bugs for binary quadratic forms whose discriminant is a square

[DaveWitteMorris]

Ticket #28989 fixes bugs for quadratic forms whose discriminant is positive, but not a square. This ticket addresses the remaining case where the discriminant is a square. Symptoms of the bugs include:

Two forms may be properly equivalent, but not equivalent, and equivalence is not reflexive:

sage: Q = BinaryQF(0, 2, 0)
sage: Q.discriminant()
4
sage: Q.is_equivalent(Q, proper=True)
True
sage: Q.is_equivalent(Q, proper=False)
False

The forms -4*x^2 + 10*x*y, -2*x^2 + 10*x*y, 10*x*y, 2*x^2 + 10*x*y, 4*x^2 + 10*x*y, and 5*x^2 + 10*x*y are not primitive (i.e., the gcd of the coefficients is not 1), but they appear in a list of primitive forms:

sage: BinaryQF_reduced_representatives(10^2, primitive_only=True)
[-4*x^2 + 10*x*y,
 -3*x^2 + 10*x*y,
 -2*x^2 + 10*x*y,
 -x^2 + 10*x*y,
 10*x*y,
 x^2 + 10*x*y,
 2*x^2 + 10*x*y,
 3*x^2 + 10*x*y,
 4*x^2 + 10*x*y,
 5*x^2 + 10*x*y]

I will upload a PR soon.

Depends on #28989

CC: @simonbrandhorst

Component: number theory

Keywords: binary quadratic form

Author: Dave Morris

Branch/Commit: 4580620

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/29028

[DaveWitteMorris]

Branch: public/29028

[DaveWitteMorris]

New commits:

aa21ee1	proper cycle should not have odd length
c24e07d	apply tau only to half of the terms
6ac626a	revise docstrings and fix another bug
2c2bc7a	discriminants that are a square

[DaveWitteMorris]

Commit: 2c2bc7a

[DaveWitteMorris]

Author: Dave Morris

[DaveWitteMorris]

Dependencies: #28989

[sagetrac-git]

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

48d6e89	docs should not have # comments
17653f7	Merge latest #28989 into #29028
028d95b	docs should not have # comments

[sagetrac-git]

Changed commit from 2c2bc7a to 028d95b

[sagetrac-git]

Changed commit from 028d95b to f2f6bd5

[sagetrac-git]

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

ee54527	fix minor issues
f2f6bd5	fix merge conflict with #28989

[DaveWitteMorris]

comment:6

Merged in #28989 again, to fix a merge conflict caused by the latest changes there.

[tscrim]

comment:7

Two little changes:

         We check that the first part of :trac:`29028` is fixed::
+
             sage: Q = BinaryQF(0, 2, 0)
             sage: Q.discriminant()
             4

     Test another part of :trac:`29028`::
+
         sage: BinaryQF_reduced_representatives(10^2, proper=False, primitive_only=False)

as you need a blankline after the :: line.

[sagetrac-git]

Changed commit from f2f6bd5 to 4580620

[sagetrac-git]

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

4580620

need blank line after comment

[DaveWitteMorris]

comment:9

Thanks for the corrections.

[tscrim]

comment:10

Thanks. LGTM.

[tscrim]

Reviewer: Travis Scrimshaw

[vbraun]

Changed branch from public/29028 to 4580620