#7096: bug in dual isogeny computation
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Reporter: cremona | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-4.2.1
Component: elliptic curves | Keywords: elliptic curve isogeny
Work_issues: | Author:
Reviewer: | Merged:
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Comment(by wuthrich):
OK. Here we go. That is a patch for this ticket that I would like to be
reviewed.
I explain all the changes it introduces as it is quite a long and
complicated patch. (I like the fact that the initial comment on the ticket
was ''"This looks like something which should be easy to fix."'' while it
took me a month of quite hard work.)
* I moved the computation of the weierstrass p-function into a seperate
file ell_wp.py.
I also completely clean it. It used to contain a lot of functions on
power series that
are already implemented in sage. There is an option now to call the
pari version.
* I added a {{{weierstrass_p}}} to ell_field.py.
* Having redone all the weierstrass_p with laurent and power series
rather than with
polynomials, also got rid of the {{{IndexError}}} mentioned above.
* The dual is now correct and not just up to an automorphism.
* When trying to give an isogeny with a codomain, it now checks if the
algorithm fails
(typically because there is no cyclic normalized isogeny of this
degree). This eliminates a
bad bug that was known in the code.
* We can now take duals of non-normalized isogenies
* There is a new function {{{formal}}} that computes the formal expansion
of the isogeny.
* This {{{formal}}} can be used to check if the isogeny is normalized;
this simplifies and
corrects the previous code (which is still there but deprecated).
* I included a check to forbid {{{dual}}} of isogenies of degree
divisible by the
charactersitic.
* I updated a lot of the documentation of isogenies.
* And I also changed the starting documentation of ell_generic.py to
clarify what we mean by
an elliptic curve in sage.
There is still a lot that should be done about isogenies for elliptic
curves. I hope this patch corrects and clarifies what is possible right
now. For further things that one could wish for in sage concerning
isogenies and endomorphisms I opened ticket #7368 as a follow up.
Note that this ticket also includes the correction asked for in #7307.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7096#comment:11>
Sage <http://www.sagemath.org>
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