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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
@staticmethod
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())
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