#16245: Compose isogenies
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Reporter: sbesnier | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.2
Component: elliptic curves | Resolution:
Keywords: | Merged in:
Authors: Sébastien Besnier | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/sbesnier/ticket/16245 | de93bbab579251ef42f03a22cec570a1ec61bc96
Dependencies: #12880 | Stopgaps:
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Comment (by defeo):
Oh, I had a bad intuition of how formal composition is implemented in
Sage. I thought that the result of composition would still be an instance
of `EllipticCurveIsogeny`. I see now that `Morhpism` does less magic than
I thought.
> Hence I would be in favour of making `phi * psi` mean "flesh-and-blood"
composition, and to have a differently named method, say `phi.chain(psi)`,
that returns chains of isogenies.
Agreed. Let's not overdesign the `EllipticCurveIsogeny` class.
Still, I am a bit concerned about efficiency. Contrary to the case of
integers and factorisations, the factored form requires much less storage
than the "normalized" form. But this is a much more general discussion,
that does not only affect isogenies.
> (There doesn't seem to be an existing class for arbitrary finite chains
of morphisms in a category; `sage.categories.map.FormalCompositeMap` only
supports compositions of two morphisms.)
Well, arbitrary chains are already supported by this class, although
associativity is broken by design. It shouldn't be too much work to modify
`FormalCompositeMap` so that it stores a list of morphisms instead of a
pair.
However, such an object seems to belong to the category framework. Haven't
the combinat people worked on this yet?
--
Ticket URL: <http://trac.sagemath.org/ticket/16245#comment:5>
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