|
define([ |
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"require", |
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"./sympy_functions", |
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"./sympy_assumptions", |
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], function (requirejs, sympy_functions, sympy_assumptions) { |
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return { |
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'name' : 'SymPy', |
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'sub-menu' : [ |
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{ |
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'name' : 'Setup', |
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'snippet' : [ |
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'from __future__ import print_function, division', |
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'from sympy import *', |
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'a, s, t, u, v, w, x, y, z = symbols("a, s, t, u, v, w, x, y, z")', |
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'k, m, n = symbols("k, m, n", integer=True)', |
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'f, g, h = symbols("f, g, h", cls=Function)', |
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'init_printing()', |
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], |
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}, |
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{ |
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'name' : 'Documentation', |
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'external-link' : 'http://docs.sympy.org/latest/index.html', |
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}, |
|
'---', |
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{ |
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'name' : 'Constants', |
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'sub-menu' : [ |
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{ |
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'name' : '1', |
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'snippet' : ['S(1)',], |
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}, |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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{ |
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'name' : '1/2', |
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'snippet' : ['S(1)/2',], |
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}, |
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{ |
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'name' : 'Rational numbers', |
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'snippet' : ['Rational(3, 7)',], |
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}, |
|
'---', |
|
{ |
|
'name' : 'Base of natural logarithm, \\(e\\)', |
|
'snippet' : ['E',], |
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}, |
|
{ |
|
'name' : 'Unit imaginary number, \\(i\\)', |
|
'snippet' : ['I',], |
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}, |
|
{ |
|
'name' : 'Geometric constant, \\(\\pi\\)', |
|
'snippet' : ['pi',], |
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}, |
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{ |
|
'name' : 'Golden ratio, \\(\\phi\\)', |
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'snippet' : ['GoldenRatio',], |
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}, |
|
{ |
|
'name' : 'Euler-Mascheroni constant, \\(\\gamma\\)', |
|
'snippet' : ['EulerGamma',], |
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}, |
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{ |
|
'name' : 'Catalan\'s constant, \\(K\\)', |
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'snippet' : ['Catalan',], |
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}, |
|
'---', |
|
{ |
|
'name' : 'Infinity, \\(\\infty\\)', |
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'snippet' : ['oo',], |
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}, |
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|
|
|
|
|
|
|
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{ |
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'name' : 'Complex infinity, \\(\\tilde{\\infty}\\)', |
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'snippet' : ['zoo'], |
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}, |
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{ |
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'name' : 'NaN', |
|
'snippet' : ['nan',], |
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}, |
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], |
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}, |
|
sympy_functions, |
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{ |
|
'name' : 'Calculus', |
|
'sub-menu' : [ |
|
{ |
|
'name' : 'Differentiate once', |
|
'snippet' : [ |
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'expr = exp(x**2)', |
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'deriv = diff(expr, x)', |
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], |
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}, |
|
{ |
|
'name' : 'Differentiate multiple times', |
|
'snippet' : [ |
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'expr = x**4', |
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'deriv = diff(expr, x, 3)', |
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], |
|
}, |
|
{ |
|
'name' : 'Mixed partial derivatives', |
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'snippet' : [ |
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'expr = exp(x*y*z)', |
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'deriv = diff(expr, x, y, 2, z, 4)', |
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], |
|
}, |
|
{ |
|
'name' : 'Finite differences', |
|
'snippet' : [ |
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'dx0, dx1 = symbols("dx0, dx1")', |
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'formula = as_finite_diff(f(x).diff(x), [x-dx0, x, x+dx1])', |
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], |
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}, |
|
'---', |
|
{ |
|
'name' : 'Indefinite integral', |
|
'snippet' : [ |
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'integral = integrate(cos(x), x)', |
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], |
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}, |
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{ |
|
'name' : 'Definite integral', |
|
'snippet' : [ |
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'integral = integrate(exp(-x), (x, 0, oo))', |
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], |
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}, |
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{ |
|
'name' : 'Double integral', |
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'snippet' : [ |
|
'integral = integrate(exp(-x**2-y**2), (x, -oo, oo), (y, -oo, oo))', |
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], |
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}, |
|
'---', |
|
{ |
|
'name' : 'Limits', |
|
'snippet' : [ |
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'lim = limit(sin(x)/x, x, 0, "+")', |
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], |
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}, |
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{ |
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'name' : 'Series expansion', |
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'snippet' : [ |
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'expr = exp(sin(x))', |
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'ser = series(expr, x, 0, 6)', |
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], |
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}, |
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{ |
|
'name' : 'Series expansion, removing order term', |
|
'snippet' : [ |
|
'expr = exp(sin(x))', |
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'ser = series(expr, x, 0, 6).removeO()', |
|
], |
|
}, |
|
{ |
|
'name' : 'Summations', |
|
'snippet' : [ |
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'ell_min,ell,ell_max = symbols("ell_min,ell,ell_max", integer=True)', |
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'summ = summation((2*ell + 1), (ell, ell_min, ell_max))', |
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], |
|
}, |
|
], |
|
}, |
|
|
|
{ |
|
'name' : 'Solvers', |
|
'sub-menu' : [ |
|
{ |
|
'name' : 'Solve for one variable', |
|
'snippet' : [ |
|
'expr = x**4 - 4*x**3 + 2*x**2 - x', |
|
'eqn = Eq(expr, 0)', |
|
'soln = solve(eqn, x)', |
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], |
|
}, |
|
{ |
|
'name' : 'Solve for two variables', |
|
'snippet' : [ |
|
'eqns = Eq(x + y, 4), Eq(x*y, 3)', |
|
'soln = solve(eqns, [x,y])', |
|
], |
|
}, |
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{ |
|
'name' : 'Solve differential equation', |
|
'snippet' : [ |
|
'expr = f(x).diff(x, x) + 9*f(x)', |
|
"eqn = Eq(expr, 1) # f''(x) + 9f(x) = 1", |
|
'soln = dsolve(eqn, f(x))', |
|
], |
|
}, |
|
], |
|
}, |
|
{ |
|
'name' : 'Manipulating expressions', |
|
'sub-menu' : [ |
|
{ |
|
'name' : 'Simplify', |
|
'snippet' : [ |
|
'expr = (x**3 + x**2 - x - 1)/(x**2 + 2*x + 1)', |
|
'expr = simplify(expr)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Refine, using assumptions', |
|
|
|
|
|
|
|
|
|
|
|
'sub-menu' : [ |
|
{ |
|
'name' : 'Refine', |
|
'snippet' : [ |
|
'expr = exp(pi*I*2*(x+y))', |
|
'assumption = Q.integer(x) & Q.integer(y)', |
|
'expr = refine(expr, assumption)', |
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], |
|
}, |
|
{ |
|
'name' : 'Refine in context manager', |
|
'snippet' : [ |
|
'expr = exp(pi*I*2*(x+y))', |
|
'with assuming(Q.integer(x) & Q.integer(y)):', |
|
' expr = refine(expr)', |
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], |
|
}, |
|
sympy_assumptions, |
|
], |
|
}, |
|
{ |
|
'name' : 'Expansion', |
|
'sub-menu' : [ |
|
{ |
|
'name' : 'Expand basic expressions', |
|
'snippet' : [ |
|
'expr = (x + 2)*(x - 3)', |
|
'expr = expand(expr)', |
|
], |
|
}, |
|
'---', |
|
{ |
|
'name' : 'Expand, including complex parts', |
|
'snippet' : [ |
|
'expr = cos(x)', |
|
'expr = expand(expr, complex=True)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Expand, including functions', |
|
'snippet' : [ |
|
'expr = gamma(x+3)', |
|
'expr = expand(expr, func=True)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Expand, including trig', |
|
'snippet' : [ |
|
'expr = sin(x+y)*(x+y)', |
|
'expr = expand(expr, trig=True)', |
|
], |
|
}, |
|
'---', |
|
{ |
|
'name' : 'Expand only real and imaginary parts', |
|
'snippet' : [ |
|
'expand_complex(x)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Expand only functions', |
|
'snippet' : [ |
|
'expr = gamma(x + 2)', |
|
'expr = expand_func(expr)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Expand only hypergeometric functions', |
|
'snippet' : [ |
|
'expr = hyper([1,1], [1,], z) + gamma(z)', |
|
'expr = hyperexpand(expr)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Expand only logarithms', |
|
'snippet' : [ |
|
'a, b = symbols("a, b", positive=True)', |
|
'expr = log(a**2*b)', |
|
'expr = expand_log(expr)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Expand only multiplication over addition', |
|
'snippet' : [ |
|
'expr = y*(x + z)', |
|
'expr = expand_mul(expr)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Expand only multinomials', |
|
'snippet' : [ |
|
'expr = (x + y + z)**3', |
|
'expr = expand_multinomial(expr)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Expand only powers of multiplied bases', |
|
'snippet' : [ |
|
'a, b = symbols("a, b", positive=True)', |
|
'expr = (a*b)**z', |
|
'expr = expand_power_base(expr)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Expand only addition in exponents', |
|
'snippet' : [ |
|
'expr = x**(y + 2)', |
|
'expr = expand_power_exp(expr)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Expand only trig', |
|
'snippet' : [ |
|
'expr = sin(x+y)*(x+y)', |
|
'expr = expand_trig(expr)', |
|
], |
|
}, |
|
], |
|
}, |
|
{ |
|
'name' : 'Collect terms', |
|
'sub-menu' : [ |
|
{ |
|
'name' : 'Collect as coefficients of one factor', |
|
'snippet' : [ |
|
'expr = y*x**2 + z*x**2 + t*x - 2*x + 3', |
|
'expr = collect(expr, x)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Collect as coefficients of multiple factors', |
|
'snippet' : [ |
|
'expr = x**2 + y*x**2 + x*y + y + z*y', |
|
'expr = collect(expr, [x, y])', |
|
], |
|
}, |
|
{ |
|
'name' : 'Collect with respect to wild card', |
|
'snippet' : [ |
|
'w = Wild("w")', |
|
'expr = z*x**y - t*z**y', |
|
'expr = collect(expr, w**y)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Collect and apply function to each coefficient', |
|
'snippet' : [ |
|
'expr = expand((x + y + 1)**3)', |
|
'expr = collect(expr, x, factor)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Recursively collect', |
|
'snippet' : [ |
|
'expr = (x**2*y + x*y + x + y)/(x*y + z*y)', |
|
'expr = rcollect(expr, y)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Collect constants', |
|
'snippet' : [ |
|
'expr = sqrt(3)*x + sqrt(7)*x + sqrt(3) + sqrt(7)', |
|
'expr = collect_const(expr)', |
|
], |
|
}, |
|
], |
|
}, |
|
{ |
|
'name' : 'Substitutions and replacements', |
|
'sub-menu' : [ |
|
{ |
|
'name' : 'Substitute one subexpression for another', |
|
'snippet' : [ |
|
'expr = 1 + x*y', |
|
'expr = expr.subs(x, pi)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Substitute multiple subexpressions successively', |
|
'snippet' : [ |
|
'expr = (x+y)/y', |
|
'substitutions = [(x+y, y), (y, x+y)]', |
|
'expr = expr.subs(substitutions)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Substitute multiple subexpressions simultaneously', |
|
'snippet' : [ |
|
'expr = (x+y)/y', |
|
'substitutions = [(x+y, y), (y, x+y)]', |
|
'expr = expr.subs(substitutions, simultaneous=True)', |
|
], |
|
}, |
|
'---', |
|
{ |
|
'name' : 'Replace one object with another', |
|
'snippet' : [ |
|
'expr = 1 + x*y', |
|
'expr = expr.replace(x, pi)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Replace one object with some function of its arguments', |
|
'snippet' : [ |
|
'expr = log(sin(x)) + tan(sin(x**2))', |
|
'expr = expr.replace(sin, lambda arg: sin(2*arg))', |
|
], |
|
}, |
|
{ |
|
'name' : 'Replace a pattern with an object', |
|
'snippet' : [ |
|
'# Note: `exclude=` specifies that the Wild cannot match any item in the list', |
|
'a, b = symbols("a, b", cls=Wild, exclude=[x,y])', |
|
'expr = 2*x + y + z', |
|
'wild = a*x + b', |
|
'replacement = b - a', |
|
'# Note: `exact=True` demands that all Wilds have nonzero matches', |
|
'expr = expr.replace(wild, replacement, exact=True)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Replace a pattern with some function of that object', |
|
'snippet' : [ |
|
'a = symbols("a", cls=Wild, exclude=[])', |
|
'expr = log(sin(x)) + tan(sin(x**2))', |
|
'expr.replace(sin(a), lambda a: sin(2*a))', |
|
], |
|
}, |
|
{ |
|
'name' : 'Replace anything with some function of that thing', |
|
'snippet' : [ |
|
'g = 2*sin(x**3)', |
|
'g.replace(lambda expr: expr.is_Function, lambda expr: expr**2)', |
|
], |
|
}, |
|
'---', |
|
{ |
|
'name' : 'Replace exact subexpressions', |
|
'snippet' : [ |
|
'expr = x**2 + x**4', |
|
'replacements = {x**2: y}', |
|
'expr = expr.xreplace(replacements)', |
|
], |
|
}, |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
], |
|
}, |
|
{ |
|
'name' : 'Evaluation', |
|
'sub-menu' : [ |
|
{ |
|
'name' : 'Evaluate numerically to arbitrary precision', |
|
'snippet' : [ |
|
'expr = x * sqrt(8)', |
|
'precision = 50', |
|
'val = N(expr, precision, subs={x:2.4})', |
|
], |
|
}, |
|
{ |
|
'name' : 'Evaluate numerically to python float', |
|
'snippet' : [ |
|
'expr = x * sqrt(8)', |
|
'val = float(expr.subs([(x, 2.4)]))', |
|
], |
|
}, |
|
{ |
|
'name' : 'Create numpy function for efficient evaluation', |
|
'snippet' : [ |
|
'import numpy', |
|
'a = numpy.arange(10)', |
|
'expr = sin(x)', |
|
'f = lambdify(x, expr, "numpy")', |
|
'vals = f(a)', |
|
], |
|
}, |
|
], |
|
}, |
|
'---', |
|
{ |
|
'name' : 'Polynomials', |
|
'sub-menu' : [ |
|
{ |
|
'name' : 'Factor polynomial over rationals', |
|
'snippet' : [ |
|
'expr = x**3 - x**2 + x - 1', |
|
'expr = factor(expr)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Collect common powers of a term', |
|
'snippet' : [ |
|
'expr = x*y + x - 3 + 2*x**2 - z*x**2 + x**3', |
|
'expr = collect(expr, x)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Extract coefficient of a term', |
|
'snippet' : [ |
|
'expr = 3+2*x+4*x**2', |
|
'expr = expr.coeff(x**2)', |
|
], |
|
}, |
|
], |
|
}, |
|
{ |
|
'name' : 'Rational functions', |
|
'sub-menu' : [ |
|
{ |
|
'name' : 'Cancel', |
|
'snippet' : [ |
|
'expr = (x**2 + 2*x + 1)/(x**2 + x)', |
|
'expr = cancel(expr)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Decompose into partial fractions', |
|
'snippet' : [ |
|
'expr = (4*x**3 + 21*x**2 + 10*x + 12)/(x**4 + 5*x**3 + 5*x**2 + 4*x)', |
|
'expr = apart(expr)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Join over common denominator', |
|
'snippet' : [ |
|
'expr = 1/x + 1/y', |
|
'expr = ratsimp(expr)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Remove square roots from denominator', |
|
'snippet' : [ |
|
'expr = 1/(1+I)', |
|
'expr = radsimp(expr)', |
|
], |
|
}, |
|
], |
|
}, |
|
{ |
|
'name' : 'Powers', |
|
'sub-menu' : [ |
|
{ |
|
'name' : 'Important caveats', |
|
'external-link' : 'http://docs.sympy.org/dev/tutorial/simplification.html#powers' |
|
}, |
|
'---', |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
{ |
|
'name' : 'Simplify powers for general arguments', |
|
'snippet' : [ |
|
'powsimp(x**y * x**z)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Simplify powers, forcing assumptions', |
|
'snippet' : [ |
|
'powsimp(x**y * x**z, force=True)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Expand powers by exponent for general arguments', |
|
'snippet' : [ |
|
'expand_power_exp(x**(y + z))', |
|
], |
|
}, |
|
{ |
|
'name' : 'Expand powers of multiplied bases, forcing assumptions', |
|
'snippet' : [ |
|
'expand_power_base((x*y)**z, force=True)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Collect exponents on powers for general arguments', |
|
'snippet' : [ |
|
'powdenest((x**y)**z)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Collect exponents on powers, forcing assumptions', |
|
'snippet' : [ |
|
'powdenest((x**y)**z, force=True)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Collect exponents on powers, forcing assumptions and polar simplifications', |
|
'snippet' : [ |
|
'powdenest((z**a)**b, force=True, polar=True)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Denest square-roots', |
|
'snippet' : [ |
|
'sqrtdenest(sqrt(5 + 2*sqrt(6)))', |
|
], |
|
}, |
|
], |
|
}, |
|
{ |
|
'name' : 'Exponentials and Logarithms', |
|
'sub-menu' : [ |
|
{ |
|
'name' : 'Important caveats', |
|
'external-link' : 'http://docs.sympy.org/dev/tutorial/simplification.html#exponentials-and-logarithms' |
|
}, |
|
'---', |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
{ |
|
'name' : 'Combine exponentials', |
|
'snippet' : [ |
|
'powsimp(exp(y) * exp(z))', |
|
], |
|
}, |
|
{ |
|
'name' : 'Expand logarithms for general arguments', |
|
'snippet' : [ |
|
'expand_log(log(x*y))', |
|
], |
|
}, |
|
{ |
|
'name' : 'Expand logarithms, forcing assumptions', |
|
'snippet' : [ |
|
'expand_log(log(z**2), force=True)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Combine logarithms for general arguments', |
|
'snippet' : [ |
|
'logcombine(log(x) + z*log(y))', |
|
], |
|
}, |
|
{ |
|
'name' : 'Combine logarithms, forcing assumptions', |
|
'snippet' : [ |
|
'logcombine(log(x) + z*log(y))', |
|
], |
|
}, |
|
{ |
|
'name' : 'Simplification, possibly to trig functions', |
|
'snippet' : [ |
|
'exptrigsimp(exp(z) + exp(-z))', |
|
], |
|
}, |
|
], |
|
}, |
|
{ |
|
'name' : 'Trigonometric functions', |
|
'sub-menu' : [ |
|
{ |
|
'name' : 'Expansion', |
|
'snippet' : [ |
|
'expr = sin(x + y)', |
|
'expr = expand(expr, trig=True)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Simplification', |
|
'snippet' : [ |
|
'expr = sin(x)**4 - 2*cos(x)**2*sin(x)**2 + cos(x)**4', |
|
'expr = trigsimp(expr)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Simplification, possibly to exponentials', |
|
'snippet' : [ |
|
'expr = cosh(z) - sinh(z)', |
|
'expr = exptrigsimp(expr)', |
|
], |
|
}, |
|
], |
|
}, |
|
{ |
|
'name' : 'Miscellaneous', |
|
'sub-menu' : [ |
|
{ |
|
'name' : 'Simplify factorials', |
|
'snippet' : [ |
|
'expr = factorial(n)/factorial(n - 3)', |
|
'expr = combsimp(expr)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Simplify binomials', |
|
'snippet' : [ |
|
'expr = binomial(n+1, k+1)/binomial(n, k)', |
|
'expr = combsimp(expr)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Simplify numerical expressions to exact values', |
|
'snippet' : [ |
|
'nsimplify(4.0/(1+sqrt(5.0)), constants=[GoldenRatio,])', |
|
], |
|
}, |
|
{ |
|
'name' : 'Expand gamma functions', |
|
'snippet' : [ |
|
'expr = gamma(z+3)', |
|
'expr = expand_func(expr)', |
|
], |
|
}, |
|
{ |
|
'name' : 'Simplify Bessel functions', |
|
'snippet' : [ |
|
'expr = besselj(x, z*polar_lift(-1))', |
|
'expr = besselsimp(expr)', |
|
], |
|
}, |
|
], |
|
}, |
|
], |
|
}, |
|
], |
|
}; |
|
}); |
|
|
