Drinfeld Modules: Default to zero endomorphism in .hom and avoid inversion of zero endomorphism
#38964
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xcaruso
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Nov 14, 2024
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….hom` and avoid inversion of zero endomorphism
This PR fixes sagemath#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.
URL: sagemath#38964
Reported by: Sebastian A. Spindler
Reviewer(s): Xavier Caruso
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This PR fixes #38953 and is inspired by the error raised in the issue:
__invert__, so thatphi.hom(a)actually returns an invertible morphism.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, whichK.zero()does not. Instead of raising an error for this special case in.hom, it seems more robust to default to the zero endomorphism ofselfinstead.isogin the.velu-method.