return Infinity from factorial of negative integer

[rwst]

sage: factorial(-5)
...
ValueError: factorial -- self = (-5) must be nonnegative

Adapt the function's behaviour to what other CASs (sympy, Wolfram) do at integer n<-1: return unsigned infinity.

Component: symbolics

Author: Ashutosh Ahelleya

Branch/Commit: u/aashu12/return_infinity_from_factorial_of_negative_integer @ 02fc09c

Issue created by migration from https://trac.sagemath.org/ticket/21560

[sagetrac-aashu12]

comment:1

I would like to work on this issue. However, one of the CASs sympy, returns a zero for a negative number given as the input. I would like to clarify if it is required to return unsigned infinity or zero. You can refer this-> http://docs.sympy.org/0.7.1/_modules/sympy/functions/combinatorial/factorials.html

[rwst]

comment:3

Note that already

sage: SR(-89).factorial()
Infinity

If you decide against Infinity then please change the above for consistency (you can find the code in libs/pynac/pynac.pyx).

[rwst]

comment:4

As to which one it should be, I guess that's arbitrary. You may need to change code that depends on the exception (maybe there is some in combinatorics) anyway. Using zero makes possibly sense, maybe to have sane behavour for some combinatorial sums.

[rwst]

comment:5

Note also

sage: factorial(-89.)
NaN

which would be the third alternative.

[sagetrac-aashu12]

comment:6

I feel that it would be better if Unsigned Infinity is returned because in case we return any other value, too many files in different components have to be modified to make sure that the consistency is proper. I will modify the function such that it returns Unsigned Infinity when the input is negative by importing unsigned_infinity from sage.rings.infinity

[sagetrac-aashu12]

comment:7

Will it be right here to import unsigned infinity from sage.rings.infinity?

[rwst]

comment:8

That's a style question. I personally import from the specific file instead of from all. I remember a discussion here that recommended that because this way less is imported and less time used. I could not find a reference, sorry. You see both styles used in Sage.

[sagetrac-aashu12]

Branch: u/aashu12/return_infinity_from_factorial_of_negative_integer

[sagetrac-aashu12]

Commit: 02fc09c

[sagetrac-aashu12]

Author: Ashutosh Ahelleya