implement a symplectic form for finding symplectic bases

[ncalexan]

Implement a symplectic_form for computing symplectic bases for alternating, anti-symmetric matrices. This is essential for computing with polarized Abelian varieties.

The attached patch computes symplectic forms over fields and the integers.

CC: @ncalexan

Component: linear algebra

Keywords: symplectic basis form integer matrix

Issue created by migration from https://trac.sagemath.org/ticket/2664

[ncalexan]

Attachment: 2664-ncalexan-symplectic-form-1.patch.gz

[craigcitro]

comment:1

Patch looks great! There are one or two tiny things I'd like to see fixed:

• I don't like the line alternating_form = symplectic_form, for the same reasons as my similar comment on clean and better document is_totally_real(), add is_totally_imaginary() to NumberField_generic #2707.

• Should the new matrix/symplectic_basis.py file have a copyright notice at the top?

• Given that there's this nice code for computing symplectic bases, it might be nice for someone to write a SymplecticSpace class that inherits from some kind of vector space class, and uses this code behind the scenes where necessary. (Do we already have an inner product space class?) I'm not saying you should implement this right now, of course! But maybe file a trac ticket? Would you use this in what you're doing with this code? (I don't personally have any need of it right now, but it seems like it would be useful in general.)

[ncalexan]

Attachment: 2664-ncalexan-symplectic-form-2.patch.gz

[sagetrac-mabshoff]

comment:3

Merged in Sage 2.11.alpha2