Improvements for morphisms of ModulesWithBasis

[nthiery]

This ticket implements:

• inverses for morphisms of finite dimensional vector spaces
• tensor products of morphisms
  and improves:
• triangular morphisms over base rings

Declares CombinatorialFreeModule indexed by a finite set as being finite dimensional.

Depends on #10668
Depends on #17160

CC: @sagetrac-sage-combinat

Component: categories

Keywords: homsets, module morphisms, days64

Author: Nicolas M. Thiéry

Branch/Commit: 71b36da

Reviewer: Franco Saliola

Issue created by migration from https://trac.sagemath.org/ticket/8678

[nthiery]

Changed keywords from homsest to homsets, module morphisms

[saraedum]

comment:3

This is is a very old ticket. Anyway, can I find the patch that fixes _test_category somewhere? This also fails for #15154. Or should I just disable these tests?

[saraedum]

comment:4

Replying to @saraedum:

This is is a very old ticket. Anyway, can I find the patch that fixes _test_category somewhere? This also fails for #15154. Or should I just disable these tests?

Since there is no reply here, I created a partial fix at #15232.

[nthiery]

Branch: u/nthiery/categories/module-morphisms-8678

[sagetrac-git]

Commit: 47e0eb9

[sagetrac-git]

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

47e0eb9

8678: Imported stuff relevant to morphisms from trac_11111-finite_dimensional_modules-nt.patch

[sagetrac-git]

Changed commit from 47e0eb9 to 553c5de

[sagetrac-git]

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

553c5de

8678: Imported module_morphism_function_extend-fh.patch

[nthiery]

Dependencies: 10668

[nthiery]

Changed dependencies from 10668 to #10668

[sagetrac-git]

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

15cd16f	8678: a CombinatorialFreeModule is FiniteDimensional as soon as the index set is in Sets().Finite()
815b826	8678: add support for the matrix of a matrix on the right + improvements to the documentation

[sagetrac-git]

Changed commit from 553c5de to 815b826

[sagetrac-git]

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

ac38eda	10668: trivial ReST fix
dc5fc3d	Merge branch 'categories/morphism-methods-10668' into categories/module-morphisms-8678
21bb24c	8678: fixed doctests: (triangular) module morphisms now inherit properly from categories

[sagetrac-git]

Changed commit from 815b826 to 21bb24c

[sagetrac-git]

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

eaa56bc	16340: super_structure_categories -> all_structure_super_categories
afc9724	Merge branch 'develop' into categories/full-subcategories-16340
21bf60a	Merge branch 'categories/full-subcategories-16340' and '6.3beta5' into categories/morphism-methods-10668
442161e	Merge branch 'categories/morphism-methods-10668' and '6.3 beta5' into categories/module-morphisms-8678
838bb3f	10668: super_structure_categories -> all_structure_super_categories
9de8909	10668: super_structure_categories -> all_structure_super_categories
0b1810b	Merge branch 'categories/morphism-methods-10668' into categories/module-morphisms-8678

[sagetrac-git]

Changed commit from 21bb24c to 0b1810b

[sagetrac-git]

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

d2e836a	8678: module_with_basis_morphism.py -> modules_with_basis/morphism.py
a2f158c	8678: module_with_basis_morphism.py -> modules_with_basis/morphism.py

[nthiery]

comment:64

Hi Franco!

Replying to @saliola:

Here is my review. I pushed some typo fixes, improved some of the
documentation and added a few doctests.

Thanks! I double checked your changes and am happy with them. This
prompted a second pass of little things here and there to make the doc
more uniform. I also implemented the two we had discussed.

Here are a few issues and questions:

• I don't understand the comment in src/sage/categories/finitely_generated_semigroups.py:

# TODO: update transitive ideal

The code uses TransitiveIdeal which is being deprecated in favor of
RecursivelyEnumeratedSet. I have added this as comment on #17160.

• a couple of doctests include the following line:

sage: import __main__; __main__.f = f  

can you explain why this is necessary?

A function defined interactively is not picklable, which prevents us
from using it to test the pickling of objects built upon them. This
classical trick fakes f being defined in a Python module.

• line 1015 of src/sage/modules/module_with_basis_morphism.py: the doc says this should work over an ring, so perhaps the following is not a valid assumption?

c = c / s[j]  # the base ring is a field

The documentation mentions:

        - ``self`` -- a triangular morphism over a field, or a
          unitriangular morphism over a ring

which is tested a couple lines above:

        if G.base_ring() not in Fields and not self._unitriangular:
            raise NotImplementedError, "coreduce for a triangular but not unitriangular morphism over a ring"

• the doctests don't pass, but this seems to be related to Finitely generated axiom for (mutiplicative) magmas, semigroups, monoids, groups #17160

Yup. Next step is to cleanup #17160. And then we will know better if
there are a couple trivial doctests that need to be updated here.

Cheers,
Nicolas

[saliola]

comment:65

The latest branch causes some problems:

> git trac pull
> sage -br
**********************************************************************

Oops, Sage crashed. We do our best to make it stable, but...

The error message in the crash report is:

ImportError: No module named modules_with_basis.morphism

[saliola]

comment:66

I wanted to make the following change:

+            sage: ult = lambda i: sum(  y[j] for j in range(i,4)  ) # uni-upper
+            sage: phi = X.module_morphism(ult, triangular="lower", codomain=Y)

The comment # uni-upper should be uni-lower.

[sagetrac-git]

Changed commit from a2f158c to d9b5507

[sagetrac-git]

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

d9b5507

8678: fixed missing __init__.py

[sagetrac-git]

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

5eca4c1

8678: doc: fixed misleading 'tolower' comment + micro phrasing improvement

[sagetrac-git]

Changed commit from d9b5507 to 5eca4c1

[saliola]

comment:69

Hello Nicolas. Thanks for the answers and the fixes. This looks good to me now. I'm ready to set this to positive review once #17160 is finalized (i.e., once all doctests here pass).

[sagetrac-git]

Changed commit from 5eca4c1 to 853a04e

[sagetrac-git]

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

853a04e

8678: sage.modules.modules_with_basis -> sage.modules.with_basis + directory doc + added doc to the ref manual

[sagetrac-git]

Changed commit from 853a04e to 7b6e495

[sagetrac-git]

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

ad5d6c0	8678: permutation groups are finitely generated, finite fields are enumerated, fixes
839200e	8678: More doctest updates. Should almost pass all tests.
919a215	Merge branch 'develop = sage 6.6 beta6' into categories/finitely-generated-magmas-17160
7b6e495	Merge branch 'categories/finitely-generated-magmas-17160 + develop=6.6beta6' into categories/module-morphisms-8678

[sagetrac-git]

Changed commit from 7b6e495 to b4b28b9

[sagetrac-git]

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

b4b28b9

8678: Trivial doctest update

[saliola]

comment:73

I've looked over all the recent changes, too. Positive review, once all doctests pass (which they appear to do here).

[sagetrac-git]

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

5e6c707	Do not build the Jinja2 docs
71b36da	Merge branch 't/18012/sphinx_depends_on_jinja2' into categories/module-morphisms-8678

[sagetrac-git]

Changed commit from b4b28b9 to 71b36da

[tscrim]

comment:75

FYI - #17160 is finalized.

[nthiery]

comment:76

On {{{Linux sagange 3.2.0-4-amd64 #1 SMP Debian 3.2.63-2+deb7u1 x86_64
GNU/Linux}}}, and after merging in 6.6.rc0, I am getting only those
errors with make ptestlong:

sage -t --long src/sage/doctest/control.py  # 1 doctest failed
sage -t --long src/sage/calculus/calculus.py  # 1 doctest failed
sage -t --long src/sage/misc/trace.py  # 2 doctests failed
sage -t --long src/sage/modular/arithgroup/arithgroup_perm.py  # Timed out
sage -t --long src/sage/homology/simplicial_complex.py  # 1 doctest failed

Sounds like they are all maxima related, and I doubt there is any
relation to this ticket; rc0 fails similarly. Hence I am setting
this to positive review on behalf of Franco.

[vbraun]

Changed branch from u/nthiery/categories/module-morphisms-8678 to 71b36da