Improve caching in EllipticCurve_generic

[saraedum]

The way caching is implemented in EllipticCurve_generic causes some trouble
at #11895. Several methods, such as _multiple_x_numerator,
_multiple_x_denominator, division_polynomial_0 should be rewritten such that they do not use a cache parameter anymore.

CC: @JohnCremona @defeo @sagetrac-sbesnier

Component: elliptic curves

Author: Julian Rüth

Branch/Commit: 4c00ee1

Reviewer: Peter Bruin

Issue created by migration from https://trac.sagemath.org/ticket/16129

[saraedum]

Branch: u/saraedum/ticket/16129

[sagetrac-git]

Commit: b9b79ca

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

b9b79ca

Use @cached_method decorator for _multiple_x_numerator/denominator in EllipticCurve_generic

[sagetrac-git]

Changed commit from b9b79ca to e12fc10

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

e12fc10

Use cached_function to cache computations in division_polynomial_0 of elliptic curves

[saraedum]

Author: Julian Rüth

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

72c46da

Fixed a typo in a reference.

[sagetrac-git]

Changed commit from e12fc10 to 72c46da

[pjbruin]

Work Issues: resolve merge conflict

[sagetrac-git]

Changed commit from 72c46da to fe8b5a9

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

fe8b5a9

Merge branch 'develop' into ticket/16129

[sagetrac-git]

Changed commit from fe8b5a9 to afdfca4

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

afdfca4

Merge branch 'develop' into ticket/16129

[saraedum]

Changed work issues from resolve merge conflict to none

[pjbruin]

comment:14

Looks good to me; now running doctests.

I'm just slightly worried that some of the methods may cache too much, because the caching key depends on x, which can just be a concrete x-value rather than a polynomial variable. However, this already seems to have been the case before this ticket, so maybe we can keep it like that for now.

[pjbruin]

Reviewer: Peter Bruin

[pjbruin]

Changed branch from u/saraedum/ticket/16129 to u/pbruin/16129-EllipticCurve_caching

[pjbruin]

comment:15

All doctests pass, but building documentation was interrupted due to a warning which was caused by missing indentation. Hence a trivial reviewer patch.

[pjbruin]

Changed commit from afdfca4 to 4c00ee1

[vbraun]

Changed branch from u/pbruin/16129-EllipticCurve_caching to 4c00ee1