablex(columns: 1fr, [1B. tablex])
2.
#block(table(columns: 1fr, [2A. table plain block]))
#block(tablex(columns: 1fr, [2B. tablex plain block]))
3.
#block(breakable: true, table(columns: 1fr, [3A. table breakable: true]))
#block(breakable: true, tablex(columns: 1fr, [3B. tablex breakable: true]))
4.
#block(breakable: false, table(columns: 1fr, [4A. table breakable: false]))
#block(breakable: false, tablex(columns: 1fr, [4B. tablex breakable: false]))
*Nested tables from issue \#41:*
- Triple-nested tables.
#tablex(
tablex(
tablex(
lorem(10)
)
)
)
- Quadruple-nested tables.
#tablex(
tablex(
tablex(
tablex(
lorem(20)
)
)
)
)
*Nested tables from issue \#28:*
#let mycell = [
#tablex(
columns: (1fr, 1fr),
[A],[A]
)
]
= table inside a table
#tablex(
columns: (1fr, 1fr),
mycell, mycell
)
= following table fails
*Problem/Observation*: just one column "C"
*Expected Outcome*: Two columns
#tablex(
columns: (1fr, 1fr),
[C],[C]
)
*Exotic strokes from issue \#49:*
#tablex(
stroke: 1em,
[C], [C]
)
// Uncomment after minimum typst version is raised enough for this
// #let s = rect(stroke: (thickness: 1em, miter-limit: 5.0)).stroke
// #tablex(
// stroke: s,
// [C], [C]
// )
*Stroke parsing regression from issue \#55:*
Red stroke:
#let s = rect(stroke: red).stroke
#tablex(
stroke: s,
[a]
)
Thick stroke with a decimal point:
#tablex(columns: 2, stroke: 5.1pt + black)[a][b]
Combining em and pt:
#tablex(columns: 2, stroke: (2.5pt + 0.75em) + black)[a][b]
Combining em and pt (with a stroke object):
#let s = rect(stroke: (2.5pt + 0.75em) + black).stroke
#tablex(
columns: 2,
stroke: s,
[a], [b]
)
*Dictionary insets from issue \#54:*
#tablex(
columns: 3,
inset: (left: 20pt, rest: 10pt),
[A], [B], [C]
)
#tablex(
columns: 2,
inset: (
left: 20pt,
right: 5pt,
top: 10pt,
bottom: 3pt,
),
[A],
[B],
)
#tablex(
columns: 2,
[a], [b],
[c], cellx(inset: (left: 2pt, right: 5pt, top: 10pt, bottom: 1pt))[d],
cellx(inset: (left: 5pt, rest: 10pt))[e], [f]
)
*RTL tables from issue \#58:*
#[
- Simple
#let simple(rtl) = tablex(
columns: 3,
rtl: rtl,
[a], [b], [c],
[d], [e], [f],
[g], [h], [i]
)
#stack(dir: ltr, simple(false), 1em, $->$, 1em, simple(true))
- Colspan, rowspan
#let colspanrowspan(rtl) = tablex(
columns: 3,
rtl: rtl,
[a], colspanx(2)[d], (),
[d], [e], rowspanx(2)[f],
[g], [h], (),
)
#stack(dir: ltr, colspanrowspan(false), 1em, $->$, 1em, colspanrowspan(true))
- No vertical lines
#let novertlines(rtl) = tablex(
columns: 3,
rtl: rtl,
auto-vlines: false,
stroke: red,
[a], colspanx(2)[d], (),
[b], [b], [b],
[d], [e], rowspanx(2)[f],
[g], [h], (),
)
#stack(dir: ltr, novertlines(false), 1em, $->$, 1em, novertlines(true))
- Line customization
#let linecustom(rtl) = tablex(
columns: 3,
rtl: rtl,
auto-lines: false,
(), vlinex(end: 1, stroke: blue),
[a], colspanx(2)[d], (),
[b], [b], [b],
hlinex(end: 2, stroke: red),
[d], [e], rowspanx(2)[f],
[g], [h], (),
)
#stack(dir: ltr, linecustom(false), 1em, $->$, 1em, linecustom(true))
- Alignment and fill
#set text(dir: rtl)
#let alignfill(rtl) = tablex(
columns: 3,
rtl: rtl,
align: (end, start, end),
fill: (x, y) => (red, green, blue, yellow).at(y).darken(20% * x),
[aaaa], colspanx(2)[ddddd], (),
[b], [bdd], [bd],
[d], [e], rowspanx(2)[f],
[g], [h], (),
)
#stack(dir: ltr, alignfill(false), 1em, $->$, 1em, alignfill(true))
- Map cells, map rows, map cols
#let mapstuff(rtl) = tablex(
columns: 3,
rtl: rtl,
align: (end, start, end),
fill: (x, y) => (red, green, blue, yellow).at(y).darken(20% * x),
map-rows: (y, cells) => {
cells.map(cell => {
if cell == none { return none }
cell.content = [#cell.content | y = #y]
cell
})
},
map-cols: (x, cells) => {
cells.map(cell => {
if cell == none { return none }
cell.content = [#cell.content | x = #x]
cell
})
},
map-cells: cell => {
cell.content = [#cell.content | HI]
cell
},
[aaaa], colspanx(2)[ddddd], (),
[b], [bdd], [bd],
[d], [e], rowspanx(2)[f],
[g], [h], (),
)
#stack(dir: ttb, mapstuff(false), 1em, $arrow.b$, 1em, mapstuff(true))
]
*Lines in tables from issue \#80*
#table(
columns: 2,
[A #box(line(length: 50pt)) B], [A #line(length: 50pt) B],
[C], [D],
style(styles => {
measure(line(length: 40pt), styles)
}),
[E]
)
#tablex(
columns: 2,
[A #box(line(length: 50pt)) B], [A #line(length: 50pt) B],
[C], [D],
style(styles => {
measure(line(length: 40pt), styles)
}),
[E]
)
*Length to pt conversion*
#let convert-length-to-pt-test(
len, expected,
page-size: 100pt, // Set 1% to 1pt
frac-amount: 10, // Set 1fr to 1pt
frac-total: 10pt,
) = {
set text(size: 1pt) // Set 1em to 1pt
style(styles => {
let actual = convert-length-to-pt(
len,
styles: styles,
page-size: page-size,
frac-amount: frac-amount,
frac-total: frac-total,
)
assert(type(actual) == _length-type)
assert(expected == actual)
})
}
// `length` tests
#convert-length-to-pt-test(0pt, 0pt)
#convert-length-to-pt-test(1pt, 1pt)
#convert-length-to-pt-test(1em, 1pt)
#convert-length-to-pt-test(-1pt, -1pt)
#convert-length-to-pt-test(-1em, -1pt)
#convert-length-to-pt-test(0.005pt, 0.005pt)
#convert-length-to-pt-test(0.005em, 0.005pt)
#convert-length-to-pt-test(-0.005pt, -0.005pt)
#convert-length-to-pt-test(-0.005em, -0.005pt)
#convert-length-to-pt-test(0.005pt + 0.005em, 0.01pt)
#convert-length-to-pt-test(0.005pt - 0.005em, 0pt)
#convert-length-to-pt-test(-0.005pt + 0.005em, 0pt)
#convert-length-to-pt-test(-0.005pt - 0.005em, -0.01pt)
// `ratio` tests
#convert-length-to-pt-test(1%, 1pt)
#convert-length-to-pt-test(-1%, -1pt)
#convert-length-to-pt-test(0.5%, 0.5pt)
#convert-length-to-pt-test(-0.5%, -0.5pt)
// `fraction` tests
#convert-length-to-pt-test(1fr, 1pt)
#convert-length-to-pt-test(-1fr, -1pt)
#convert-length-to-pt-test(0.5fr, 0.5pt)
#convert-length-to-pt-test(-0.5fr, -0.5pt)
// `relative` tests
#convert-length-to-pt-test(0% + 0pt + 0em, 0pt)
#convert-length-to-pt-test(0% + 0pt + 1em, 1pt)
#convert-length-to-pt-test(0% + 1pt + 0em, 1pt)
#convert-length-to-pt-test(0% + 1pt + 1em, 2pt)
#convert-length-to-pt-test(1% + 0pt + 0em, 1pt)
#convert-length-to-pt-test(1% + 0pt + 1em, 2pt)
#convert-length-to-pt-test(1% + 1pt + 0em, 2pt)
#convert-length-to-pt-test(1% + 1pt + 1em, 3pt)
#convert-length-to-pt-test(0% + 0pt + 0.005em, 0.005pt)
#convert-length-to-pt-test(0% + 0.005pt + 0em, 0.005pt)
#convert-length-to-pt-test(0% + 0.005pt + 0.005em, 0.01pt)
#convert-length-to-pt-test(0.005% + 0pt + 0em, 0.005pt)
#convert-length-to-pt-test(0.005% + 0pt + 0.005em, 0.01pt)
#convert-length-to-pt-test(0.005% + 0.005pt + 0em, 0.01pt)
#convert-length-to-pt-test(0.005% + 0.005pt + 0.005em, 0.015pt)
#convert-length-to-pt-test(0% + 0pt - 0.005em, -0.005pt)
#convert-length-to-pt-test(0% - 0.005pt + 0em, -0.005pt)
#convert-length-to-pt-test(0% - 0.005pt - 0.005em, -0.01pt)
#convert-length-to-pt-test(-0.005% + 0pt + 0em, -0.005pt)
#convert-length-to-pt-test(-0.005% + 0pt - 0.005em, -0.01pt)
#convert-length-to-pt-test(-0.005% - 0.005pt + 0em, -0.01pt)
#convert-length-to-pt-test(-0.005% - 0.005pt - 0.005em, -0.015pt)
// Stroke thickness calculation
#let stroke-thickness-test(
value, expected,
compare-repr: false,
) = {
set text(size: 1pt) // Set 1em to 1pt
style(styles => {
let actual = stroke-len(
value,
styles: styles,
)
assert(type(actual) == _length-type)
// Re-assign so we can modify the variable
let expected = expected
if compare-repr {
expected = repr(expected)
actual = repr(actual)
}
assert(expected == actual, message: "Expected " + repr(expected) + ", found " + repr(actual))
})
}
#stroke-thickness-test(2pt, 2pt)
#stroke-thickness-test(2pt + 1em, 3pt)
#stroke-thickness-test(2pt + red, 2pt)
#stroke-thickness-test(2pt + 2em + red, 4pt)
#stroke-thickness-test(2.2pt - 2.2em + red, 0pt)
#stroke-thickness-test(0.005em + black, 0.005pt)
#stroke-thickness-test(red, 1pt)
#stroke-thickness-test((does-not-specify-thickness: 5), 1pt)
#stroke-thickness-test((thickness: 5pt + 2em, what: 55%), 7pt)
#stroke-thickness-test((thickness: 5pt + 2.005em, what: 55%), 7.005pt)
#stroke-thickness-test(rect(stroke: 2.002pt - 3.003em + red).stroke, -1.001pt, compare-repr: true)
*Line expansion - issue \#74:*
#let wrap-for-linex-expansion-test(tabx) = {
set text(size: 1pt) // Set 1em to 1pt
box(
width: 100pt, // Set 1% to 1pt
height: 100pt,
tabx
)
}
- Positive single-cell hlinex expansion
#wrap-for-linex-expansion-test(
tablex(
columns: 3pt,
auto-lines: false,
hlinex(),
[],
hlinex(expand: 3pt),
[],
hlinex(expand: 3em),
[],
hlinex(expand: 3%),
[],
hlinex(expand: 1% + 1pt + 1em),
)
)
- Positive multi-cell hlinex expansion
#wrap-for-linex-expansion-test(
tablex(
columns: (1pt, 1pt, 1pt),
auto-lines: false,
hlinex(),
[], [], [],
hlinex(expand: 3pt),
[], [], [],
hlinex(expand: 3em),
[], [], [],
hlinex(expand: 3%),
[], [], [],
hlinex(expand: 1% + 1pt + 1em),
)
)
- Negative single-cell hlinex expansion
#wrap-for-linex-expansion-test(
tablex(
columns: 15pt,
auto-lines: false,
hlinex(),
[],
hlinex(expand: -6pt),
[],
hlinex(expand: -6em),
[],
hlinex(expand: -6%),
[],
hlinex(expand: -(2% + 2pt + 2em)),
)
)
// TODO: currently does not work as intended (https://github.com/PgBiel/typst-tablex/issues/85)
- Negative multi-cell hlinex expansion
#wrap-for-linex-expansion-test(
tablex(
columns: (5pt, 5pt, 5pt),
auto-lines: false,
hlinex(),
[], [], [],
hlinex(expand: -6pt),
[], [], [],
hlinex(expand: -6em),
[], [], [],
hlinex(expand: -6%),
[], [], [],
hlinex(expand: -(2% + 2pt + 2em)),
)
)
- Positive single-cell vlinex expansion
#wrap-for-linex-expansion-test(
tablex(
columns: 5,
rows: 3pt,
auto-lines: false,
vlinex(),
vlinex(expand: 3pt),
vlinex(expand: 3em),
vlinex(expand: 3%),
vlinex(expand: 1% + 1pt + 1em),
)
)
- Positive multi-cell vlinex expansion
#wrap-for-linex-expansion-test(
tablex(
columns: 5,
rows: (1pt, 1pt, 1pt),
auto-lines: false,
vlinex(),
vlinex(expand: 3pt),
vlinex(expand: 3em),
vlinex(expand: 3%),
vlinex(expand: 1% + 1pt + 1em),
)
)
- Negative single-cell vlinex expansion
#wrap-for-linex-expansion-test(
tablex(
columns: 5,
rows: 15pt,
auto-lines: false,
vlinex(),
vlinex(expand: -6pt),
vlinex(expand: -6em),
vlinex(expand: -6%),
vlinex(expand: -(2% + 2pt + 2em)),
)
)
// TODO: currently does not work as intended (https://github.com/PgBiel/typst-tablex/issues/85)
- Negative multi-cell vlinex expansion
#wrap-for-linex-expansion-test(
tablex(
columns: 5,
rows: (5pt, 5pt, 5pt),
auto-lines: false,
vlinex(),
vlinex(expand: -6pt),
vlinex(expand: -6em),
vlinex(expand: -6%),
vlinex(expand: -(2% + 2pt + 2em)),
)
)
*Full-width rowspans displayed with the wrong height (Issue \#105)*
#tablex(
columns: (auto, auto, auto, auto),
colspanx(4, rowspanx(3)[ONE]),
[TWO], [THREE], [FOUR], [FIVE],
)
#block(breakable: false)[
a
#tablex(
columns: 3,
colspanx(3, rowspanx(2)[a])
)
b
]
*More overlapping rowspans (Issue \#82)*
#tablex(
auto-lines: false,
stroke: 1pt,
columns: (auto,auto,auto,auto),
align:center,
//hlinex(),
//vlinex(), vlinex(), vlinex(),vlinex(),
[Name], [He],[Rack],[Beschreibung],
hlinex(),
cellx(rowspan:2,align:center)["mt01"], cellx(fill: rgb("#b9edffff"), align: left,rowspan:2)[42],
cellx(rowspan:2,align:center)["WAT"],
//hlinex(),
cellx(rowspan:2,align:center)["Löschgasflasche"],
cellx(rowspan:2,align:center)["mt2"], cellx(fill: rgb("#b9edffff"), align: left,rowspan:2)[41],
cellx(rowspan:2,align:center)["WAT"],"test",
(""),"","","","",
cellx(rowspan:2,align:center)["mt3"], cellx(fill: rgb("#b9edffff"), align: left,rowspan:2)[40],
cellx(rowspan:2,align:center)["WAT"],"test",
"","","","","",
cellx(rowspan:2,align:center)["mt3"], cellx(fill: rgb("#b9edffff"), align: left,rowspan:2)[40],
cellx(rowspan:2,align:center)["WAT"],"test",
"","","","","",
)
*Extra rows should inherit the last row size (Issue \#97)*
#tablex(
rows: 5pt,
cellx(x: 0, y: 1)[a\ a\ a\ a]
)
#v(4em)
#[
#tablex(
align: center + horizon,
rows: 5mm,
columns: (7mm, 10mm, 23mm, 15mm, 10mm, 70mm, 5mm, 5mm, 5mm, 5mm, 12mm, 18mm),
..range(5), cellx(rowspan: 3, colspan: 7)[],
..range(5),
..range(5),
..range(5), rowspanx(5)[], colspanx(3)[], colspanx(2)[], [],
..range(5), rowspanx(3)[], rowspanx(3)[], rowspanx(3)[], cellx(rowspan: 3, colspan: 2)[], rowspanx(3)[],
colspanx(2)[], ..range(3),
colspanx(2)[], ..range(3),
colspanx(2)[], ..range(3), colspanx(4)[], colspanx(2)[],
colspanx(2)[], ..range(3), rowspanx(3)[], cellx(rowspan: 3, colspan: 6)[],
colspanx(2)[], ..range(3),
colspanx(2)[], ..range(3),
)
#tablex(
align: center + horizon,
rows: 5mm,
columns: (7mm, 10mm, 23mm, 15mm, 10mm, 70mm, 5mm, 5mm, 5mm, 5mm, 12mm, 18mm),
..range(5), cellx(x: 5, rowspan: 3, colspan: 7)[],
..range(5),
..range(5),
..range(5), rowspanx(5)[], colspanx(3)[], colspanx(2)[], [],
..range(5), rowspanx(3)[], rowspanx(3)[], rowspanx(3)[], cellx(rowspan: 3, colspan: 2)[], rowspanx(3)[],
colspanx(2)[], ..range(3),
colspanx(2)[], ..range(3),
colspanx(2)[], ..range(3), colspanx(4)[], colspanx(2)[],
colspanx(2)[], ..range(3), rowspanx(3)[], cellx(rowspan: 3, colspan: 6)[],
colspanx(2)[], ..range(3),
colspanx(2)[], ..range(3),
)
#tablex(
align: center + horizon,
rows: 5mm,
columns: (7mm, 10mm, 23mm, 15mm, 10mm, 70mm, 5mm, 5mm, 5mm, 5mm, 12mm, 18mm),
cellx(x: 5, rowspan: 3, colspan: 7)[],
..range(5),
..range(5),
..range(5), rowspanx(5)[], colspanx(3)[], colspanx(2)[], [],
..range(5), rowspanx(3)[], rowspanx(3)[], rowspanx(3)[], cellx(rowspan: 3, colspan: 2)[], rowspanx(3)[],
colspanx(2)[], ..range(3),
colspanx(2)[], ..range(3),
colspanx(2)[], ..range(3), colspanx(4)[], colspanx(2)[],
colspanx(2)[], ..range(3), rowspanx(3)[], cellx(rowspan: 3, colspan: 6)[],
colspanx(2)[], ..range(3),
colspanx(2)[], ..range(3),
)
]
#set page("a4")
*Overflowing cells (Issues \#48 and \#75)*
#tablex(
columns: 3,
[a: #lorem(7)], [b: $T h i s I s A L o n g A n d R a n d o m M a t h E p r e s s i o n$], [c]
)
#tablex(columns: (auto, auto, auto, auto),
[lorem_ipsum_dolor_sit_amet], [lorem], [lorem_ipsum_dolor_sit_amet_consectetur_adipisici], [lorem],
)
*Rowspans spanning 1fr and auto with 'fit-spans'*
#let unbreakable-tablex(..args) = block(breakable: false, tablex(..args))
- Normal sizes:
#unbreakable-tablex(
columns: (auto, auto, 1fr, 1fr),
[A], [BC], [D], [E],
[A], [BC], [D], [E],
[A], [BC], [D], [E],
[A], [BC], [D], [E]
)
- With colspan over auto and 1fr (but not all fractional columns):
#unbreakable-tablex(
columns: (auto, auto, 1fr, 1fr),
colspanx(3)[Hello world! Hello!], [E],
[A], [BC], [D], [E],
[A], [BC], [D], [E],
[A], [BC], [D], [E],
[A], [BC], [D], [E]
)
- Using `fit-spans`, column sizes should be identical to the first table (in all three below):
#unbreakable-tablex(
columns: (auto, auto, 1fr, 1fr),
fit-spans: (x: true),
colspanx(3)[Hello world! Hello!], [E],
[A], [BC], [D], [E],
[A], [BC], [D], [E],
[A], [BC], [D], [E],
[A], [BC], [D], [E]
)
#unbreakable-tablex(
columns: (auto, auto, 1fr, 1fr),
fit-spans: true,
colspanx(3)[Hello world! Hello!], [E],
[A], [BC], [D], [E],
[A], [BC], [D], [E],
[A], [BC], [D], [E],
[A], [BC], [D], [E]
)
#unbreakable-tablex(
columns: (auto, auto, 1fr, 1fr),
colspanx(3, fit-spans: (x: true))[Hello world! Hello!], [E],
[A], [BC], [D], [E],
[A], [BC], [D], [E],
[A], [BC], [D], [E],
[A], [BC], [D], [E]
)
*Other `fit-spans` tests*
1. Columns
#unbreakable-tablex(
columns: 4,
[A], [B], [C], [D],
)
#unbreakable-tablex(
columns: 4,
colspanx(4, lorem(20)),
[A], [B], [C], [D],
)
#unbreakable-tablex(
columns: 4,
fit-spans: (x: true),
colspanx(4, lorem(20)),
[A], [B], [C], [D],
)
#unbreakable-tablex(
columns: 4,
fit-spans: true,
colspanx(4, lorem(20)),
[A], [B], [C], [D],
)
2. Rows
#unbreakable-tablex(
columns: (auto, 4em),
[A], [B],
[C], [B],
[D], [E]
)
#unbreakable-tablex(
columns: (auto, 4em),
[A], rowspanx(2, line(start: (0pt, 0pt), end: (0pt, 6em))),
[C], (),
[D], [E]
)
#unbreakable-tablex(
columns: (auto, 4em),
fit-spans: (y: true),
[A], rowspanx(2, line(start: (0pt, 0pt), end: (0pt, 6em))),
[C], (),
[D], [E #v(2em)]
)
#unbreakable-tablex(
columns: (auto, 4em),
fit-spans: true,
[A], rowspanx(2, line(start: (0pt, 0pt), end: (0pt, 6em))),
[C], (),
[D], [E #v(2em)]
)
*Rowspans spanning all fractional columns and auto (Issues \#56 and \#78)*
_For issue \#78_
- Columns should have the same size in all samples below:
#unbreakable-tablex(
columns: (1fr, 1fr, auto, auto, auto),
[a], [b], [c], [d], [e],
cellx(colspan: 5)[#lorem(5)],
[a], [b], [c], [d], [e],
cellx(colspan: 2)[#lorem(10)], none, none, none,
[a], [b], [c], [d], [e],
)
#unbreakable-tablex(
columns: (1fr, 1fr, auto, auto, auto),
[a], [b], [c], [d], [e],
cellx(colspan: 5)[#lorem(5)],
[a], [b], [c], [d], [e],
cellx(colspan: 2)[#lorem(10)], none, none, none,
[a], [b], [c], [d], [e],
cellx(colspan: 3)[#lorem(15)], none, none,
)
#unbreakable-tablex(
columns: (1fr, 1fr, auto, auto, auto),
fit-spans: (x: true),
[a], [b], [c], [d], [e],
cellx(colspan: 5)[#lorem(5)],
[a], [b], [c], [d], [e],
cellx(colspan: 2)[#lorem(10)], none, none, none,
[a], [b], [c], [d], [e],
cellx(colspan: 3)[#lorem(15)], none, none,
)
_For issue \#56_
- Columns should have the same size in all samples below:
#unbreakable-tablex(
columns: (auto, auto, 1fr),
[A], [BC], [D],
[A], [BC], [D],
[A], [BC], [D],
[A], [BC], [D]
)
#unbreakable-tablex(
columns: (auto, auto, 1fr),
colspanx(3)[Hello world! Hello!],
[A], [BC], [D],
[A], [BC], [D],
[A], [BC], [D],
[A], [BC], [D]
)
#unbreakable-tablex(
columns: (auto, auto, 1fr),
fit-spans: (x: true),
colspanx(3)[Hello world! Hello!],
[A], [BC], [D],
[A], [BC], [D],
[A], [BC], [D],
[A], [BC], [D]
)
#set page(height: auto, width: auto)
Ensure the heuristic doesn't apply on auto width pages.
Second table should have a longer second column.
#tablex(
columns: (auto, auto, 1fr),
[A], [BC], [D],
[A], [BC], [D],
[A], [BC], [D],
[A], [BC], [D]
)
#tablex(
columns: (auto, auto, 1fr),
colspanx(3)[Hello world! Hello!],
[A], [BC], [D],
[A], [BC], [D],
[A], [BC], [D],
[A], [BC], [D]
)
#tablex(
columns: (auto, auto, 1fr),
fit-spans: (x: true),
colspanx(3)[Hello world! Hello!],
[A], [BC], [D],
[A], [BC], [D],
[A], [BC], [D],
[A], [BC], [D]
)
|
https://github.com/VisualFP/docs | https://raw.githubusercontent.com/VisualFP/docs/main/SA/project_documentation/content/meeting_minutes/week_02.typ | typst | #import "../../../acronyms.typ": *
= Project Meeting 26.09.2023 08:15 - 09:00 (MS Teams)
== Participants
- Prof. Dr. <NAME>
- <NAME>
- <NAME>
== Agenda
- Presentation of the rough project plan
- Presentation of researched tools (Snap!, Eros, Flo, Enso)
- Questions:
- Is there a deadline for signing the official documents for #ac("SA")? -> end of project
- Do we need to create meeting minutes? -> Yes, very briefly document important decisions
- Input from advisor:
- Maybe hold presentation for #ac("SA") -> decide at about half-time
- Tools/Projects to look at:
- Doctor Racket
- Wingman for Haskell
- Dependently-typed languages
- Maybe we can profit from synergies with projects from master students he advises
- Define three scenarios to test our considered designs with (small programs using easy, intermediate, and advanced #ac("FP") concept)
|
|
https://github.com/jamesrswift/pixel-pipeline | https://raw.githubusercontent.com/jamesrswift/pixel-pipeline/main/src/layers/debug.typ | typst | The Unlicense | #import "../pipeline/primitives.typ"
#let validation(input, output, next) = {
output += input.map(it=>{
if type(it) != dictionary {return "Unexpected command structure " + repr(it)}
}).filter(it=>it!=none)
next(input, output)
}
#let input-assembler(input, output, next)={
next(input, output)
}
#let compute(input, output, next)={
next(input, output)
}
#let vertex(input, output, next)={
next(input, output)
}
#let render(input, output, next)={
next(input, input)
}
#let layer() = (:
validation: validation,
input-assembler: input-assembler,
compute: compute,
vertex: vertex,
render: render,
) |
https://github.com/Myriad-Dreamin/typst.ts | https://raw.githubusercontent.com/Myriad-Dreamin/typst.ts/main/fuzzers/corpora/layout/place-nested_02.typ | typst | Apache License 2.0 |
#import "/contrib/templates/std-tests/preset.typ": *
#show: test-page
#box(fill: aqua)[
#place(bottom + right)[Hi]
Hello World \
How are \
you?
]
|
https://github.com/DashieTM/ost-5semester | https://raw.githubusercontent.com/DashieTM/ost-5semester/main/web3/weeks/week9.typ | typst | #import "../../utils.typ": *
#align(
center,
[#image("../../Screenshots/2023_11_16_03_56_28.png", width: 80%)],
)
#subsection("Base href")
- uses history.pushState() -> lmao
- HTML5 style navigation
- can be overriden with \#navigation
- Register provider for LocationStrategy as HashLocationStrategy class
- or configure RouterModule with useHash: RouterModule.forRoot(routes, { useHash:
true })
- HTML needs a base ref tag in order to access relative file paths:
```html
<html>
<head>
<base href="/">
</head>
</html>
```
- or provide the base href in angular ts:
```ts
providers: [{provide: APP_BASE_HREF, useValue : '/' }]
```
#subsection("ForRoot")
With the forRoot directive, the given routes and the router service exist in one
singleton instance of the router. ```ts
@NgModule({
imports: [ RouterModule.forRoot(appRoutes) ],
exports: [ RouterModule ]
})
export class AppRoutingModule {}
```
#subsection("ForChild")
With the forChild directive, the given routes exist on this module, but not the
router service itself -> e.g. that needs to be done by the main forRoot router.
```ts
@NgModule({
imports: [ RouterModule.forChild(welcomeRoutes) ],
exports: [ RouterModule ]
})
export class WelcomeRoutingModule {}
```
#subsection("Routing example")
#align(
center,
[#image("../../Screenshots/2023_11_16_04_17_28.png", width: 80%)],
)
#subsection("Router Outlet")
- RouterOutlet is a directive from the Router module
- Defines where the router should display the views
- Can also be specified within a child component
```HTML
<h1>WE3 - App Component</h1>
<nav>
<a routerLink="/dashboard">Open Dashboard</a>
</nav>
<router-outlet></router-outlet>
```
#align(
center,
[#image("../../Screenshots/2023_11_16_04_26_41.png", width: 80%)],
)
#subsection("Routing examples")
```ts
const appRoutes: Routes = [
{ path: 'crisis-center', component: CrisisListComponent },
// Maps the /crisis-center path to the CrisisListComponent
{ path: 'hero/:id', component: HeroDetailComponent },
// Maps the /hero/42 path to the HeroDetailComponent
// "42" is variable, specifies the value of the id parameter; can be read out by code
{ path: '', redirectTo: '/heroes', pathMatch: 'full' },
// Redirects the default route (/) path to the /heroes path. '' must be exactly matched.
{ path: '**', component: PageNotFoundComponent }
// Specifies a wildcard route (two asterisks) which matches every URL.
// Used if the requested URL doesn't match any of the defined routes.
];
```
- first route that matches wins -> enum like
- wildcard route on the last entry -> handle all routes that don't match otherwise
- guards for route activation -> authentication
- pathMatch: 'full' -> whether or not the path should exactly be matched and
consumed
- aka no further matching -> don't match on wildcard
#subsection("Child Route Example")
```ts
const routes: Routes = [
{ path: 'samples', component: SamplesComponent,
// Maps /samples path to the SamplesComponent . This component also
// contains a router outlet.
// http://localhost:4200/samples
children: [
{ path: ':id', component: SamplesDetailComponent },
// Defines the router outlet of SamplesComponent should be filled with the
// SamplesDetailComponent if an id has specified.
// http://localhost:4200/samples/42
{ path: '', component: SamplesListComponent }
// Defines the router outlet of SamplesComponent should be filled with the
// SamplesListComponent if no sub-path given.
// http://localhost:4200/samples/
]
}
];
```
#align(
center,
[#image("../../Screenshots/2023_11_16_04_59_33.png", width: 90%)],
)
#subsubsection("Lazy Routes")
The issue with lazy routes is that if you use lazy components, you need to
define your models in routes like this(see below), as the components would
otherwise not be ready for the router on application start. (The solution is to
just use a function lmao)\
```ts
const routes: Routes = [
{ path: 'samples', component: SamplesComponent },
{
path: 'config',
loadChildren: () => import('./cfg/cfg.module').then(m => m.CfgModule),
canLoad: [ AuthGuard ]
// authentication thing
}
];
```
#section("Module Imports")
#subsection("Default Import")
- Imports all Components, Pipes, Directives from the given ForeignModule (by
exports property)
- Declarations will be re-instantiated on the current module level
- Providers are registered into the current DI container, if registration not yet
made
- is a forChild import without options
```ts
@NgModule( { imports: [ ForeignModule ] })
```
#subsection("forChild Import")
- forChild(config?) represents a static method on a module class (by convention)
- It returns an object with a providers property and a ngModule property
- basically same as default import
- but allows you to configure services for the current Module level
```ts
@NgModule( { imports: [ ForeignModule.forChild( { } ) ] })
```
#subsection("forRoot Import")
```ts
@NgModule( { imports: [ ForeignModule.forRoot( { } ) ] })
```
- imports things
- configures services -> *hence can't be called by anyone other than the root
module*
- e.g. these services will be loaded for the entire application
- you can define forRoot and forChild yourself -> define what services your module
needs
Example:\
#align(
center,
[#image("../../Screenshots/2023_11_16_05_38_24.png", width: 80%)],
)
#section("Module Types")
#align(
center,
[#image("../../Screenshots/2023_11_16_05_41_24.png", width: 80%)],
)
#subsection("Root Module")
- provides main view -> root component
- a root module has no reason to export anything
- by convention names AppModule in app.module.ts
- imports BrowserModule -> necessary
- bootstrapped by the main.ts
- Accomplished according the used compilation mechanism (dynamic / AOT)
#subsection("Feature Modules")
- splits the application into a set of modules
- differentiation of responsibilities
- can expose or hide it's implementation from other modules
subcategories:
- Domain Modules
- Deliver a UI dedicated to a particular application domain.
- Routing Modules
- Specifies the routing specific configuration settings of the Feature (or Root)
Module.
- Service Modules
- Provides utility services such as data access and messaging.
- Widget Modules
- Makes components, directives, and pipes available to external modules.
- Lazy Modules (Routed Modules)
- Represents lazily loaded Feature Modules.
#subsection("Shared Module")
- provides *globally* used components/directives/pipes
- Do not specify app-wide singleton providers (services) in a shared module
- A lazy-loaded module that imports that shared module makes its own copy of the
service
- Specify these providers in the Root Module instead
#subsection("Core Module")
- provides globally required services
- helps keep the root module clean
- only the root module should import the core module
- guard against imports:
```ts
constructor (@Optional() @SkipSelf() parentModule: CoreModule) {
if (parentModule) {
throw new Error(
'CoreModule is already loaded. Import it in the AppModule only.');
}
}
```
#subsection("Lazy Modules")
- Provides similar features as Feature Modules but not loaded at start
- Angular creates a lazy-loaded module with its own Dependency Injection container
- A child of the root injector
- Required because the Root DI container mustn’t be modified after the
initialization
- May cause some strange behavior if forRoot() rules are violated
Dependency injection due to reloading of other modules when modules inside of
root container change -> Aka there is never an addition or removal of a module,
the addition happens within the root DI container that already exists. And the
lazy modules are loaded to this already loaded container.
#align(
center,
[#image("../../Screenshots/2023_11_16_05_48_44.png", width: 80%)],
)
#text(
teal,
)[In order to not double define providers, you need to import with forRoot on
feature modules that have lazy modules as a child component. The reason is, if
you don't do that, then the root module, which in this case would be the Root DI
container, will import everything and therefore configure the service again with
the lazy load, which leads to a dualton instead of a singleton.]
|
|
https://github.com/polarkac/MTG-Stories | https://raw.githubusercontent.com/polarkac/MTG-Stories/master/stories/007%20-%20Theros/010_Building%20Toward%20a%20Dream%2C%20Part%201.typ | typst | #import "@local/mtgstory:0.2.0": conf
#show: doc => conf(
"Building Toward a Dream, Part 1",
set_name: "Theros",
story_date: datetime(day: 27, month: 11, year: 2013),
author: "<NAME>",
doc
)
My dearest Klytessa—
Will you open this letter? Will you read it? Or will you toss it into the fire? As you watch the paper curl and flicker into flame, will you feel regret? Or satisfaction? Will you tell Lara about it?
I am responsible for the lives of ten thousand people. We are on the precipice of the greatest achievement our kingdom has known... and these are the questions that plague me.
I tell myself we are brokering this peace for the future of Iretis. It is for our men and women, and their children, and their children's children. It brings us out of the shadow of Meletis, accomplishing a peace they never achieved. These things are all true.
But they are not the whole truth.
The formal signing with the leonin is in a fortnight. Udaen is with their tribal councils even now, making the last arrangements. You would marvel at Udaen's spark and energy. Two months ago he was near death, an old and sick man breathing his last. His recovery was a direct answer to my prayers. We have both long relied on his sage counsel, and the prospect of forging this peace without him was impossible. In his recovery from sickness he gained a vitality that is astonishing. I have put that vitality to good use, making him my main factor in the dealings with the various tribes.
Peace, Klytessa. Peace in our lifetimes. I remember that day you first arrived from Meletis. The sun glinting in your hair, and I didn't know which was brighter. Your smile outshining them both as you beheld what must have seemed the humble charms of my kingdom, compared to the wonders of Meletis you had known. With your smile I knew that you were the right choice for me, for our people. That night, your first night, #emph[our] first night, as the survivors, bloody and scarred, came in with their report of yet another border skirmish between the leonin (how tempting it is to still refer to them as cats, or worse... the old prejudices die hard) and our people, when you saw the bloody toll that comes from living in Iretis, the first time I saw your smile dim. Sometimes I wonder if your smile ever truly came back, the way it was in the sun with the gentle wind heralding your arrival. The peace is coming, Klytessa.
#figure(image("010_Building Toward a Dream, Part 1/01.jpg", width: 100%), caption: [], supplement: none, numbering: none)
It comes with a cost. The outer settlements report atrocities committed by impossible monsters, more ferocious than any leonin, and difficult to kill. Nonsense, Udaen says, and I agree. The expansionists always want more land, and they see this potential peace as a direct blow to their dreams of expansion. I ask them for bodies of these creatures as proof, and they claim the bodies disappear into dust. Instead, they present me the bodies of their own, and indeed they are mangled with a ferocity and violence rarely seen. I don't wish to believe our people could do this to themselves in order to sabotage the peace, but I agree with Udaen's caution.
Men will do terrible things in pursuit of their dreams.
I remember a night, soon after Lara was born. We had spent the day with our baby, putting the cares of our kingdom aside, just for a day. #emph[One day for our baby] , you had said, and I agreed. Surely she deserved that much. The day she was born, I felt like I had known her my entire life, that there had never been a part of my life that did not have her in it. It was the first time I had ever resented being king, having to sacrifice so much for people who were not you and Lara. So I gave you and her the day, and gave it gladly. We spent the day at the lake, splashing and walking and talking, and I think for a while you even forgot the guards. It was a wonderful day. And after we returned to the palace that wonderful day became a wonderful night. As you lay sleeping, the moonlight on your shoulders, my hand on your back feeling your breath slowly enter and leave your perfect body, I knew I wanted this moment to last forever. If I could capture that moment, the moonlight framing our intertwined bodies, and have it never change, I would. The moment was perfect, and change could only make it worse.
I think about that night often.
I choose to hope, Klytessa. I choose to believe the leonin will keep their word and sign this peace treaty with us two weeks from now. I choose to believe that the expansionists will come to understand the benefits of peace, of stability, and stop their attempts at sabotage. I choose to believe that you did open this letter, that you opened it and are reading it right now. I choose to believe that there is a path forward for us. A path that has you here at my side in Iretis, where you belong. Where I need you.
I love you. There will be peace. You are beautiful. I miss our daughter. I could not come up with the right combination of words to stop you from leaving. I hope I can find the right combination of words to make you return.
Kedarick
#v(0.35em)
#line(length: 100%, stroke: rgb(90%, 90%, 90%))
#v(0.35em)
Klytessa—
A difficult and dark day. I have known <NAME> for over thirty years. We grew up together, trained together, fought together. He has saved my life against the cats many times. He was my friend. I killed him today. With my sword I parted his head from his body, neatly cleaving his neck. It was a clean cut, and quick.
You used to ask me how I could go into battle seemingly so unafraid. I would have had a different answer many years ago, but now my answer is this—a battle kills you quickly, but life kills you slowly. Every day, another part of you dies.
I long for the simplicity of battle.
The day started off well enough. Thoros had sent word he was coming to offer his support for the upcoming peace treaty. It was a major victory, to have such a prominent expansionist come around to the side of peace. I greeted him in the throne room and there we embraced and smiled. Thoros had brought a small group of his men, and although they were armored and armed, I expected nothing else from the warriors of the outer settlements. Not all journeys to the heart of Iretis are free from violence. The rest of the palace staff was busy with the preparations for the signing a week from now, but Udaen himself was on hand to welcome such an important guest, one who might bring the entirety of the expansionists to our side. As I made to go to the banquet hall for the welcoming lunch, Thoros held up a hand. We stopped, and Thoros put his hand into a satchel and pulled out a head. It was that of a young man, although I did not recognize him. The neck had been ripped savagely from the body; there was no sign of a clean or straight cut. The guards drew their swords but Thoros and his men made no attempt to draw theirs.
"My nephew," Thoros said. "Killed by the cats, last night."
#figure(image("010_Building Toward a Dream, Part 1/02.jpg", width: 100%), caption: [], supplement: none, numbering: none)
I asked him if he had proof.
"Once, my word would have been proof." I could not deny his truth, but we weren't warriors fighting cats anymore. I was the king, trying to forge a peace, and I needed proof.
"I saw it with my own eyes. It was the largest cat I ever saw, seven or eight feet tall. Built like a bear. It had four arms, two heads, and teeth and claws as long as daggers. A cat out of our nightmares. It just appeared in the middle of the scout camp. It ripped Teralos's head off of his body. We lost ten others trying to bring it down." I'm capturing his exact words because I find them so hard to believe. Four arms? Two heads? Did he think me a fool? I looked closely at him and his men, but only stoic faces glared at me in response.
I asked him if they killed the monster. They hadn't. The cat disappeared in the middle of battle, evaporating into mist, leaving only the slain and wounded. I asked him what he wanted of me.
"Justice," he said. "Justice for Teralos. Justice for the dead. Justice for the living. Why do you seek peace with those who do this to your people?" He was shouting at the end.
I had no answer. It's a lesson I told you long ago—never show uncertainty. And yet I looked at my friend and I did not know what to do, and I said nothing.
Udaen broke the silence. "I wonder," he said, "who is the largest landowner in the Greenhills settlement? Who has the biggest claims on land we have sought to take from the leonin?" This broke the stony resolve of Thoros's men. Now there were open rumblings of anger. Udaen was cruel, but he was right. Thoros was my friend, and my compatriot in battle, but he also stood to lose much if the peace with the leonin held. I could not forget that.
I had decided, Klytessa, to be kind. Remember that. Please. My friend was furious and still grieving over the loss of his nephew and his people. While I was angry at the pretense of his visit, I understood it. And a part of me wanted to make the world right for my friend. I told him I would think on the matter, and would have my men investigate to see if there was proof to be found. It was not decisive action, but it would give us time. Time I desperately needed to reconcile such bizarre accounts of these attacks.
It was not the answer Thoros was looking for.
Even now, I almost believe that Thoros looked as surprised at his actions as I was. I had finished speaking, and turned to leave, to give Thoros and his men the privacy to grieve and regain their composure. As I turned, I saw the look come over Thoros's face, that familiar look of rage and battlelust... but never had I seen it directed at me. Before I had time to react, Udaen was there, interposing his frail body between myself and Thoros, shouting, "For the King!" He jammed his staff in between the legs of Thoros, sending Thoros sprawling forward to the ground, and only then did I see the dagger fly from Thoros's hands, the dagger he had begun swinging at my back.
#figure(image("010_Building Toward a Dream, Part 1/03.jpg", width: 100%), caption: [], supplement: none, numbering: none)
The slaughter of Thoros's men was quick. If they had been a part of his assassination plot, they were ill-prepared for it. They seemed as surprised by the attempt as I had been. Thoros himself seemed in a daze, even after he was hauled up by my guards, his face beaten and bruised, as he looked over his slain comrades.
"They said... they said you had gone blind. That your quest for peace, your quest for your... queen, had blinded you to the needs of your people. I told them you would listen to me. That you would see me, and see the... truth. That you would open your eyes and stop this nightmare." I want to capture every word he spoke. I want to remember every drop of blood he coughed up as he spoke them.
I had my eyes wide open as I passed judgment on Thoros Clawkiller, my friend. I saw my blade descend down swiftly, and pass cleanly through his neck. No ragged edges for my friend, not like his nephew. A quick and clean cut.
It is the kindness of a king.
Kedarick
#v(0.35em)
#line(length: 100%, stroke: rgb(90%, 90%, 90%))
#v(0.35em)
My darling Klytessa—
I've carried the secret with me all day. Udaen handed me the letter this morning. It has been my shield, my armor, my sword. I could do no wrong today, because I had my secret.
Tomorrow is the signing ceremony with the leonin. Elders from several tribes ("Six tribes, Kedarick, six. Shall I have you name them again?" That was Udaen this morning. He is being quite thorny, but given all he has done to set up this ceremony, I can forgive it) will meet with me and Udaen for the signing. They will give us a ceremonial weapon. We will give them formal land rights to their current areas, with lucrative trade privileges for each clan. They get better of the exchange, but if it gives us lasting peace, how worth it!
I gave a speech today. The last speech I had given was shortly after you left, when the kingdom needed my voice and my reassurance. That speech was a disaster, but how could it not be? My heart was gone. I know no man who can speak convincingly without his heart.
Today's speech was beautiful. There have been few times in my life when I've spoken to my subjects, and realized they hung on my every word, that they were captivated by the power of my voice and my message. Today was such a day. I spoke of the historic occasion of tomorrow's signing. I told them we were ushering in a new age of prosperity and safety, that we were here to glimpse the early dawn of Iretis's golden age. I told them the rumors of the expansionists's newly formed army, the rumors of terrors that stalk the night, these were ephemeral, and would evaporate like the morning dew against the power of the sun, the power of our peace with the leonin. It was a triumphant moment, and the cheers and cries of our people were sublime.
Yet it was a pale shadow of the joy from my secret.
After the speech, Udaen wanted to brief me on the scouting reports of the expansionists. Thoros's brothers and sons had gathered a small army of several hundred men from the settlements. But they would still need more before challenging us, and Udaen was confident that the peace with the leonin would shrivel the expansionists' support. I dismissed Udaen from the room as quickly as I could. What need had I to talk of the expansionists or the final details of tomorrow?
I want to talk about Lara. How much has she grown in the last year? Are figs still her favorite food? Does she speak of me often? Does she still play the lute? It has only been a year, and yet I tremble at the thought of seeing her again, her auburn hair, her smile, the way she stubbornly sets her arms in the exact way you do, with the upturn in her nose and resolve in her eyes.
Ignore my tears that stain the edge of this page, for I have my secret and I am invulnerable. You are coming back. You are coming back!
My darling, my love, until a few days when we see each other again. I tremble at the thought. A new age is starting for Iretis tomorrow, and you and I shall preside!
Your love,
Kedarick
|
|
https://github.com/jgm/typst-hs | https://raw.githubusercontent.com/jgm/typst-hs/main/test/typ/text/font-03.typ | typst | Other | // Error: 18-24 expected "normal", "italic", or "oblique"
#set text(style: "bold", weight: "thin")
|
https://github.com/barrel111/readings | https://raw.githubusercontent.com/barrel111/readings/main/notes/randomized-algo.typ | typst | #import "@local/preamble:0.1.0": *
#import "@preview/lovelace:0.2.0": *
#show: setup-lovelace
#show: project.with(
course: "",
sem: "",
title: "randomized algorithms",
subtitle: "wow its different",
authors: ("<NAME>",),
authors_label: "author:",
)
= Introduction
#algorithm(caption: [`KN-GREEDY`], pseudocode-list[
+ $O = emptyset$
+ $s = 0$
+ *sort* such that $w_1>= w_2>= dots.c >= w_n$.
+ *while* $i < n$ and $s + w_(i + 1)<= W$ *do*
+ $O = O union w_(i + 1)$
+ $s = s + w_(i + 1)$
+ $i = i + 1$
+ *end*
+ *return* $O$
])
== A Min-Cut Algorithm
== Las Vegas and Monte Carlo
== Binary Planar Partitions
== A Probabilistic Recurrence
== Computation Model and Complexity Classes
= Game-Theoretic Techniques
== Game Tree Evaluation
== The Minimax Principle
== Randomness and Non-uniformity
= Moments and Deviation
== Occupancy Problems
== The Markov and Chebyshev Inequalities
== Randomized Selection
== Two-Point Sampling
== The Stable Marriage Problem
== The Coupon Collector's Problem
|
|
https://github.com/DVDTSB/ctheorems | https://raw.githubusercontent.com/DVDTSB/ctheorems/main/0.1.0/README.md | markdown | # ctheorems
Theorem library based on (and compatible) with [typst-theorems](https://github.com/sahasatvik/typst-theorems).
### Features
- Numbered theorem environments can be created and customized.
- Awesome presets (coming soon!)
- Environments can share the same counter, via same `identifier`s.
- Environment counters can be _attached_ (just as subheadings are attached to headings) to other environments, headings, or keep a global count via `base`.
- The depth of a counter can be manually set, via `base_level`.
- Environment numbers can be referenced, via `#thmref(<label>)[]`.
Currently, the `<label>` must be placed _inside_ the environment.
## Manual and Examples
Get acquainted with `ctheorems` by checking out the minimal example below!
You can read the [manual](assets/manual.pdf) (im working on it haha) for a full walkthrough of functionality offered by this module.
### Preamble
```typst
#import "@preview/ctheorems:0.1.0": *
#set page(width: 16cm, height: auto, margin: 1.5cm)
#set heading(numbering: "1.1.")
#let theorem = thmbox("theorem", "Theorem", fill: rgb( "#E1F5FE"),stroke:rgb("#4FC3F7"))
#let corollary = thmplain(
"corollary",
"Corollary",
base: "theorem",
titlefmt: strong
)
#let definition = thmbox("definition", "Definition", inset: (x: 1.2em, top: 1em))
#let example = thmplain("example", "Example", numbering:none)
#let proof = thmplain(
"proof",
"Proof",
base: "theorem",
bodyfmt: body => [#body #h(1fr) $square$],
).with(numbering:none)
```
### Document
```typst
= Prime numbers
#definition[
A natural number is called a _prime number_ if it is greater than 1
and cannot be written as the product of two smaller natural numbers.
]
#example[
The numbers $2$, $3$, and $17$ are prime.
#thmref(<cor_largest_prime>)[Corollary] shows that this list is not
exhaustive!
]
#theorem(name: "Euclid")[
There are infinitely many primes.
]
#proof[
Suppose to the contrary that $p_1, p_2, dots, p_n$ is a finite enumeration
of all primes. Set $P = p_1 p_2 dots p_n$. Since $P + 1$ is not in our list,
it cannot be prime. Thus, some prime factor $p_j$ divides $P + 1$. Since
$p_j$ also divides $P$, it must divide the difference $(P + 1) - P = 1$, a
contradiction.
]
#corollary[
There is no largest prime number. <cor_largest_prime>
]
#corollary[
There are infinitely many composite numbers.
]
```
## Credits
- [@sahasatvik (<NAME>)](https://github.com/sahasatvik)
- [@rmolinari (<NAME>)](https://github.com/rmolinari)
- [@MJHutchinson (<NAME>)](https://github.com/MJHutchinson)
- [@DVDTSB](https://github.com/DVDTSB) |
|
https://github.com/taooceros/MATH-542-HW | https://raw.githubusercontent.com/taooceros/MATH-542-HW/main/HW8/HW8.typ | typst | #import "@local/homework-template:0.1.0": *
// Take a look at the file `template.typ` in the file panel
// to customize this template and discover how it works.
#show: project.with(title: "Math 542 HW7", authors: ("<NAME>",))
= Factorization of Cyclotomic Polynomials
Let $l$ be a prime and let $Phi_l (x) = (x^l - 1)/(x-1) = x^(l-1) + x^(l-2) ... + x + 1 in ZZ[x]$ be the $l^"th"$ cyclotomic polynomial, which is irreduciable in $ZZ[x]$. This exercise determines the factorization of $Phi_l(x)$ modulo $p$ for any prime $p$. Let $zeta$ denote any fixed primitive $l^("th")$ root of unity.
==
Show that $p=l => Phi_l (x) = (x-1)^(l-1) in FF_l[x]$
#solution[
$
(x-1)^(l-1) = sum_(i=0)^(l-1) binom(l-1, i) x^i (-1)^(l-1-i)
$
Consider each binomial coefficient $binom(l-1, i)$ modulo $l$. Since $l$ is prime, $(l-1)! equiv -1 mod n$.
$
binom(l-1, i) = ((l-1)!)/((l-1-i)!i!) \
<=> binom(l-1, i)(l-1-i)!i! equiv (l-1)! equiv -1 mod l #h(1em) ("Wilson Theorem")\
<=> binom(l-1, i) equiv - 1/((l-1-i)!i!) mod l
$
]
== <q8b>
Suppose $p!=l$ and let $f$ denote the order of $p mod l$, i.e. $f$ is the smallest power of $p$ with $p^f equiv 1 mod l$. Use the fact that $FF^times_(p^n)$ is a cyclic group to show that $n=f$ is the smallest power $p^n$ of $p$ with $zeta in FF_(p^n)$. Conclude that the minimal polynomial of $zeta$ over $FF_p$ has degree $f$.
#solution[
Since $FF^times_p^n$ is a cyclic group, and $zeta$ is a $l$-th primitive root of unity, for $zeta$ to be in $FF_p^n$, we must have some element that has order $l$. Therefore $n=f$ is the smallest power of $p^n$ of $p$ with $zeta in FF_p^n$ by construction.
]
#solution[
Because we have the minimum extension of $zeta$ to be in $FF_p^n$, which is a degree $n$ extension, the minimal polynomial of $zeta$ over $FF_p$ has degree $n = f$.
]
==
Show that $FF_p (zeta) = FF_p (zeta^a)$ for any integer $a$ not divisible by $l$. [Hint:]
#solution[
One direction, it suffices to check that $zeta^a$ can be generated by $zeta$, which is obvious.
The other direction suffices to check that $zeta$ can be generated by $zeta^a$, which follows from the hint that $zeta=(zeta^a)^b$ where $b$ is the multiplicative inverse of $a mod l$.
]
Conclude using (@q8b) that, in $FF_p [x]$, $Phi_l (x)$ is the product of $(l-1)/f$ distinct irreducible polynomials of degree $f$.
#solution[
Since all primitive roots of unity have $f$-degree minimal polynomial, and all other roots of unity are generated by primitive roots of unity, we have that $Phi_l(x)$ is the product of $(l-1)/f$ distinct irreducible polynomials of degree $f$.
]
==
In particular, prove that, viewed in $FF_p [x]$, $Phi_7(x) = x^6 + x^5 + ... + x + 1$ is $(x-1)^6$ for $p=7$, a product of distint linear factor for $p equiv 1 mod 7$, a product of $3$ irreducible quadratics for $p equiv 6 mod 7$, a product of 2 irreducible cubics for $p equiv 2,4 mod 7$, and is irreducible for $p equiv 3,5 mod 7$.
#solution[
By previous part, we have $FF_p (zeta) = FF_p (zeta^a)$ for any integer $a$ not divisible by $l$.
Therefore we naturlly have the conjugacy classes of $zeta^k$ by the modulo subgroup of $l$.
For $p=7$, $Phi_l$ is $(x-1)^6$ because $1$ is the only element having degree $7$.
For $p equiv 1 mod 7$, $Phi_l$ is a product of distinct linear factors based on last part since $f=1$.
For $p equiv 6 mod 7$, $Phi_l$ is a product of $3$ irreducible quadratics based on last part since $f=2$.
For $p equiv 2,4 mod 7$, $Phi_l$ is a product of $2$ irreducible cubics based on last part since $f=3$.
For $p equiv 3,5 mod 7$, $Phi_l$ is irreducible based on last part since $f=6$.
]
=
==
Let $phi$ denote the Frobenius map $x arrow.bar x^p$ on the finite field $FF_p^n$ as in the previous exercise. Determine the rational canonical form over $FF_p$ for $phi$ considered as an $FF_p$-linear transformation of the $n$-dimensional $FF_p$-vector space $FF_p^n$.
#solution[
To derive the rational canonical form over $FF_p$ it suffices to find the minimal polynomial of $phi$.
#lemma[
The minimal polynomial of $phi$ is $x^p^n - 1$.
]
#proof[
Suppose we have lower degree polynomial $P$ such that $P(phi) = 0$. We can write this polynomial as $sum a sigma_p^k$, and we know that it is $0$.
Then
$
(sum a sigma_p^k) (x) = sum a sigma_p^k (x) = sum a x^(p^k) = 0
$
Thus all $x$ is a root of $P$, which is a contradiction because the degree of this polynomial is less than $p^n$.
]
Thus the rational canonical form is
$
mat(
0 , 0 , ... , 0 , 1 ;
1 , 0 , ... , 0 , 0 ;
0 , 1 , ... , 0 , 0 ;
... , ... , ... , ... , ... ;
0 , 0 , ... , 1 , 0;
)
$
]
==
Let $phi$ denote the Frobenius map $x arrow.bar x^p$ on the finite field $FF_p^n$ as in the previous exercise. Determine the Jordan canonical form (over a field containing all the eigenvalues) for $phi$ considered as an $FF_p$-linear transformation of the $n$-dimensional $FF_p$-vector space $FF_p^n$.
#solution[
Follow a similar construction, it suffices to consider the chraacteristic polynomial of $phi$.
However, since the degree of the characteristic polynomial is $p^n$, we have the minimal polynomial is the characteristic polynomial.
$x^p^n - 1$ is separable when $p$ does not divides $n$.
Thus the Jordan canonical form is
$
mat(
zeta_1 , 0 , ... , 0 ;
0 , zeta_2 , ... , 0 ;
0 , 0 , ... , zeta_n ;
)
$
where $zeta_i$ are the $p^n$-th primitive root of unity.
When $p$ divides $n$, we have the minimal polynomial $x^q^p^k - 1^p^k = (x^q -1)^p^k$, and let $lambda_1,...,lambda_q$ be the roots of $x^q - 1$, we have the Jordan canonical form is
$
mat(
lambda_1 , 1 , ... , 0, 0 ;
0 , lambda_1 , ... , 0, 0 ;
0 , 0 , ... , lambda_q, 1 ;
0 , 0 , ... , 0, lambda_q ;
)
$
where each jordan block are size $p^k$.
]
= Wedderburn's Theorem on Finite Division Rings
The exercise outline a proof of Wedderburn's Theorem that a finite division ring $D$ is a field.
==
Let $Z$ denote the center of $D$. Prove that $Z$ is a field containing $FF_p$ for some prime $p$. If $Z = FF_q$ prove that $D$ has order $q^n$ for some integer $n$.
#solution[
Because we know that the center of $D$ is finite and commutative, and thus is a finite field. Further, we know that any finite field containing some $FF_p$ for some prime $p$.
We also know that $D$ is a finite dimensional vector space over $Z$, since the regular ring addition and multiplication can be used, and thus $D$ has order $q^n$ for some integer $n$.
]
==
The nonzero elements $D^times$ of $D$ form a multiplicative group. For any $x in D^times$ shows that the elements of $D$ which commute with $x$ form a division ring which contains $Z$. Show that this division ring is of order $q^m$ for some integer $m$ and that $m < n$ if $x$ is not an element of $Z$.
#solution[
Since $Z$ is the center, so all elements of $D^times$ commute with $x$ will contain $Z$.
It suffices to verify that this is a ring, which follows from that we cannot goes from commute with $x$ to something not commute with $x$ by addition and multiplication.
Since this division ring is also a vector space over $Z$, we have its order equal to some $m$, and $m<n$ because if $m=n$ then this division ring has to be the whole ring and thus $x$ has to be in $Z$.
]
==
Show that the class equation for the group $D^times$ is
$
q^n-1=(q-1) + sum_(i=1)^r (q^n -1)/(abs(C_D^times (x_i)))
$
where $x_i$ are representatives of the distinct conjugacy classes in $D^times$ not contained in the center of $D^times$. Conclude that for each $i$, $abs(C_D^times (x_i))=q^(m_i)-1$ for some $m_i < n$.
#solution[
We have the class equation for the group $D^times$ is
$
abs(Z(D)^times) + sum_(i=1)^r abs(D^times)/(abs(C_D^times (x_i))) = q^n-1 = (q-1) + sum_(i=1)^r (q^n -1)/(abs(C_D^times (x_i)))
$
Thus
$
sum (q^n -1)/(abs(C_D^times (x_i))) = q^(n-1)
$
From previous part we know that $abs(C_D^times (x_i))=q^(m_i)-1$ for some $m_i < n$.
]
==
Prove that since $(q^n-1)/(q^m_i = 1) = abs(D^times : C_D^times (x_i))$ is an integer then $m_i$ divides $n$. Conclude that $Phi_n (x)$ divides $(x^n-1)/(x^(m_i)-1)$ and hence that the integer $Phi_n (q)$ divides $(q^n-1)/(q^(m_i)-1)$ for $i=1,2,...,r$.
#solution[
Since $(q^n-1)/(q^(m_i) - 1) = abs(D^times : C_D^times (x_i))$ is an integer
Let $n = k m_i + r$
$
(q^n-1) - (q^r - 1) = q^n - q^r = q^(k m) - 1 = (q^m - 1) l
$ for some $l$.
Thus it is equivqlent to prove thqt $q^n - 1 | q^r - 1$ by euclideqn qlgorithm.
However since $n > r$ by construction, we hqve $q^n - 1 | q^r - 1 <=> q^r - 1 = 0 <=> r = 0$ which implies the claim.
Note that $Phi_n(q) = (x^n - 1)/(x-1)$, thus it suffices to check $x^(m_i)-1 | x-1$, which is always true.
]
==
Prove that $Phi_n (q) = product_(zeta "primitive") (q-zeta)$ divides $q-1$. Prove that $abs(q-zeta) > q-1$ (complex absolute value) for any root of unity $zeta != 1$. [note that $1$ is the closest point on the unit circle in $CC$ to the point $q$ on the real line]
Conclude that $n=1 <=> D=Z$.
#solution[
We have $Phi_n (x) = product_(d | n) Phi_d = product_(zeta "primitive") (x-zeta)$. We have $Phi_n (q)$ divides $(q^n - 1)/(q^(m_i) - 1)$. Since we can have all kind of $m_i < n$, their LCM will be $q^(n-1)-1$, and thus $Phi_n (q) | q - 1$.
Since $q$ is prime, so $p > 1$ and $p in RR$. Therefore, since $zeta$ lies on the unit circle, and $1$ is the closest points to $p$ lying on the unit circle, $abs(q-zeta) > q - 1$.
Therefore, since $Phi_n (q) = product_(zeta "primitive") (x-zeta)$, $abs(Phi_n (q)) = product_(zeta "primitive") abs(x-zeta)$, and thus $n=1$, since it divides $q-1$.
]
= Dirichlet's Theorem
== <dirichlet_1>
#image("13.6.14.png")
Suppose $p_1, p_2,..., p_k$ are the only primes the dividing values $P(n)$.
Consider a integer $N$ such that $P(N) = a != 0$. Consider the polynomial $Q(x) = a^(-1) P(N + a p_1 p_2 ... p_k x)$.
#lemma[
$ Q(x) in ZZ[x] $
]
#proof[
Since $P$ is a polynomial, we can write $P=b_1 x^n + b_2 x^(n-1) + ... b_(n+1)$. Then consider $P(N + a p_1 p_2...p_k x)$, by binomial theorem we have each terms being writeen as some product of $N$ and $a p_1 p_2...p_k x$. Any term involving the second part is certainly divisible by $a$, and the grouping of term that only contains $N$ is equal to $P(N)$, and by assumpition, is divisible by $a$ since $P(N) = a$. Therefore $Q(x) in ZZ[x]$.
]
#lemma[
$
Q(n) = 1
$
]
#proof[
We can show the following by a similar construction as above: #h(1fr)
$
Q(n) = P(N + n a p_1 p_2...p_k) / a equiv P(N) / a equiv 1 #h(1em) (mod p_1 p_2 ... p_k)
$
]
#corollary[
There are some $M in ZZ$ such that $Q(M)$ is coprime with $p_1 p_2...p_k$.
]
#proof[
It suffices to check that $Q(n)$ is not $1$ for some integer $n$. #h(1fr)
Assume $Q(n) = 1 forall n$, we have $Q$ is a degree $0$ polynomial, which is a contradiction because $Q = a^(-1) P(N + a p_1 ... p_k x)$, but $P$ has degree greater than $1$.
]
#corollary[
$P(N + a p_1 p_2...p_k M)$ is divisible by some prime $p$ not in $p_1 p_2...p_k$.
]
#proof[
This is trivial given that $Q(M)$ is coprime with $p_1 p_2...p_k$ and $P(N+a p_1 p_2...p_k M) = a Q(M)$.
]
==
#image("13.6.15.png")
Since $a in ZZ$ satisfied $Phi_m(a) equiv 0 mod p$. We have $a$ is a root of $Phi_m$ in $FF_p$. Thus the order of $a mod p$ were less than $m$ and $exists d: a^d equiv 1 mod p$ for some $d | m$.
Further we know that $x^m - 1 = product_(d | m) Phi_d (x) = Phi_m (x) product_(d | m \ d<m ) Phi_d (x)$.
Since $a^d equiv 1 mod p$ and $d | m$, we have $Phi_d (a) equiv 0 mod p$.
However this suggests that we have $x^m - 1$ is not separable because two of its factor contains $a$ as a root, which is a contradiction when $p$ does not divides $m$.
Then since $p$ does not divides $m$, we have $a$ is relatively prime to $p$ because its order is $m$.
==
Let $a in ZZ$. Show that if $p$ is an odd prime dividing $Phi_m (a)$ then either $p$ divides $m$ or $p equiv 1 mod m$.
#solution[
If $p$ divides $Phi_m (a)$, then $a$ is a solution of $Phi_m$ under $FF_p$. From previous exercise we have shown that $a$ is relatively prime to $p$ and the order of $a$ in $(ZZ \/ p)^times$ is precisely $m$ if $p$ does not divides $m$.
Since we know that the order of an arbitary element of a group divides the order of the group, we have $m | p-1$.
]
==
Prove there are infinitely many primes $p$ with $p equiv 1 mod m$.
#solution[
It suffices to find infinitely many pairs of $p,a$ such that $p$ divides $Phi_m (a)$ by previous part.
By @dirichlet_1 we know that for any monic polynomial $P$, there are infinitely many prime factors of the sequence $P(1), P(2), ...$. Thus for any $m$, there are infinitely many primes $p$ with such that it divides $Phi_m (a)$ for a sequences of $a$. Thus we know that we have infinitely many pair of $p$ and $a$ satisfying the condition we have for previous parts.
] |
|
https://github.com/tfachada/thesist | https://raw.githubusercontent.com/tfachada/thesist/main/src/figure-numbering.typ | typst | MIT License | // Set/reset numbering in the given format for figures of different kinds, as well as equations
// Does NOT apply to figures with subfigures
#let set-figure-numbering(it, new-format: none) = {
// Set chapter-relative numbering for images
let image-numbering = super => numbering(new-format, counter(heading).get().first(), super)
show heading.where(level: 1): it => it + counter(figure.where(kind: image)).update(0)
show figure.where(kind: image): set figure(numbering: image-numbering)
// Same for tables
let table-numbering = super => numbering(new-format, counter(heading).get().first(), super)
show heading.where(level: 1): it => it + counter(figure.where(kind: table)).update(0)
show figure.where(kind: table): set figure(numbering: table-numbering)
// Same for code snippets
let code-numbering = super => numbering(new-format, counter(heading).get().first(), super)
show heading.where(level: 1): it => it + counter(figure.where(kind: raw)).update(0)
show figure.where(kind: raw): set figure(numbering: code-numbering)
// Same for algorithms
let algorithm-numbering = super => numbering(new-format, counter(heading).get().first(), super)
show heading.where(level: 1): it => it + counter(figure.where(kind: "algorithm")).update(0)
show figure.where(kind: "algorithm"): set figure(numbering: algorithm-numbering)
// Same for equations
let equation-numbering = super => numbering("("+new-format+")", counter(heading).get().first(), super)
show heading.where(level: 1): it => it + counter(math.equation).update(0)
set math.equation(numbering: equation-numbering)
it
}
|
https://github.com/goshakowska/Typstdiff | https://raw.githubusercontent.com/goshakowska/Typstdiff/main/tests/test_working_types/display_math/display_math.typ | typst | $ Q = rho A v + C $
$ a^2 + b^2 = c^2 $ |
|
https://github.com/kdog3682/2024-typst | https://raw.githubusercontent.com/kdog3682/2024-typst/main/src/te-legend-movement.typ | typst | // https://typst.app/project/pfWcjFhGMJUyVTvJ8daQrR,
#import "@preview/cetz:0.2.0"
#let typst-rotate = rotate
// we rotate the vertical legend so that it is not sideways
// rename the rotate function because it exists in cetz
#let graph(o) = {
// we can import cetz inside of function scopes
cetz.canvas({
import cetz.draw: *
import cetz.chart
let data = (("A", 10), ("B", 20), ("C", 13))
group(name: "a", {
chart.columnchart(
y-tick-step: 4,
// x-ticks: (1,2,3),
// this messes up the centering
size: (4, 3), o.data,
// still not sure what this does
y-label: y-label(o.labels.x),
x-label: x-label(o.labels.y),
outer-label-radius: 200%,
// dont know what this does
inner-label-radius: 200%,
// dont know what this does
x-inset: 2.5,
labels: o.labels.labels
// the spacing is kind of messed up for these items
)
})
})
}
#{
let a = graph(1)
rect(inset: 20pt,
// two graphs stacked
}
// util
#let flex(..args) = {
let base-attrs = (
dir: "ltr",
spacing: 20pt,
)
let named-attrs = args.named()
let attrs = util.merge(base-attrs, named-attrs)
let value = stack(..attrs, ..items))
// if attrs.border ... i mean just compose it
// too many conditionals hard to remember
}
#let to-content(x) = {
if is-string(x) {
return text(x)
}
if is-content(x) {
return x
}
// parse object to content
let base = text(..x.style, x.text)
return base
}
// util for
#let y-label(x) = {
h(-10pt)
return rotate(90deg, to-content(x))
}
#let x-label(x) = {
v(-10pt)
return to-content(x)
}
|
|
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/unichar/0.1.0/ucd/block-1A00.typ | typst | Apache License 2.0 | #let data = (
("BUGINESE LETTER KA", "Lo", 0),
("BUGINESE LETTER GA", "Lo", 0),
("BUGINESE LETTER NGA", "Lo", 0),
("BUGINESE LETTER NGKA", "Lo", 0),
("BUGINESE LETTER PA", "Lo", 0),
("BUGINESE LETTER BA", "Lo", 0),
("BUGINESE LETTER MA", "Lo", 0),
("BUGINESE LETTER MPA", "Lo", 0),
("BUGINESE LETTER TA", "Lo", 0),
("BUGINESE LETTER DA", "Lo", 0),
("BUGINESE LETTER NA", "Lo", 0),
("BUGINESE LETTER NRA", "Lo", 0),
("BUGINESE LETTER CA", "Lo", 0),
("BUGINESE LETTER JA", "Lo", 0),
("BUGINESE LETTER NYA", "Lo", 0),
("BUGINESE LETTER NYCA", "Lo", 0),
("BUGINESE LETTER YA", "Lo", 0),
("BUGINESE LETTER RA", "Lo", 0),
("BUGINESE LETTER LA", "Lo", 0),
("BUGINESE LETTER VA", "Lo", 0),
("BUGINESE LETTER SA", "Lo", 0),
("BUGINESE LETTER A", "Lo", 0),
("BUGINESE LETTER HA", "Lo", 0),
("BUGINESE VOWEL SIGN I", "Mn", 230),
("BUGINESE VOWEL SIGN U", "Mn", 220),
("BUGINESE VOWEL SIGN E", "Mc", 0),
("BUGINESE VOWEL SIGN O", "Mc", 0),
("BUGINESE VOWEL SIGN AE", "Mn", 0),
(),
(),
("BUGINESE PALLAWA", "Po", 0),
("BUGINESE END OF SECTION", "Po", 0),
)
|
https://github.com/LDemetrios/Typst4k | https://raw.githubusercontent.com/LDemetrios/Typst4k/master/src/test/resources/suite/foundations/duration.typ | typst | // Test durations.
--- duration-negate ---
// Test negating durations.
#test(-duration(hours: 2), duration(hours: -2))
--- duration-add-and-subtract ---
// Test adding and subtracting durations.
#test(duration(weeks: 1, hours: 1), duration(weeks: 1) + duration(hours: 1))
#test(duration(weeks: 1, hours: -1), duration(weeks: 1) - duration(hours: 1))
#test(duration(days: 6, hours: 23), duration(weeks: 1) - duration(hours: 1))
--- duration-add-and-subtract-dates ---
// Test adding and subtracting durations and dates.
#let d = datetime(day: 1, month: 1, year: 2000)
#let d2 = datetime(day: 1, month: 2, year: 2000)
#test(d + duration(weeks: 2), datetime(day: 15, month: 1, year: 2000))
#test(d + duration(days: 3), datetime(day: 4, month: 1, year: 2000))
#test(d + duration(weeks: 1, days: 3), datetime(day: 11, month: 1, year: 2000))
#test(d2 + duration(days: -1), datetime(day: 31, month: 1, year: 2000))
#test(d2 + duration(days: -3), datetime(day: 29, month: 1, year: 2000))
#test(d2 + duration(weeks: -1), datetime(day: 25, month: 1, year: 2000))
#test(d + duration(days: -1), datetime(day: 31, month: 12, year: 1999))
#test(d + duration(weeks: 1, days: -7), datetime(day: 1, month: 1, year: 2000))
#test(d2 - duration(days: 1), datetime(day: 31, month: 1, year: 2000))
#test(d2 - duration(days: 3), datetime(day: 29, month: 1, year: 2000))
#test(d2 - duration(weeks: 1), datetime(day: 25, month: 1, year: 2000))
#test(d - duration(days: 1), datetime(day: 31, month: 12, year: 1999))
#test(datetime(day: 31, month: 1, year: 2000) + duration(days: 1), d2)
#test(
datetime(day: 31, month: 12, year: 2000) + duration(days: 1),
datetime(day: 1, month: 1, year: 2001),
)
--- duration-add-and-subtract-times ---
// Test adding and subtracting durations and times.
#let a = datetime(hour: 12, minute: 0, second: 0)
#test(a + duration(hours: 1, minutes: -60), datetime(hour: 12, minute: 0, second: 0))
#test(a + duration(hours: 2), datetime(hour: 14, minute: 0, second: 0))
#test(a + duration(minutes: 10), datetime(hour: 12, minute: 10, second: 0))
#test(a + duration(seconds: 30), datetime(hour: 12, minute: 0, second: 30))
#test(a + duration(hours: -2), datetime(hour: 10, minute: 0, second: 0))
#test(a - duration(hours: 2), datetime(hour: 10, minute: 0, second: 0))
#test(a + duration(minutes: -10), datetime(hour: 11, minute: 50, second: 0))
#test(a - duration(minutes: 10), datetime(hour: 11, minute: 50, second: 0))
#test(a + duration(seconds: -30), datetime(hour: 11, minute: 59, second: 30))
#test(a - duration(seconds: 30), datetime(hour: 11, minute: 59, second: 30))
#test(
a + duration(hours: 1, minutes: 13, seconds: 13),
datetime(hour: 13, minute: 13, second: 13),
)
--- duration-add-and-subtract-datetimes ---
// Test adding and subtracting durations and datetimes.
#test(
datetime(day: 1, month: 1, year: 2000, hour: 12, minute: 0, second: 0)
+ duration(weeks: 1, days: 3, hours: -13, minutes: 10, seconds: -10 ),
datetime(day: 10, month: 1, year: 2000, hour: 23, minute: 9, second: 50),
)
#test(
datetime(day: 1, month: 1, year: 2000, hour: 12, minute: 0, second: 0)
+ duration(weeks: 1, days: 3, minutes: 10)
- duration(hours: 13, seconds: 10),
datetime(day: 10, month: 1, year: 2000, hour: 23, minute: 9, second: 50),
)
--- duration-from-date-subtraction ---
// Test subtracting dates.
#let a = datetime(hour: 12, minute: 0, second: 0)
#let b = datetime(day: 1, month: 1, year: 2000)
#test(datetime(hour: 14, minute: 0, second: 0) - a, duration(hours: 2))
#test(datetime(hour: 14, minute: 0, second: 0) - a, duration(minutes: 120))
#test(datetime(hour: 13, minute: 0, second: 0) - a, duration(seconds: 3600))
#test(datetime(day: 1, month: 2, year: 2000) - b, duration(days: 31))
#test(datetime(day: 15, month: 1, year: 2000) - b, duration(weeks: 2))
--- duration-multiply-with-number ---
// Test multiplying and dividing durations with numbers.
#test(duration(minutes: 10) * 6, duration(hours: 1))
#test(duration(minutes: 10) * 2, duration(minutes: 20))
#test(duration(minutes: 10) * 2.5, duration(minutes: 25))
#test(duration(minutes: 10) / 2, duration(minutes: 5))
#test(duration(minutes: 10) / 2.5, duration(minutes: 4))
--- duration-divide ---
// Test dividing durations with durations
#test(duration(minutes: 20) / duration(hours: 1), 1 / 3)
#test(duration(minutes: 20) / duration(minutes: 10), 2)
#test(duration(minutes: 20) / duration(minutes: 8), 2.5)
--- duration-compare ---
// Test comparing durations
#test(duration(minutes: 20) > duration(minutes: 10), true)
#test(duration(minutes: 20) >= duration(minutes: 10), true)
#test(duration(minutes: 10) < duration(minutes: 20), true)
#test(duration(minutes: 10) <= duration(minutes: 20), true)
#test(duration(minutes: 10) == duration(minutes: 10), true)
#test(duration(minutes: 10) != duration(minutes: 20), true)
#test(duration(minutes: 10) <= duration(minutes: 10), true)
#test(duration(minutes: 10) >= duration(minutes: 10), true)
#test(duration(minutes: 20) < duration(minutes: 10), false)
#test(duration(minutes: 20) <= duration(minutes: 10), false)
#test(duration(minutes: 20) == duration(minutes: 10), false)
|
|
https://github.com/Ryoga-itf/numerical-analysis | https://raw.githubusercontent.com/Ryoga-itf/numerical-analysis/main/report2/report.typ | typst | #import "../template.typ": *
#import "@preview/codelst:2.0.1": sourcecode, sourcefile
#show: project.with(
week: 2,
authors: (
(
name: sys.inputs.STUDENT_NAME,
id: sys.inputs.STUDENT_ID,
affiliation: "情報科学類2年"
),
),
date: "2024 年 6 月 17 日",
)
== 課題1
=== (1.1)
コードは以下のようになった。
補間多項式の係数を求め、その後、求めた多項式のグラフと $f(x)$ のグラフ及び 及び補完点を重ねて描画している。
左側のグラフでは $[−1,1]$ の区間で等間隔に取った値を補間点の分布としたものを、
右側では $[0, pi]$ の区間で $theta_i$ を等間隔に取った時の $cos(theta_i)$ の値を補間点の分布としたものを描画している。
#sourcefile(read("src/1-1.jl"), file:"src/1-1.jl")
結果を以下に示す。
補間多項式の係数は以下のようになった。
#sourcecode[```
normal: 0.499801 - 1.14278*x - 3.37146*x^2 + 12.4799*x^3 + 10.6908*x^4 - 47.234*x^5 - 14.5098*x^6 + 69.2239*x^7 + 6.72901*x^8 - 33.3342*x^9
cos : 0.4691 - 0.905097*x - 2.3341*x^2 + 6.17519*x^3 + 5.08622*x^4 - 14.9626*x^5 - 4.91201*x^6 + 15.1669*x^7 + 1.72914*x^8 - 5.48153*x^9
```]
すなわち、
/ $[−1,1]$ の区間で等間隔に取った値を補間点の分布としたもの:
- $0.499801 - 1.14278x - 3.37146x^2 + 12.4799x^3 + 10.6908x^4 - 47.234x^5 - 14.5098x^6 + 69.2239x^7 + 6.72901x^8 - 33.3342x^9$
/ $[0, pi]$ の区間で $theta_i$ を等間隔に取った時の $cos(theta_i)$ の値を補間点の分布としたもの:
- $0.4691 - 0.905097x - 2.3341x^2 + 6.17519x^3 + 5.08622x^4 - 14.9626x^5 - 4.91201x^6 + 15.1669x^7 + 1.72914x^8 - 5.48153x^9$
となった。
また、描画した図は以下のようになった。
#figure(
image("fig/fig1.svg"),
caption: "課題 1 (1.1) の結果"
)
図を見ると、Runge の現象が確認できる。
特に、$x$ の絶対値が大きい点の間において、大きくずれていることが確認できる。
補完点の分布を工夫したものは $x$ の絶対値が大きい箇所においては比較的乖離した値は出ていない。
== 課題2
=== (2.1)
作成した関数は以下の通り
#sourcefile(read("src/2-1.jl"), file:"src/2-1.jl")
例えば `calcA([1, 2, 4, 8], 4)` を実行すると以下の結果が得られた。
#sourcecode[```
4×4 Matrix{Float64}:
1.0 1.0 1.0 1.0
1.0 2.0 4.0 8.0
1.0 4.0 16.0 64.0
1.0 8.0 64.0 512.0
```]
=== (2.2)
以下のコードを実行して描画した。
#sourcefile(read("src/2-2.jl"), file:"src/2-2.jl")
結果は以下のようになった。
#figure(
image("fig/fig2.svg", width: 70%),
caption: "表1のデータをプロットした結果"
)
=== (2.3)
コードは以下の通り
#sourcefile(read("src/2-3.jl"), file:"src/2-3.jl")
結果を以下に示す
#figure(
image("fig/fig3.svg", width: 70%),
caption: "近似した多項式のグラフを(2.2)のグラフに重ねて表示した結果"
)
=== (2.4)
それぞれ以下のようなプログラムを書き実行した。
#sourcefile(read("src/2-4.jl"), file:"src/2-4.jl")
==== (2.4-1)
$4.280592151994875 [10^(-8) Omega "m"]$
==== (2.4-2)
$65.33316000373105 [℃]$
== 課題3
=== (3.1)
以下に示すコードを書き、実行して確認した。
Julia の `sin` 関数との絶対誤差をグラフ上に表示している。
なお、$n$ を $15$ 以上にすると絶対誤差は 0 となったため省略している。
#sourcefile(read("src/3-1.jl"), file:"src/3-1.jl")
結果は以下のようになった。
#figure(
image("fig/fig4.svg", width: 70%),
caption: "課題 3 (3.1) プログラムを実行した結果"
)
=== (3.2)
以下に示すコードを書き、実行した。
#sourcefile(read("src/3-2.jl"), file:"src/3-2.jl")
結果は以下のようになった。
#figure(
image("fig/fig5.svg", width: 70%),
caption: "課題3 (3.2) プログラムを実行した結果"
)
=== (3.3)
本課題は、次数 $n$ を十分に大きくすると、項を足し込んでも多項式の値の計算に寄与しなくなる原因を考えろというものである。
$sin(x)$ のマクローリン展開の $2k + 1$ 次の項は
$
(-1)^k x^(2k + 1) / (2k + 1)!
$
であるから $k$ が大きいとき、この項は $0$ に近くなる。
Julia では実数は浮動小数点数（IEEE754形式）で処理されるため、
絶対値が大きな値と小さな値とを加えた場合に小さい方の数値がもつ情報が失われる、いわゆる「情報落ち」が発生する。そのため項を足し込んでも多項式の値の計算に寄与しなくなる。
== 課題4
=== (4.1)
コードは以下のようになった。
#sourcefile(read("src/4-1.jl"), file:"src/4-1.jl")
=== (4.2)
コードは以下のようになった。
#sourcefile(read("src/4-2.jl"), file:"src/4-2.jl")
=== (4.3)
コードは以下のようになった。
#sourcefile(read("src/4-3.jl"), file:"src/4-3.jl")
=== (4.4)
与えられた条件のグラフを描画するために以下のコードを作成し、実行した。
なお、`myexp`、`myexp2`、`myexp3` の定義は省略している。
#sourcefile(read("src/4-4.jl"), file:"src/4-4.jl")
次に結果を以下に示す。
なお、左上、右上、左下、右下の順に：
- $n = 200$ で区間が $[-50, 50]$
- $n = 1000$ で区間が $[-50, 50]$
- $n = 200$ で区間が $[-500, 500]$
- $n = 1000$ で区間が $[-500, 500]$
のグラフを描画している。また、すべてのグラフにおいて $y$ 軸が片対数グラフである。
#figure(
image("fig/fig6.svg"),
caption: "課題4のプログラムを実行した結果"
)
|
|
https://github.com/donghoony/typst_editorial | https://raw.githubusercontent.com/donghoony/typst_editorial/main/main.typ | typst | MIT License | #import "template.typ": *
#import "result.typ": result_page
#import "colors.typ": *
#import "division_abstract.typ" : abstract_page
#import "problem_title.typ" : problem_text
#import "description.typ" : descriptions
#import "details.typ" : *
#set page(flipped: true)
#show: project.with(
title: "230622 모의대회 해설",
authors: (
"<NAME>",
),
logo: "images/balloon.png"
)
#result_page()
#for (div_num, problems, d) in (
("3", div3_problems, div3_descriptions),
("2", div2_problems, div2_descriptions),
("1", div1_problems, div1_descriptions)) {
abstract_page(
division: div_num,
problems: problems
)
for p in problems.enumerate() {
let (idx, problem) = p
let (number, title, diff, tier, tag) = problem
problem_text(div_num + number, title, tag)
descriptions(d.at(idx))
}
} |
https://github.com/Maso03/Bachelor | https://raw.githubusercontent.com/Maso03/Bachelor/main/Bachelorarbeit/chapters/timeline.typ | typst | MIT License | #import "@preview/timeliney:0.0.1"
#timeliney.timeline(
show-grid: true,
{
import timeliney: *
headerline(
group(([*KW28*], 1)), group(([*KW29*], 1)), group(([*KW30*], 1)),
group(([*KW31*], 1)), group(([*KW32*], 1)), group(([*KW33*], 1)), group(([*KW34*], 1)),
group(([*KW35*], 1)), group(([*KW36*], 1)), group(([*KW37*], 1))
)
taskgroup(title: [*Bachelorarbeit*], {
task("Projektbeschreibung", (0.5, 2), style: (stroke: 2pt + gray))
task("Lückenanalyse", (1, 2.5), style: (stroke: 2pt + gray))
task("Lösungsentwicklung", (2, 7), style: (stroke: 2pt + gray))
task("Conclusion", (7, 8.5), style: (stroke: 2pt + gray))
task("Introduction", (7, 8.5), style: (stroke: 2pt + gray))
task("Abstract", (7, 8.5), style: (stroke: 2pt + gray))
task("Finale Überarbeitung", (8.5, 9), style: (stroke: 2pt + gray))
})
milestone(
at: 8.5,
style: (stroke: (dash: "dashed")),
align(center, [
*Überarbeitung*\
28.08.2024
])
)
milestone(
at: 10,
style: (stroke: (dash: "dashed")),
align(center, [
*Abgabe*\
09.09.2024
])
)
}
)
|
https://github.com/liuguangxi/erdos | https://raw.githubusercontent.com/liuguangxi/erdos/master/Problems/typstdoc/figures/p321_2_1.typ | typst | #import "@preview/cetz:0.2.1"
#cetz.canvas(length: 6pt, {
import cetz.draw: *
let a = 6
let b = 18
let dx = a
let dy = calc.sqrt(3)*a
line(stroke: none, fill: orange.lighten(30%), close: true,
(a - dx, 0 - dy), (0.5*a - dx, 0.5*calc.sqrt(3)*a - dy), (-0.5*a - dx, 0.5*calc.sqrt(3)*a - dy), (-a - dx, 0 - dy), (-0.5*a - dx, -0.5*calc.sqrt(3)*a - dy), (0.5*a - dx, -0.5*calc.sqrt(3)*a - dy)
)
line(stroke: 2pt, close: true,
(b, 0), (0.5*b, 0.5*calc.sqrt(3)*b), (-0.5*b, 0.5*calc.sqrt(3)*b), (-b, 0), (-0.5*b, -0.5*calc.sqrt(3)*b), (0.5*b, -0.5*calc.sqrt(3)*b)
)
line(stroke: purple+1.5pt, mark: (end: "stealth", fill: purple),
(-dx, -dy), (-dx+2, -dy+3*calc.sqrt(3)*2)
)
})
|
|
https://github.com/Myriad-Dreamin/tinymist | https://raw.githubusercontent.com/Myriad-Dreamin/tinymist/main/docs/tinymist/principles.typ | typst | Apache License 2.0 | #import "mod.typ": *
#show: book-page.with(title: "Tinymist Principles")
Four principles are followed.
== Multiple Actors
The main component, #link("https://github.com/Myriad-Dreamin/tinymist/tree/main/crates/tinymist")[tinymist], starts as a thread or process, obeying the #link("https://microsoft.github.io/language-server-protocol/")[Language Server Protocol]. tinymist will bootstrap multiple actors, each of which provides some typst feature.
The each actor holds and maintains some resources exclusively. For example, the compile server actor holds the well known ```rs trait World``` resource.
The actors communicate with each other by channels. An actor should own many receivers as its input, and many senders as output. The actor will take input from receivers _sequentially_. For example, when some LSP request or notification is coming as an LSP event, multiple actors serve the event collaboratively, as shown in @fig:actor-serve-lsp-requests.
#figure(
align(
center,
diagram(
edge-stroke: 0.85pt,
node-corner-radius: 3pt,
edge-corner-radius: 4pt,
mark-scale: 80%,
node((0, 0), [LSP Requests/\ Notifications\ (Channel)], fill: colors.at(0), shape: fletcher.shapes.hexagon),
node((2, +1), [RenderActor], fill: colors.at(1)),
node((2, 0), align(center)[`CompileServerActor`], fill: colors.at(1)),
node((2, -1), [`LspActor` (Main Thread)], fill: colors.at(1)),
node((4, 0), [LSP Responses\ (Channel)], fill: colors.at(2), shape: fletcher.shapes.hexagon),
edge((0, 0), "r,u,r", "-}>"),
edge((2, -1), "r,d,r", "-}>"),
edge((2, 0), "rr", "-}>"),
edge((2, 1), "r,u,r", "-}>"),
edge((2, 0), (2, 1), align(center)[Rendering\ Requests], "-}>"),
edge((2, -1), (2, 0), align(center)[Analysis\ Requests], "-}>"),
),
),
caption: [The IO Graph of actors serving a LSP request or notification],
) <fig:actor-serve-lsp-requests>
A _Hover_ request is taken as example of that events.
A global unique `LspActor` takes the event and _mutates_ a global server state by the event. If the event requires some additional code analysis, it is converted into an analysis request, #link("https://github.com/search?q=repo%3AMyriad-Dreamin/tinymist%20CompilerQueryRequest&type=code")[```rs struct CompilerQueryRequest```], and pushed to the actors owning compiler resources. Otherwise, `LspActor` responds to the event directly. Obviously, the _Hover_ on code request requires code analysis.
The `CompileServerActor`s are created for workspaces and main entries (files/documents) in workspaces. When a compiler query is coming, a subset of that actors will take it and give project-specific responses, combining into a final concluded LSP response. Some analysis requests even require rendering features, and those requests will be pushed to the actors owning rendering resources. If you enable the periscope feature, a `Hover` on content request requires rendering on documents.
The `RenderActor`s don't do compilations, but own project-specific rendering cache. They are designed for rendering documents in _low latency_. This is the last sink of `Hover` requests. A `RenderActor` will receive an additional compiled `Document` object, and render the compiled frames in needed. After finishing rendering, a response attached with the rendered picture is sent to the LSP response channel intermediately.
== Multi-level Analysis
he most critical features are lsp functions, built on the #link("https://github.com/Myriad-Dreamin/tinymist/tree/main/crates/tinymist-query")[tinymist-query] crate. To achieve higher concurrency, functions are classified into different levels of analysis.
// + `query_token_cache` – `TokenRequest` – locks and accesses token cache.
+ `query_source` – `SyntaxRequest` – locks and accesses a single source unit.
+ `query_world` – `SemanticRequest` – locks and accesses multiple source units.
+ `query_state` – `StatefulRequest` – acquires to accesses a specific version of compile results.
When an analysis request is coming, tinymist _upgrades_ it to a suitable level as needed, as shown in @fig:analysis-upgrading-level. A higher level requires to hold more resources and takes longer time to prepare.
#let pg-node = node.with(corner-radius: 2pt, shape: "rect");
#figure(
align(
center,
diagram(
node-stroke: 1pt,
edge-stroke: 1pt,
edge("-|>", align(center)[Analysis\ Request], label-pos: 0.1),
pg-node((1, 0), [Syntax\ Level]),
edge("-|>", []),
pg-node((3, 0), [Semantic\ Level]),
edge("-|>"),
pg-node((5, 0), [Stateful\ Level]),
edge((5, 0), (6, 0), "-|>", align(center)[Analysis\ Response], label-pos: 1),
for i in (1, 3, 5) {
edge((i, 0), (i, -0.5), (5.5, -0.5), (5.6, 0), "-|>")
},
edge(
(0.3, 0.4),
(0.3, 0),
"-|>",
align(center)[clone #typst-func("Source")],
label-anchor: "center",
label-pos: -0.5,
),
edge(
(2, 0.4),
(2, 0),
"-|>",
align(center)[snapshot ```rs trait World```],
label-anchor: "center",
label-pos: -0.5,
),
edge(
(4, 0.4),
(4, 0),
"-|>",
align(center)[acquire #typst-func("Document")],
label-anchor: "center",
label-pos: -0.5,
),
),
),
caption: [The analyzer upgrades the level to acquire necessary resources],
) <fig:analysis-upgrading-level>
== Optional Non-LSP Features
All non-LSP features in tinymist are *optional*. They are optional, as they can be disabled *totally* on compiling the tinymist binary. The significant features are enabled by default, but you can disable them with feature flags. For example, `tinymist` provides preview server features powered by `typst-preview`.
== Minimal Editor Frontends
Leveraging the interface of LSP, tinymist provides frontends to each editor, located in the #link("https://github.com/Myriad-Dreamin/tinymist/tree/main/editors")[editor folders]. They are minimal, meaning that LSP should finish its main LSP features as many as possible without help of editor frontends. The editor frontends just enhances your code experience. For example, the vscode frontend takes responsibility on providing some nice editor tools. It is recommended to install these editors frontend for your editors.
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https://github.com/0x6e66/hbrs-typst | https://raw.githubusercontent.com/0x6e66/hbrs-typst/main/template/titlepage.typ | typst | #import "../ads/meta.typ": *
#import "utils.typ": *
#let titlepage = {
set page(
background: {
place(center + horizon, circle(radius: 12cm, fill: rgb("#009fd6"), stroke: none), dx: 16cm)
place(center + horizon, circle(radius: 12cm, fill: rgb("#009fd6"), stroke: none), dx: -16cm)
place(center + horizon, circle(radius: 8.5cm, fill: rgb("#ffffff"), stroke: none), dx: -16cm)
},
margin: (
left: 2cm,
right: 2cm,
top: 2.5cm,
bottom: 2cm,
),
)
grid(
columns: (20%, 80%),
gutter: 10pt,
{
place(center + horizon, circle(radius: .5cm, fill: rgb("#009fd6"), stroke: none), dx: 1.2cm, dy: -1cm)
place(center + horizon, circle(radius: .5cm, fill: rgb("#009fd6"), stroke: none), dx: 0cm, dy: -1cm)
place(center + horizon, circle(radius: .3cm, fill: rgb("#ffffff"), stroke: none), dx: 0cm, dy: -1cm)
},
align(left, text([*Hochschule \ Bonn-Rhein-Sieg* \ _University of Applied Sciences_ \ \ *Fachbereich Informatik* \ _Department of Computer Science_])),
)
v(2cm)
align(
center,
text(
size: 25pt,
language_switch(thesis_subject_type),
)
)
v(-0.2cm)
align(
center,
text(
size: 15pt,
{
if language == "de" {
[im #text(thesis_type)-Studiengang #language_switch(thesis_study_course)]
}else if language == "en" {
[for the #text(thesis_type)-course #language_switch(thesis_study_course)]
}
}
)
)
v(2cm)
align(
center,
text(
size: 25pt,
language_switch(thesis_title),
)
)
if language_switch(thesis_sub_title) != "" {
v(-0.8cm)
align(
center,
text(
size: 15pt,
[-],
)
)
v(-0.5cm)
align(
center,
text(
size: 18pt,
language_switch(thesis_sub_title),
)
)
}
v(0.8cm)
align(
center,
text(
size: 15pt,
{
if language == "de" {
[von \ *#author_first_name #author_last_name*]
}else if language == "en" {
[by \ *#author_first_name #author_last_name*]
}
}
)
)
align(
left + bottom,
text(
size: 12pt,
{
table(
columns: (auto, auto),
stroke: none,
align: (x, y) => (right, left).at(x),
{
if language == "de" {"Erstprüfer"}
else if language == "en" {"First Supervisor"}
}, thesis_supervisor_first,
{
if language == "de" {"Zweitprüfer"}
else if language == "en" {"Second Supervisor"}
}, thesis_supervisor_second,
{
if language == "de" {"Betreuer"}
else if language == "en" {"Third Supervisor"}
}, thesis_supervisor_third,
{
if language == "de" {"Abgegeben am"}
else if language == "en" {"Date of submission"}
}, today,
{
if language == "de" {"Matrukelnummer, Kurs"}
else if language == "en" {"Matrukelnumber, Course"}
}, [#author_matrikel_number, #author_course]
)
}
)
)
}
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https://github.com/MilanR312/ugent_typst_template | https://raw.githubusercontent.com/MilanR312/ugent_typst_template/main/template/prependices.typ | typst | MIT License | // add all prependices here like "woord vooraf"
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Subsets and Splits