add class groups of binary quadratic forms #36184
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GiacomoPope
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vbraun
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This patch adds an implementation of the form class group for positive
definite binary quadratic forms. (We restrict to definite forms for now
since it is the easier case: Every class contains a unique reduced
form.)
Most of the required functionality was already available in PARI or
Sage, but the types introduced in this patch make it easier to
manipulate form classes and interface with existing algorithms for
generic abelian groups.
URL: sagemath#36184
Reported by: Lorenz Panny
Reviewer(s): Giacomo Pope, Lorenz Panny
vbraun
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Jan 21, 2024
...for class groups of binary quadratic forms, which we have since sagemath#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 $\mathrm{cl}(f^2D) \twoheadrightarrow \mathrm{cl}(D)$. URL: sagemath#37074 Reported by: Lorenz Panny Reviewer(s): Lorenz Panny, Travis Scrimshaw
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This patch adds an implementation of the form class group for positive definite binary quadratic forms. (We restrict to definite forms for now since it is the easier case: Every class contains a unique reduced form.)
Most of the required functionality was already available in PARI or Sage, but the types introduced in this patch make it easier to manipulate form classes and interface with existing algorithms for generic abelian groups.