Implement square check for power series over Z/nZ

[cxzhong]

Add Chinese Remainder Theorem support for checking squares in power series over squarefree moduli.
Fix #41220 And return a NotImplement for prime power case

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• The title is concise and informative.
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⌛ Dependencies

#41239

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[user202729]

Use \Zmod LaTeX macro.

Is there any test that previously fail but succeed with this pull request?

[cxzhong]

Use \Zmod LaTeX macro.

Is there any test that previously fail but succeed with this pull request?

I think maybe for prime power, we need to use Hensel lift to compute. and for 2^n, the situation is complexity.
So I do not try to implement it.
I wrote a case

sage: R.<x> = PowerSeriesRing(Zmod(8))
sage: ((x + 1)^2).is_square()
Traceback (most recent call last):
...
NotImplementedError: is_square() not implemented for power series over Zmod(p^k) with k > 1

[user202729]

So the only change is the additional check instead of return wrong answer?

I'd rather modifying the generic method to check that the ring has zero nilradical. (The only case where (f^2).valuation() is odd is that f[f.valuation()]^2 = 0.) (caveat: #41222. One easy way to get ZZ.nilradical() to work is to make ZZ(0).radical() == 0, which looks like the consensus is +2/-0 right now, so should be good)