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| from sympy.abc import a, b, c, x | |
| from output_util import to_latex, sign2cmp | |
| from sgntools import sq_func_sgn | |
| from solution import * | |
| class PiIntegrate(GetIntegrateFromData): | |
| # sympy 算力不够，以下由 MMA 算出 | |
| # PiIF[n_] := | |
| # Collect[ Collect[ | |
| # PowerExpand[ Expand[ | |
| # Integrate[x^n*(1 - x)^n*(a + b x + c x^2)/(x^2 + 1), | |
| # {x, 0, 1}] | |
| # ]], | |
| # Log[2]], Pi] | |
| data = { | |
| 1: { | |
| "pi_term": (a - b - c) / 4, | |
| "log2_term": (a + b - c) / 2, | |
| CONSTANT_TERM_KEY: -a + b / 2 + 7 * c / 6, | |
| }, | |
| 2: { | |
| "pi_term": -b / 2, | |
| "log2_term": a - c, | |
| CONSTANT_TERM_KEY: (-2 * a / 3 + 19 * b / 12 + 7 * c / 10), | |
| }, | |
| 3: { | |
| "pi_term": (-a - b + c) / 2, | |
| "log2_term": a - b - c, | |
| CONSTANT_TERM_KEY: 53 * a / 60 + 34 * b / 15 - 92 * c / 105, | |
| }, | |
| 4: { | |
| "pi_term": -a + c, | |
| "log2_term": 2 * b, | |
| CONSTANT_TERM_KEY: 22 * a / 7 + 233 * b / 168 - 1979 * c / 630, | |
| }, | |
| 5: { | |
| "pi_term": -a + b + c, | |
| "log2_term": 2 * (-a - b + c), | |
| CONSTANT_TERM_KEY: 11411 * a / 2520 - 4423 * b / 2520 - 41837 * c / 9240, | |
| }, | |
| 6: { | |
| "pi_term": 2 * b, | |
| "log2_term": -4 * a + 4 * c, | |
| CONSTANT_TERM_KEY: (38429 * a) / 13860 | |
| - (174169 * b) / 27720 | |
| - (35683 * c) / 12870, | |
| }, | |
| 7: { | |
| "pi_term": 2 * (a + b - c), | |
| "log2_term": 4 * (-a + b + c), | |
| CONSTANT_TERM_KEY: -((421691 * a) / 120120) | |
| - (407917 * b) / 45045 | |
| + (31627 * c) / 9009, | |
| }, | |
| 8: { | |
| "pi_term": 4 * (a - c), | |
| "log2_term": 8 * b, | |
| CONSTANT_TERM_KEY: -(188684 * a) / 15015 | |
| - (1332173 * b) / 240240 | |
| + (3849155 * c) / 306306, | |
| }, | |
| 9: { | |
| "pi_term": 4 * (a - b - c), | |
| "log2_term": 8 * (-c + a + b), | |
| CONSTANT_TERM_KEY: -((17069771 * a) / 942480) | |
| + (86025349 * b) / 12252240 | |
| + (4216233689 * c) / 232792560, | |
| }, | |
| 10: { | |
| "pi_term": -8 * b, | |
| "log2_term": 16 * (a - c), | |
| CONSTANT_TERM_KEY: -((1290876029 * a) / 116396280) | |
| + (325039733 * b) / 12932920 | |
| + (117352369 * c) / 10581480, | |
| }, | |
| 11: { | |
| "pi_term": 8 * (-a - b + c), | |
| "log2_term": 16 * (a - b - c), | |
| CONSTANT_TERM_KEY: (817240769 * a) / 58198140 | |
| + (4216233641 * b) / 116396280 | |
| - (37593075209 * c) / 2677114440, | |
| }, | |
| 12: { | |
| "pi_term": -16 * a + 16 * c, | |
| "log2_term": -32 * b, | |
| CONSTANT_TERM_KEY: (431302721 * a) / 8580495 | |
| + (9135430531 * b) / 411863760 | |
| - (5902037233 * c) / 117417300, | |
| }, | |
| } | |
| def get_integrate_args(self, n): | |
| return x**n * (1 - x) ** n * (a + b * x + c * x**2) / (1 + x**2), (x, 0, 1) | |
| class PiSolution(Solution): | |
| def __init__(self, p, q): | |
| self.p = p | |
| self.q = q | |
| if self.q == 0: | |
| raise BadInput() | |
| self.get_integrate = PiIntegrate() | |
| self.symbols = (a, b, c) | |
| self.integrate_result_classes_eq = { | |
| "pi_term": q, | |
| "log2_term": 0, | |
| CONSTANT_TERM_KEY: -p, | |
| } | |
| # check | |
| self.check_sgn = sq_func_sgn | |
| def get_tries_args(): | |
| return PiIntegrate.data.keys() | |
| def get_latex_ans(self): | |
| try_arg, symbol_val, sgn = self.try_times() | |
| print(f"{(try_arg, symbol_val, sgn)=}") | |
| if try_arg is None: | |
| return None | |
| p = to_latex(self.p) | |
| q = to_latex(self.q, is_coeff=True) | |
| I = self.get_integrate.get_latex(try_arg, symbol_val) | |
| return rf"{q}\pi-{p} = {I} {sign2cmp[sgn]} 0" | |
| register("π", PiSolution, top=True) | |
| if __name__ == "__main__": | |
| while True: | |
| p = int(input(">>> ")) | |
| q = int(input(" / ")) | |
| print(PiSolution(p, q).get_latex_ans()) | |