#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 pbruin):
To continue the discussion from comment:17:ticket:12880 and
comment:21:ticket:12880, I agree it is useful to have "formal" composition
(returning a chain of isogenies) besides "flesh-and-blood" composition
(returning a single isogeny).
Which of the two the user wants depends of course on the application. The
"principle of least surprise" suggests that if `phi` and `psi` are of type
`EllipticCurveIsogeny`, then `phi * psi` should again be an
`EllipticCurveIsogeny`. I am thinking of the analogy with integers: if
`m` and `n` are of type `Integer`, then `m * n` returns an `Integer`,
which does not remember `m` and `n`; there is a separate `Factorization`
class for that.
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. (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.)
--
Ticket URL: <http://trac.sagemath.org/ticket/16245#comment:4>
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