File size: 4,437 Bytes
cc646d3 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 |
from typing import Iterable, Callable
from sympy import Eq, linsolve, simplify, latex, Expr, Symbol
class CannotCalculate(Exception):
pass
class BadInput(Exception):
pass
CONSTANT_TERM_KEY = "constant_term"
class GetIntegrate:
integrate_result_classes: dict[str, Expr | None]
def integrate_and_separate(
self, integrate_formula: Expr, integrate_args: tuple
) -> dict[str, Expr]:
"""
解积分，分离各项
"""
raise NotImplementedError(
"该函数已弃用，请使用 GetIntegrateFromData 类。如果想要使用它预处理，见 pre/old_solution.py"
)
# # 解积分
# res = integrate(integrate_formula, integrate_args)
# res = expand(expand(res))
# print(f'integrate[0,1] {integrate_formula}={res}')
#
# # 分离各项
# di = {}
# exprs = []
# for key, expr in self.integrate_result_classes.items():
# if key == CONSTANT_TERM_KEY:
# continue
# exprs.append(expr)
# di[key] = res.coeff(expr)
#
# constant_term, _ = res.as_independent(*exprs)
# return {**di, CONSTANT_TERM_KEY: constant_term}
def get_integrate_args(self, try_arg):
"""
:return: integrand_function, (independent_variable, lower_limit, upper_limit)
被积函数, (自变量, 下限, 上限)
"""
raise NotImplementedError()
def tries(self, try_arg):
"""
:return: {term_name: coefficient_of_the_term}
{该项的名称: 该项系数}
"""
return self.integrate_and_separate(*self.get_integrate_args(try_arg))
def get_latex(self, try_arg, subs):
expr, args = self.get_integrate_args(try_arg)
expr = simplify(expr).subs(subs)
sym, low, high = args
return r"\int_{%s}^{%s} {%s} \mathrm{d} {%s}" % (
low,
high,
latex(simplify(expr)),
sym,
)
class GetIntegrateFromData(GetIntegrate):
data: dict[object, dict[str, Expr]]
def tries(self, try_arg):
return self.data[try_arg]
class Solution:
get_integrate: GetIntegrate
# gui: Pattern
get_tries_args: Callable[[], Iterable[Expr]]
"""
Generate try_arg for each trial
生成每一次尝试的 try_arg
"""
symbols: tuple[Symbol, ...]
"""
The undetermined variable to solve.
要求的待定系数
"""
integrate_result_classes_eq: dict[str, Expr]
"""
{term_name: coefficient}
The value to which each term's coefficient is equal.
每个项系数分别要等于的值
"""
check_sgn: Callable
"""
Input: unpacked solution of undetermined variables;
Output: 0 (cannot determine), 1 or -1 (can determine; 1 and -1 are interchangeable for greater or less than).
Module sgntools provides lin_func_sgn and sq_func_sgn. Call help() for further details.
输入：解包的待定系数的值列表；
输出: 0(无法确定), 1或-1(可以确定, 1和-1哪个代表大于、哪个代表小于, 是可以互换的)
sgntools 模块提供了 lin_func_sgn 和 sq_func_sgn 函数，详见 help()
"""
# check_sgn: Callable[?, 1 | 0 | -1]
def get_symbols(self, separate_result):
"""凑积分结果系数"""
system = [
Eq(int_term, self.integrate_result_classes_eq[key])
for key, int_term in separate_result.items()
]
print(f"{system=}")
return linsolve(system, *self.symbols)
def try_times(self) -> tuple[Expr, dict, int] | tuple[None, None, None]:
for try_arg in self.get_tries_args():
separate = self.get_integrate.tries(try_arg)
for symbol_solution in self.get_symbols(separate):
if sgn := self.check_sgn(*symbol_solution):
return try_arg, dict(zip(self.symbols, symbol_solution)), sgn
return None, None, None
def get_latex_ans(self):
"""
:return: None if it can't be solved; Otherwise, LaTeX (without "$$")
"""
raise NotImplementedError()
# 插件注册（历史遗留问题）
solutions = {}
solution_sort = []
def register(name, solution, top=False):
solutions[name] = solution
if top:
solution_sort.insert(0, name)
else:
solution_sort.append(name)
|