Implemented Mobius Function in residue_ntheory module

[skirpichev]

rebase of stalled pr #2825.

[asmeurer]

It would be better if these new functions were implemented as subclasses of Function (even if no symbolic behavior is implemented yet).

[skirpichev]

@asmeurer, do you suggest to move this code from ntheory to functions module?

[asmeurer]

Ideally all the functions in ntheory would be subclasses of Function (all the actual mathematical functions that is, isprime and factorint don't need to be).

[skirpichev]

Ok, done.

[skirpichev]

@asmeurer, any comments? I'm going to merge this in 24hr.

[asmeurer]

I'm not so sure about the assumptions type checking, although there is some precedent to it in other places. It can be annoying though, and especially so if the assumptions aren't smart enough to compute if an expression is a positive integer.

[skirpichev]

Should we do return None instead?

[asmeurer]

I think a good practice is to not fail when the assumptions give None, only when they give False (i.e., you know they are wrong). Isn't this what the relationals do. You can do x > y unless it knows that x is not real (in this case it might just be when it is explicitly not real, but the basic idea is the same I think).