#18589: isogeny efficiency improvement
-------------------------+-------------------------------------------------
Reporter: | Owner:
cremona | Status: needs_review
Type: | Milestone: sage-6.8
enhancement | Resolution:
Priority: major | Merged in:
Component: | Reviewers:
elliptic curves | Work issues:
Keywords: | Commit:
isogeny | 47ccfd587402b953c612fcd3cddaa541a6847bd3
Authors: John | Stopgaps:
Cremona |
Report Upstream: N/A |
Branch: |
u/cremona/18589 |
Dependencies: |
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Changes (by cremona):
* status: new => needs_review
* commit: => 47ccfd587402b953c612fcd3cddaa541a6847bd3
* branch: => u/cremona/18589
Old description:
> Computation of isogenies of prime degree p is expensive when the degree
> is neither a "genus zero" prime [2,3,5,7,13] or a "hyperelliptic prime"
> [11, 17, 19, 23, 29, 31, 41, 47, 59, 71] (for these there is special code
> written). In one situation we can save time, after factoring the degree
> {{{(p^2-1)/2}}} division polynomial, if there is exactly one factor of
> degree (p-1)/2, or one subset of factors whose product has that degree,
> then the factor of degree (p-1)/2 must be a kernel polynomial. Then we
> do not need to check consistency, which is very expensive.
>
> The example which led me to this was with p=89 over a quadratic number
> field, where E.isogeny_class() was taking days. After the change here
> that goes down to 3 hours. (There are 4 curves in the isogeny class and
> thec ode requires factoring the 89-division polynomial of each!) I will
> find a less extreme example for a doctest.
New description:
Computation of isogenies of prime degree p is expensive when the degree is
neither a "genus zero" prime [2,3,5,7,13] or a "hyperelliptic prime" [11,
17, 19, 23, 29, 31, 41, 47, 59, 71] (for these there is special code
written). In one situation we can save time, after factoring the degree
{{{(p^2-1)/2}}} division polynomial, if there is exactly one factor of
degree (p-1)/2, or one subset of factors whose product has that degree,
then the factor of degree (p-1)/2 must be a kernel polynomial. Then we do
not need to check consistency, which is very expensive.
The example which led me to this was with p=89 over a quadratic number
field, where E.isogeny_class() was taking days. After the change here
that goes down to 3 hours. (There are 4 curves in the isogeny class and
the code requires factoring the 89-division polynomial of each!) I used a
less extreme example for a doctest: a 37-isogeny.
--
Comment:
New commits:
||[http://git.sagemath.org/sage.git/commit/?id=47ccfd587402b953c612fcd3cddaa541a6847bd3
47ccfd5]||{{{#18589 isogeny improvement}}}||
--
Ticket URL: <http://trac.sagemath.org/ticket/18589#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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