Add support for toric lattices

[novoselt]

Toric lattices are ZZⁿ's with distinction of their roles (in the simplest case - standard dual lattices M and N).

This patch is a part of the following series adding support for cones/fans and toric varieties to Sage:

Prerequisites:

#8675 - Remove AmbientSpace._constructor and fix consequences

#8682 - Improve AlgebraicScheme_subscheme.__init__ and AmbientSpace._validate

#8694 - Improve schemes printing and LaTeXing

#8934 - Trivial bug in computing faces of non-full-dimensional lattice polytopes

#8936 - Expose facet inequalities for lattice polytopes

#8941 - _latex_ and origin for lattice polytopes

Main patches adding new modules:

#9062 - Add support for toric lattices

#8986 - Add support for convex rational polyhedral cones

#8987 - Add support for rational polyhedral fans

#8988 - Add support for toric varieties

#8989 - Add support for Fano toric varieties

CC: @vbraun

Component: geometry

Author: Andrey Novoseltsev

Reviewer: Volker Braun

Merged: sage-4.5.2.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/9062

[vbraun]

comment:2

Looks good, I'll be happy to review the final version!

[novoselt]

Attachment: trac_9062_add_support_toric_lattices.patch.gz

Fixed version.

[novoselt]

Attachment: trac_9062_add_support_for_toric_lattices.patch.gz

Apply this patch only.

[novoselt]

comment:3

It will probably work without other "prerequisites," but I tested it with them applied since all got positive review already and hopefully will be merged soon...

[novoselt]

comment:4

Functions is_ToricLattice and __hash__ for elements will be added to these new modules in the coming patch for cones at #8986.

[vbraun]

comment:5

Very nice. I like it how the M/N lattice elements derive from Vector_integer_dense. Positive review. Applies to Sage 4.4.2.

[vbraun]

Reviewer: vbraun

[novoselt]

Changed reviewer from vbraun to Volker Braun

[novoselt]

comment:7

Thank you! (I think authors and reviewers should be listed with their full names rather than trac accounts, this simplifies the job of release managers.)

[loefflerd]

comment:8

While testing I found a heisenbug caused by this patch. If you run "make ptestlong", there is a failure in toric_lattice_element.pyx; but it works fine if you doctest just that file.

The problem is this comparison function:

    def __cmp__(self, right):
        r"""
[...]
            sage: cmp(n, 1)
            -1
        """
        c = cmp(type(self), type(right))
        if c:
            return c

The doctest is sensitively dependent on the exact memory locations of different classes, because cmp(type(self), type(right)) compares on memory addresses. I suggest changing the doctest to

sage: n == 1
False

which is much more robust.

David

[loefflerd]

Apply this patch over trac_9062_add_support_for_toric_lattices.patch

[loefflerd]

comment:9

Attachment: trac_9062-cmp_fix.patch.gz

Here's a tiny patch which makes the fix I suggested.

[vbraun]

comment:10

The same potential issue is in toric_lattice.py. Here is an updated patch that fixes this one, too. I think this is fine now, if you agree please set to "positive review".

[vbraun]

Updated patch

[loefflerd]

comment:11

Attachment: trac_9062-cmp_fix.2.patch.gz

Looks good to me. Apply trac_9062_add_support_for_toric_lattices.patch and trac_9062-cmp_fix.2.patch.

[qed777]

Merged: sage-4.5.2.alpha0

[qed777]

comment:13

One or more of #8986, #8987, and #9062 may cause the doctest failures listed at #9590.