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from sympy.core.numbers import Rational |
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from sympy.core.symbol import symbols |
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from sympy.functions.combinatorial.factorials import (FallingFactorial, RisingFactorial, binomial, factorial) |
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from sympy.functions.special.gamma_functions import gamma |
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from sympy.simplify.combsimp import combsimp |
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from sympy.abc import x |
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def test_combsimp(): |
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k, m, n = symbols('k m n', integer = True) |
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assert combsimp(factorial(n)) == factorial(n) |
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assert combsimp(binomial(n, k)) == binomial(n, k) |
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assert combsimp(factorial(n)/factorial(n - 3)) == n*(-1 + n)*(-2 + n) |
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assert combsimp(binomial(n + 1, k + 1)/binomial(n, k)) == (1 + n)/(1 + k) |
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assert combsimp(binomial(3*n + 4, n + 1)/binomial(3*n + 1, n)) == \ |
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Rational(3, 2)*((3*n + 2)*(3*n + 4)/((n + 1)*(2*n + 3))) |
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assert combsimp(factorial(n)**2/factorial(n - 3)) == \ |
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factorial(n)*n*(-1 + n)*(-2 + n) |
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assert combsimp(factorial(n)*binomial(n + 1, k + 1)/binomial(n, k)) == \ |
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factorial(n + 1)/(1 + k) |
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assert combsimp(gamma(n + 3)) == factorial(n + 2) |
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assert combsimp(factorial(x)) == gamma(x + 1) |
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assert combsimp((n + 1)*factorial(n)) == factorial(n + 1) |
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assert combsimp(factorial(n)/n) == factorial(n-1) |
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assert combsimp(binomial(n, n - k)) == binomial(n, k) |
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assert combsimp(factorial(n)/(factorial(k)*factorial(n - k))) == \ |
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binomial(n, k) |
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assert combsimp(factorial(k)*factorial(n - k)/factorial(n)) == \ |
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1/binomial(n, k) |
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assert combsimp(factorial(2*n)/factorial(n)**2) == binomial(2*n, n) |
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assert combsimp(factorial(2*n)*factorial(k)*factorial(n - k)/ |
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factorial(n)**3) == binomial(2*n, n)/binomial(n, k) |
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assert combsimp(factorial(n*(1 + n) - n**2 - n)) == 1 |
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assert combsimp(6*FallingFactorial(-4, n)/factorial(n)) == \ |
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(-1)**n*(n + 1)*(n + 2)*(n + 3) |
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assert combsimp(6*FallingFactorial(-4, n - 1)/factorial(n - 1)) == \ |
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(-1)**(n - 1)*n*(n + 1)*(n + 2) |
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assert combsimp(6*FallingFactorial(-4, n - 3)/factorial(n - 3)) == \ |
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(-1)**(n - 3)*n*(n - 1)*(n - 2) |
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assert combsimp(6*FallingFactorial(-4, -n - 1)/factorial(-n - 1)) == \ |
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-(-1)**(-n - 1)*n*(n - 1)*(n - 2) |
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assert combsimp(6*RisingFactorial(4, n)/factorial(n)) == \ |
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(n + 1)*(n + 2)*(n + 3) |
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assert combsimp(6*RisingFactorial(4, n - 1)/factorial(n - 1)) == \ |
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n*(n + 1)*(n + 2) |
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assert combsimp(6*RisingFactorial(4, n - 3)/factorial(n - 3)) == \ |
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n*(n - 1)*(n - 2) |
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assert combsimp(6*RisingFactorial(4, -n - 1)/factorial(-n - 1)) == \ |
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-n*(n - 1)*(n - 2) |
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def test_issue_6878(): |
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n = symbols('n', integer=True) |
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assert combsimp(RisingFactorial(-10, n)) == 3628800*(-1)**n/factorial(10 - n) |
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def test_issue_14528(): |
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p = symbols("p", integer=True, positive=True) |
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assert combsimp(binomial(1,p)) == 1/(factorial(p)*factorial(1-p)) |
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assert combsimp(factorial(2-p)) == factorial(2-p) |
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