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.

[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?

[saraedum]

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.

[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

[git]

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

​553c5de

8678: Imported module_morphism_function_extend-fh.patch

[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

[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

[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

[git]

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

​b62ebe9

8678: trivial ReST fix

[git]

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

​8b971f4

8678: bug fix and doctests for CombinatorialFreeModule being automatically finite dimensional

[git]

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

​494da74

8678: trivial ReST fix

[git]

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

​cb5a236

8678: trivial doctests fix (more categories are finite dimensional now)

[git]

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

​aa7fe1d

8678: noted known pickling issue

[nthiery]

Now mosts tests pass. The remaining failing ones are because of some finite dimensional algebras over a finite field become finite, hence finite semigroups. And currently finite semigroups are automatically made into enumerated sets using their generators; however those generators are not always available.

[git]

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

​445c925

8768: Fixed doctests

[git]

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

​93273a7	Merge branch 'u/nthiery/categories/full-subcategories-16340' of trac.sagemath.org:sage into public/categories/full_subcategories-16340
​edb29e6	Fixed trivial doctest failures.
​99a8eb1	Merge branch 'public/categories/full_subcategories-16340' of trac.sagemath.org:sage into categories/full-subcategories-16340
​8bc456c	Merge branch 'master=6.3' into categories/full-subcategories-16340
​56e982e	Merge branch 'categories/full-subcategories-16340' and 6.3 into categories/morphism-methods-10668
​016cd16	#16340: Revert ReST typo fix in ell_curve_isogeny.py to avoid conflict with other ticket handling it
​d147678	Merge branch 'develop=6.4.beta0' into categories/morphism-methods-10668
​8054997	Merge branch 'categories/morphism-methods-10668' into categories/module-morphisms-8678

[git]

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

​16acc6c	8678: complete proofreading
​a2a1614	8678: removed explicit doctest:xxx: source line number from a doctest
​737a8f0	16340: improved warnings about the current limitation of the model
​282ac4e	16340: fixed typos reported by Darij
​1e4418f	Merge branch 'develop' into categories/full-subcategories-16340
​314ee44	Merge branch 'categories/full-subcategories-16340' into categories/module-morphisms-8678

[git]

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

​6907024

8678: trivial doctest update after merge with develop

[git]

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

​9852173	8678: rewrote a few tests introduced by #16296 so that they do not depend on the number of axioms defined in Sage
​6136990	See discussion on: https://groups.google.com/d/msg/sage-devel/IT_gI_cx0co/QhxdAZeaJzMJ for details.

[tscrim]

From the diff, you've accidentally removed the i += 1, so it should run forever (provided the 0th component is non-trivial). Ah what I wouldn't give for a python builtin do-while loop...

[git]

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

​ce2a56b

8678: oops, restored accidently deleted increment

[virmaux]

Humph, so two points:

1- The last push correct a bug in TriangularModuleMorphism? with on_basis.

2- I did not know that my push would have change the branch (but I should as it is a 'private' one) and do not know how to replace back the right branch, which is u/nthiery/categories/module-morphisms-8678. Sorry for the noise :s

At least, if my correction is wrong it should be very easy to reset :)

---

New commits:

​0b4b010

#8678: fixed on_basis in TriangularModuleMoprhism

[git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

​d8a8373	Fixing some typos
​75615b5	10668: trivial doctest updates
​d5d3a97	10668: improved description of the HomsetsOf class
​5416ba0	Add a note on the MRO used for Homset._abstract_element_class
​23639a9	Fix more typos
​02a6a8a	10668: fixed representation of the category of endsets
​477d381	10668: Homsets.Endset.super_category -> extra_super_category + documentation
​877bfdb	10668: fix: Modules.EndCategory -> Modules.Homsets.Endset + made it functional: endsets of modules are algebras
​f86824e	10668: documentation for HomsetsCategory.category_of + fixed typo in doctest nearby
​9bb4b48	8678: merge in #10668, including develop=6.4 beta4

[SimonKing]

Last 10 new commits:

​d8a8373	Fixing some typos
​75615b5	10668: trivial doctest updates
​d5d3a97	10668: improved description of the HomsetsOf class
​5416ba0	Add a note on the MRO used for Homset._abstract_element_class
​23639a9	Fix more typos
​02a6a8a	10668: fixed representation of the category of endsets
​477d381	10668: Homsets.Endset.super_category -> extra_super_category + documentation
​877bfdb	10668: fix: Modules.EndCategory -> Modules.Homsets.Endset + made it functional: endsets of modules are algebras
​f86824e	10668: documentation for HomsetsCategory.category_of + fixed typo in doctest nearby
​9bb4b48	8678: merge in #10668, including develop=6.4 beta4

[nthiery]

#17160 I am working on now should fix the failing tests.

[git]

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

​9c939ae	16340: Merge branch 'develop=6.4 beta6' into categories/full-subcategories-16340
​5f96686	17160: Merge branch 'categories/morphism-methods-10668'
​f027ce2	17610: first draft of finitely generated axiom for magmas/groups/axioms
​dabcafd	Merge branch 'develop' into t/17160/categories/finitely-generated-magmas-17160
​6f22b72	Merge branch 't/17160/categories/finitely-generated-magmas-17160' into t/8678/categories/module-morphisms-8678

[git]

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

​830c550

8678: fixed missing import

[git]

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

​0e89bb7

Fixed ReST typo

[git]

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

​a117dc5

8678: co_reduced -> coreduced + added check (valid only for a field or unitriangular + doc improvements here and there

[git]

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

​b2b10fc

8678: unitriangular=lower as shorthand for triangular=lower, unitriangular=True; added sanity checks and tests for cokernel_basis_indices

[git]

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

​9390838	8678: moved ModuleMorphism's code from sage.categories.modules_with_basis to sage.modules.module_with_basis_morphism
​05634b4	8678: Follow up on the previous commit: updating paths + extracted new abstract class ModuleMorphism

[git]

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

​fa9e2a6

8678: Added ModuleMorphismFromMatrix class + better API for constructing them through module_morphism(matrix=...)

[git]

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

​5409f2f

8678: More doc and small fixes for previous commit

[git]

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

​87cd8ca

8678: Added comment about element class creation for module morphisms

[git]

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

​42d9861

8678: Small Rest fixes to let the doc compile

[git]

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

​2f0c203

#8678: trivial doctest update (group algebras of finite groups are finite dimensional)

[git]

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

​078b562

#8678: trivial doctest update (group algebras of finite groups are finite dimensional)

[git]

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

​d948281	8678: implemented (triangular) module morphisms from a function; more doc and tests needed
​eaded97	8678: systematic doc and tests for the various ModuleMorphism classes + minor fixes (e.g. on_basis)

[git]

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

​4125b2a

8678: more doc improvements

[nthiery]

Hi Franco,

I believe I have taken care of everything we discussed on Monday. So back to needs review! There remains to little points to be discussed in Davis:

• Should the user documentation about triangular morphisms be in the class or in module_morphism?

• triangular=True led to triangular="lower" while the default value for triangular is "upper"

Cheers from warm Davis!

Nicolas

[git]

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

​1a4e897

8678: Added abstract methods Sets.MorphismMethods.__invert__

[git]

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

​f9b1f87

8678: fixed bug introduced recently about the initialization of TriangularModuleMorphism._invertible

[git]

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

​cf9b429	Fixed ReST typo
​aff2689	17160: fixed category for finite set endomaps + minor __init__ refactoring
​1f9981f	Merge branch 'categories/finitely-generated-magmas-17160' into categories/module-morphisms-8678

[darij]

Needs review, but depends on a blue ticket, and work issues listed?

[nthiery]

Just a tip: given the many modifications here and there, and the new classes, it's might be simpler to review directly the whole new file src/sage/modules/module_with_basis_morphism.py rather than looking at its diff. Otherwise, I took care of the moving of the code from modules_with_basis.py in a separate commit, so that you can diff from there.

[nthiery]

I had forgotten to clear the issue. #17160 is just waiting for feedback on the sage mailing list to be finalized. In any cases both tickets are rather independent, so the review of the code of this one can start right away. Of course it will be necessary to rerun the tests once the failures coming from #17160 will be fixed

[git]

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

​34ee60d	8678: improved support for pickling and default value of the invertible option
​24ed527	8678: specify explicitly that one morphism in sage.algebras.hall_algebra is invertible to make up for the change in 4125b2a6394cbf3f594991513394fa5958ae841b
​7861e32	8678: ReST fix

[git]

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

​4b3d74c	Merge branch 'develop' into categories/finitely-generated-magmas-17160
​6de563d	Merge branch 'categories/finitely-generated-magmas-17160 + develop=6.6beta5' into categories/module-morphisms-8678

[saliola]

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

• a couple of doctests include the following line:

  sage: import __main__; __main__.f = f  
  

can you explain why this is necessary?

• 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 doctests don't pass, but this seems to be related to #17160

---

New commits:

​0d3af4d

8678: typo fixes and some new doctests

[git]

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

​a2ee49b

8678: deprecated triangular=True; added more sanity checks; spacing improvements

[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]

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 #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]

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]

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.

[git]

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

​d9b5507

8678: fixed missing __init__.py

[git]

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

​5eca4c1

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

[saliola]

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).

[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

[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

[git]

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

​b4b28b9

8678: Trivial doctest update

[saliola]

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

[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

[tscrim]

FYI - #17160 is finalized.

[nthiery]

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.