factorial(n)*(n+1) rewriting

[Gaurav Dhingra]

Hi all

I was looking on the issue https://github.com/sympy/sympy/issues/8531 though i disagree for that simplification to occur. 

>>> n = Symbol('n', integer=True, positiv=True)

>>> factrial(n)*(n+1)   # i think this should not be simplified to factorial(n+1)

factorial(n)*(n+1)        # currently happens, which i think is correct.

>>> n = Symbol('n', integer=True, positiv=True)

>>> ( factorial(n)*(n+1) ).rewrite(factorial)

factorial(n)*(n + 1)            # why not returned as factorial(n + 1) ??

I was thinking if there is currently any way of rewriting it as `factorial(n + 1)`

Gaurav Dhingra

[Richard Fateman]

I thiink this hack is pretty worthless unless you have a better notion of "one more than".

e.g. factorial( (n-1)*(n+1)) * n^2  is factorial(n^2), right?

[Aaron Meurer]

combsimp() would be the place for this. In general, rewrite() doesn't do any advanced simplification. It just rewrites functions in terms of other functions (like factorial(x).rewrite(gamma) just replaces all 'factorial' instances with gamma with the appropriate shift).

It seems combsimp(factorial(n)*(n+1)) doesn't work, but it's only because it doesn't know about factorial, only gamma. This works:

In [5]: combsimp((factorial(n)*(n+1)).rewrite(gamma)).rewrite(factorial)

Out[5]: (n + 1)!

I opened https://github.com/sympy/sympy/issues/9699 for this.

Aaron Meurer

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[Gaurav Dhingra]

Thanks @asmeurer, that will be good.