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Fixes Rising Factorial #39409

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Fixes Rising Factorial #39409

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d5b5819
updated docs
Jan 30, 2025
2219f1e
Updated Docs
Jan 30, 2025
6fbd654
rising fact updated
Jan 30, 2025
a7be917
rising fact updated
Jan 30, 2025
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13 changes: 13 additions & 0 deletions src/sage/arith/misc.py
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Original file line number Diff line number Diff line change
Expand Up @@ -5259,12 +5259,25 @@ def rising_factorial(x, a):
- Jaap Spies (2006-03-05)
"""
from sage.structure.element import Expression
from sage.rings.integer import Integer
x = py_scalar_to_element(x)
a = py_scalar_to_element(a)

# Handle negative integer x and non-negative integer a
if isinstance(x, Integer) and x < 0 and isinstance(a, Integer) and a >= 0:
if a > -x: # If a > |x|, the product includes zero
return x.parent().zero()
else:
# Compute the product for a <= |x|
return prod((x + i for i in range(a)), z=x.parent().one())

# General case for non-negative integer a
if (isinstance(a, Integer) or
(isinstance(a, Expression) and
a.is_integer())) and a >= 0:
return prod(((x + i) for i in range(a)), z=x.parent().one())

# Fallback to gamma function for other cases
from sage.functions.all import gamma
return gamma(x + a) / gamma(x)

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