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Drinfeld Modules: Default to zero endomorphism in .hom and avoid inversion of zero endomorphism #38964

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merged 1 commit into from
Nov 16, 2024

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@S17A05 S17A05 commented Nov 13, 2024

This PR fixes #38953 and is inspired by the error raised in the issue:

  • The main fix is to avoid sampling the zero element of the base field in the test of __invert__, so that phi.hom(a) actually returns an invertible morphism.
  • However, the error raised in the issue named above was slightly confusing, as the call of phi.hom(K.zero()) does not return any homomorphism: Since the codomain is not specified, it tries to find a codomain via the .velu-method, but this only works if the given element defines an isogeny, which K.zero() does not. Instead of raising an error for this special case in .hom, it seems more robust to default to the zero endomorphism of self instead.
  • Also added the mention of isog in the .velu-method.

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xcaruso commented Nov 14, 2024

Looks good to me. Thanks.

@vbraun vbraun merged commit 54af5b3 into sagemath:develop Nov 16, 2024
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@S17A05 S17A05 deleted the drinfeld_inversion_nonzero branch November 17, 2024 21:05
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random doctest error in DrinfeldModuleMorphism
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