def binom(n, k):
if type(n) == str: n = polynomial.polynomial_parser(n)
if type(k) == str: k = polynomial.polynomial_parser(k)
num = expression_add([expression_mult([factor.factorial(n)])])
den = expression_add([
expression_mult([
factor.factorial(k),
factor.factorial(
polynomial.polynomial_parser('{}-({})'.format(
n.to_string(), k.to_string())))
])
])
return expression_rat(num, den)
def test_function_validates_input(self):
f = factorial(5)
self.assertEqual(f, 126)
import random
from cmath import sqrt, cos
# from math import *
from math import sqrt as normal_sqrt
from factor import factorial
mamama = ["м", "a"]
print(random.choice(mamama))
print(sqrt(-1))
print(normal_sqrt(4))
# print(randint(0,10))
n = int(input("Введите число "))
print(factorial(n))
def expression_parser(s):
def simplify(stack):
if len(stack) == 1: return stack
if stack[-2] == '(': return stack
if stack[-1] == '(':
stack.append(to_expr_r(polynomial.constant(0)))
return stack
b, op, a = stack.pop(), stack.pop(), stack.pop()
if a == '(':
stack.append(a)
assert op == '-', 'Something is weird'
stack.append(b.negate())
return simplify(stack)
if op == '+':
stack.append(a.add(b))
elif op == '-':
stack.append(a.subtract(b))
elif op == '*':
stack.append(a.multiply(b))
elif op == '/':
stack.append(a.divide(b))
else:
print('SOMETHING IS GOING WRONG')
print('TRYING TO SIMPLIFY AND HAVE a, op, b AS')
try:
print(type(a))
a.PRINT()
except:
print(a)
try:
print(type(op))
op.PRINT()
except:
print(op)
try:
print(type(b))
b.PRINT()
except:
print(b)
raise Exception('Parse general error')
return simplify(stack)
to_split = ['B[', 'F[', 'P[', ']', ',', '/', '*', '+', '-', '(', ')', '^']
s = s.replace(' ', '')
for x in to_split:
s = s.replace(x, ' {} '.format(x))
parts = s.split()
stack = []
i = 0
while i < len(parts):
part = parts[i]
if len(part) == 0:
i += 1
continue
assert part != ',' and part != ']', 'Parse general error for string {}'.format(
s)
if part == '(':
if stack and type(stack[-1]) == expression_rat:
stack.append('*')
stack.append('(')
i += 1
elif part == ')':
stack = simplify(stack)
stack = stack[:-2] + stack[-1:]
i += 1
elif part == 'B[':
if stack and type(stack[-1]) == expression_rat:
stack.append('*')
j = i + 1
while parts[j] != ',':
j += 1
n = polynomial.polynomial_parser(''.join(parts[i + 1:j]))
i = j
j = i + 1
while parts[j] != ']':
j += 1
k = polynomial.polynomial_parser(''.join(parts[i + 1:j]))
stack.append(to_expr_r(binom(n, k)))
i = j + 1
elif part == 'F[':
if stack and type(stack[-1]) == expression_rat:
stack.append('*')
j = i + 1
while parts[j] != ']':
j += 1
stack.append(
to_expr_r(
factor.factorial(
polynomial.polynomial_parser(''.join(parts[i +
1:j])))))
i = j + 1
elif part == 'P[':
if stack and type(stack[-1]) == expression_rat:
stack.append('*')
j = i + 1
while parts[j] != ',':
j += 1
a = int(''.join(parts[i + 1:j]))
i = j
j = i + 1
while parts[j] != ']':
j += 1
n = polynomial.polynomial_parser(''.join(parts[i + 1:j]))
stack.append(to_expr_r(factor.power(a, n)))
i = j + 1
elif part in ['/', '*']:
stack.append(part)
i += 1
elif part in ['+', '-']:
stack = simplify(stack)
stack.append(part)
i += 1
elif part == '^':
cur = stack.pop()
stack.append(cur.power(int(parts[i + 1])))
i += 2
else:
if stack and type(stack[-1]) == expression_rat:
stack.append('*')
stack.append(to_expr_r(polynomial.polynomial_parser(part)))
i += 1
stack = simplify(stack)
return stack[0]
'''Used for testing. Gets F(n,k) and returns a_k/a_{k-1}'''
def get_quotient(fnk):
num_string = '({})-({})'.format(fnk.replace('n', '(n+1)'), fnk)
den_string = num_string.replace('k', '(k-1)')
quot_string = '({})/({})'.format(num_string, den_string)
out = expression_parser(quot_string)
out.simplify_complete()
return out
if __name__ == '__main__':
print('TESTING EXPRESSIONS')
p1 = polynomial.polynomial_parser('mn+k^2')
f1 = factor.factorial(polynomial.polynomial_parser('n'))
p2 = polynomial.polynomial_parser('m^2n^2+k')
f2 = factor.factorial(polynomial.polynomial_parser('n+m'))
em1 = expression_mult([p1, f1])
em2 = expression_mult([p1, f2])
em3 = expression_mult([p2, f1])
em4 = expression_mult([p2, f2])
ea1 = expression_add([em1, em2])
ea2 = expression_add([em3, em4])
er1 = expression_rat(ea1, ea2)
p1.PRINT()
f1.PRINT()
p2.PRINT()
f2.PRINT()
em1.PRINT()
em2.PRINT()