#11039: Write a framework for computing with Galois cohomology classes.
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Reporter: weigandt | Owner: weigandt
Type: enhancement | Status: new
Priority: major | Milestone: sage-feature
Component: number theory | Keywords: galois cohomology, Selmer groups
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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There are several independent algorithms which compute various Selmer
groups associated to elliptic curves. Unfortunately, none of them interact
very well. You can't piece together partial information given by mwrank
with partial information given by Simon's two_descent scripts. You also
cannot modify the local conditions used to compute the relevant Selmer
groups to investigate Kolyvagin systems.
We need to create at Galois cohomology class in Sage that can pointed to
by as much of the existing code that computes Shafarevich-Tate groups,
Kolyvagin classes, Selmer groups, and principal homogenous spaces as
possible, while more importantly forming a backdrop to implement more of
this functionality, such especially Kolyvagin classes and higher descents,
in a consistent and elegant way.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11039>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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