implement natural morphism from cl(f²D) to cl(D) #37074
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tscrim
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vbraun
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Feb 7, 2024
…documentation
The possibility to pass discriminants to the constructor instead of
`BQFClassGroup` objects was present for an earlier version of sagemath#37074,
but it was removed during review. However, it seems I forgot to update
the docstring accordingly.
URL: sagemath#37233
Reported by: Lorenz Panny
Reviewer(s): Travis Scrimshaw
vbraun
pushed a commit
to vbraun/sage
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Feb 11, 2024
…documentation
The possibility to pass discriminants to the constructor instead of
`BQFClassGroup` objects was present for an earlier version of sagemath#37074,
but it was removed during review. However, it seems I forgot to update
the docstring accordingly.
URL: sagemath#37233
Reported by: Lorenz Panny
Reviewer(s): Travis Scrimshaw
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...for class groups of binary quadratic forms, which we have since #36184.
This map is defined by finding a class representative$[a,b,c]$ for which $f^2 \mid a$ (and $f \mid b$ ) and then applying the substitution $x \mapsto x/f$ . In the code, we do it in prime steps, since that makes finding a suitable representative a little easier.
This can be used, among other things, for determining the kernel of the surjection$\mathrm{cl}(f^2D) \twoheadrightarrow \mathrm{cl}(D)$ .