Simplification of zero to the symbolic power n

[phul-ste]

Steps To Reproduce

If we run
n=var('n')
a=0^n
b=a.simplify_full()
(a({n:0}),b({n:0}))
we get (1,0) as a result

Expected Behavior

I would expect that simplify_full applied at 0^n would not convert it to 0, since most (all?) mathematical formulas on non-negative integers are more compatible with 0^0=1 (as currently implemented, see the above-evaluation of a({n:0})).

I currently think that simplifications should preserve the form 0^n.

Actual Behavior

even with assumptions like
assume(n, 'integer')
assume(n>=0) or even assume(n==0), the simplification of 0^n yields to 0.

Additional Information

This is a more general issue than #36838 where we (yet) replaced 0^n by kronecker_delta(0, n).
Note that such basic replacement assumes n to be a non-negative integer.

Environment

- **OS**: Ubuntu 20.04
- **Sage Version**: 9.0
- Jupyter Notebook

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide

[RuchitJagodara]

I worked on this, and found that the problem is with the maxima function, the function simplify_full() is calling maxima many times and when it is called for first time 0^n is resolved to 0 as you can see in below output.

sage: n = SR.var("n",domain="complex"); n
n
sage: maxima(0^n)
0

We had a same probelm with maxima function which can be found from the discussion in #36841. Where we had a problem that maxima function is simplifying conjugate(y) to y where y's domain is not defined. Here, I think this is also a problem with maxima function although we have defined the domain but here it is simplifying (0^n) to 0, no matter whatever the domain is. I think maxima does not have a condition to handle (0^n), I might be wrong but this was my observation.

I found another discussion based on this link .
So, I think this can be resolved only when maxima will change these things or sage implement its own system instead of maxima. But I think we can implement similar thing as we did in #36838.