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Implement inverse of polynomials over non-field rings #39398

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Previously the check was done in #13303 . This pull request improves the situation in that it actually allows the functions to work (though occasionally print out the spurious error message)

📝 Checklist

  • The title is concise and informative.
  • The description explains in detail what this PR is about.
  • I have linked a relevant issue or discussion.
  • I have created tests covering the changes.
  • I have updated the documentation and checked the documentation preview.

⌛ Dependencies

@user202729 user202729 marked this pull request as draft January 28, 2025 05:17
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user202729 commented Jan 28, 2025

Actually this isn't completely correct either…

Difficult case:

sage: R.<x> = Zmod(6)[]
sage: R.quotient(x^2+x)((2*x+1)*(-4*x+1))
1

We can use the non-invertibility to factorize the base to prime powers, then…?

See also flintlib/flint#2199

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#39401 plus CRT should be sufficient.

@user202729 user202729 closed this Jan 29, 2025
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