Genus representatives

[simonbrandhorst]

Implements a function which returns representatives for a genus of quadratic forms.
Optional sage and Magma backend.

sage: IntegralLattice(9).genus().representatives()                           
(
[1 0 0 0 0 0 0 0 0]  [1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]  [0 2 1 1 1 1 1 1 1]
[0 0 1 0 0 0 0 0 0]  [0 1 2 1 1 0 0 0 0]
[0 0 0 1 0 0 0 0 0]  [0 1 1 2 1 1 1 1 1]
[0 0 0 0 1 0 0 0 0]  [0 1 1 1 2 1 1 0 0]
[0 0 0 0 0 1 0 0 0]  [0 1 0 1 1 2 1 1 1]
[0 0 0 0 0 0 1 0 0]  [0 1 0 1 1 1 2 1 1]
[0 0 0 0 0 0 0 1 0]  [0 1 0 1 0 1 1 2 1]
[0 0 0 0 0 0 0 0 1], [0 1 0 1 0 1 1 1 2]
)

Depends on #30843

Component: quadratic forms

Author: Simon Brandhorst

Branch/Commit: f6d82ea

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/30842

[simonbrandhorst]

Dependencies: #30843

[simonbrandhorst]

Branch: u/sbrandhorst/genus_representatives

[sagetrac-git]

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

b15922d	Added a Note block.
b6657af	formatting
3bfdccf	Merge branch 't/30843/abeliangroup_gap_quotient_group' into t/30842/genus_representatives
4e786f2	docs

[sagetrac-git]

Commit: 4e786f2

[tscrim]

comment:5

Some quick comments (I haven't had time to fully read through it): You need to change MATH:: -> .. MATH::. Also, there are some PEP8 spacing that would be good to implement; mainly the ==0 -> == 0 and similar.

[simonbrandhorst]

comment:6

Which one is better?

1)a==b and c==d

2)a == b and c == d
I tend to 1) since it
is the analogue of a*b + c*d vs a * b + c * d

[sagetrac-git]

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

ab9361f

pep

[sagetrac-git]

Changed commit from 4e786f2 to ab9361f

[tscrim]

comment:8

That is an interesting point with and being another operator. However, I would still say 1 because it seems to be what is most widely used (and I am so used to seeing it that way, but that is my personal bias).

[sagetrac-git]

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

63ce0a2

pep pep pep pep pep pep

[sagetrac-git]

Changed commit from ab9361f to 63ce0a2

[simonbrandhorst]

comment:10

There you go. Pep'ed all the files touched.

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:11

Thank you. Just add your name to the authors and set a positive review.

[simonbrandhorst]

Author: Simon Brandhorst

[fchapoton]

comment:13

come on guys, there are some OUTPUT:: lurking around ! Please look at the patchbot complaints.

[simonbrandhorst]

comment:14

Hi you are right of course, I should have waited for a green bot.
Let's do that.

[sagetrac-git]

Changed commit from 63ce0a2 to 121eff2

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

3fccfb5	take care of patchbot complaints
121eff2	fix a failing doctest

[sagetrac-git]

Changed commit from 121eff2 to f6d82ea

[sagetrac-git]

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

f6d82ea

lazy import and pickling

[tscrim]

comment:17

Now there is a morally green patchbot.

[vbraun]

Changed branch from u/sbrandhorst/genus_representatives to f6d82ea