Add support for homogeneous components of a filtered module #19397

tscrim · 2015-10-13T00:47:51Z

Separates out functionality of subset(d) for finite dimensional filtered modules with basis and implements a method to get the submodule spanned by a homogeneous piece.

Depends on #17096

CC: @sagetrac-sage-combinat @darijgr @nthiery @simon-king-jena

Component: categories

Author: Travis Scrimshaw

Branch/Commit: f9aaad5

Reviewer: John Palmieri

Issue created by migration from https://trac.sagemath.org/ticket/19397

The text was updated successfully, but these errors were encountered:

tscrim · 2015-10-13T00:49:41Z

comment:1

This will be useful along with the changes I'm making in #6102, which I think will be our first naturally graded finite-dimensional algebra in Sage.

Last 10 new commits:

`570bc49`	`Merge branch 'public/categories/super_categories-18044' into 6.9.b1`
`b91cd82`	`trac #18044 correct one typo in the doc`
`7fd1df2`	`Merge branch 'public/categories/super_categories-18044' of trac.sagemath.org:sage into public/categories/super_categories-18044`
`0579337`	`Some reviewer tweaks and doc additions.`
`aec22cc`	`Added one more test.`
`4b2046f`	`Merge branch 'public/categories/super_categories-18044' into public/categories/filtered_algebras-17096`
`3f67b6b`	`Fixing trivial doctest due to changes in category heirarchy.`
`fa476dd`	`Fixing double-colon in INPUT block.`
`6cc8b84`	`Reviewer changes with Darij.`
`9c51a4c`	`Merge branch 'public/categories/filtered_algebras-17096' of trac.sagemath.org:sage into public/categories/graded_components-TBA`

tscrim · 2015-10-13T00:49:41Z

Commit: 9c51a4c

tscrim · 2015-10-13T00:49:41Z

Branch: public/categories/homogeneous_components-19397

jhpalmieri · 2015-10-13T01:30:18Z

comment:2

You have the comment starting with

# TODO: which syntax do we prefer?

twice, along with two different basis methods in filtered_modules_with_basis.py.

sagetrac-git · 2015-10-13T01:36:20Z

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

`ae81aa7`	`Fixing bad copying.`

sagetrac-git · 2015-10-13T01:36:20Z

Changed commit from 9c51a4c to ae81aa7

jhpalmieri · 2015-10-21T17:32:34Z

comment:4

Is this a problem?

sage: A = GradedModulesWithBasis(ZZ).example()
sage: A.homogeneous_component(3).an_element()   # not printed like elements of A
3*B[[1, 1, 1]] + 3*B[[2, 1]] + B[[3]]
sage: a = A.homogeneous_component(3).an_element()
sage: a in A
False

Also, A(a) leads to a NotImplementedError. So once you have an element in a homogeneous component, there isn't an obvious way to view it as an element of the whole module.

tscrim · 2015-10-21T19:42:47Z

comment:5

I was originally taking care of this on #19359, but I've now moved this to #19448 (which you can set as a dependency if you feel it is warranted).

jhpalmieri · 2015-10-22T18:07:59Z

comment:6

Will #19448 also make

list(A.homogeneous_component(4).basis())

and

list(A.homogeneous_component_basis(4))

equal? (Can they be equal? The elements in the first are elements in a particular homogeneous component. The elements in the second are elements in the whole module. At least they should look the same when you print them, and I think #19448 should take care of that.)

jhpalmieri · 2015-10-22T18:18:02Z

comment:7

One mathematical issue: in defining homogeneous_component, you have

category = ModulesWithBasis(self.category().base_ring())

A homogeneous component of an R-module need not be an R-module itself in a natural way: for example, if the base ring is the graded ring R=k[x, x^-1] with x in some nonzero degree, then for any homogeneous component of any graded R-module, x would have to act trivially (because x has nonzero degree). On the other hand, x is supposed to be invertible.

It will always be a module over the degree 0 part of the base ring, though.

darijgr · 2015-10-24T14:34:15Z

comment:8

John: I fear that this notion of grading is not currently implemented in Sage (again, hardly anyone's deliberate design choice, but an artifact of ungraded base rings being the de-facto standard in combinatorics). Almost all of the current code in FilteredModulesWithBasis currently assumes that the base ring is ungraded :(

Incidentally, IMHO this issue shows that we are mistaken in the assumption that in order to equip an algebra with a grading, we should add degree and similar functions to the class. Many algebras have several natural gradings, and each of them comes with its own notion of a graded module. When you speak of a "graded R[x]-module", you have to specify whether x has degree 1 or 0 (or anything else); even in combinatorics, both of these cases happen. So if/when we make R[x] into a graded ring, what should its grading be? I think it shouldn't. There should be a two graded rings, called PolynomialRing(QQ).trivial_grading() and PolynomialRing().degree_grading() or something like this, while PolynomialRing(QQ) itself should just be a QQ-algebra. Actually the trivial_grading() function should be defined generically on any module and return the corresponding graded module with trivial grading. And there can be further gradings and filtrations likewise (I can see good uses for filtered the tensor algebra by word length, number of distinct letters, maximal multiplicity of a letter, etc. -- there is no way the code should decide between them for the user!).

jhpalmieri · 2015-10-24T14:51:29Z

comment:9

For this situation, what about code like

try:
    R = self.base_ring().homogeneous_component(0)
    # or R = self.base_ring().base_ring()??
except AttributeError:
    R = self.base_ring()
category = ModulesWithBasis(self.category().R)

This may end up calling homogeneous_component recursively, but eventually that should end with an ungraded base ring.

Yes, I also agree that we need to allow for multiple possible gradings. I think this has been discussed before. To construct a graded ring you should specify a ring and a grading on it, and different gradings give different graded rings.

tscrim · 2015-10-26T14:20:25Z

comment:10

However there is a technical problem with doing that in the short-term in that submodule currently does not differentiate between coordinate rings and base rings (think ZZ-submodule in a QQ-module). See also Jeroen's comments in #18310.

So if we were decided to do do the above, then we should add coordinate ring support in #19448 and make that a dependency of this one.

Alternatively we could just raise a NotImplementedError for now if the module and base ring are both graded.

jhpalmieri · 2015-10-26T15:39:08Z

comment:11

I think we should do something, just to acknowledge that it is an issue that we might address later. A NotImplementedError sounds fine to me. Whatever is simplest, I think.

sagetrac-git · 2015-10-26T16:21:23Z

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

`cd186d0`	`Merge branch 'public/categories/homogeneous_components-19397' of trac.sagemath.org:sage into public/categories/homogeneous_components-19397`
`f89275b`	`Raise a NotImplementedError if the base ring is filtered.`

sagetrac-git · 2015-10-26T16:21:23Z

Changed commit from ae81aa7 to f89275b

tscrim · 2015-10-26T16:22:52Z

comment:13

The simple way is to raise a NotImplementedError for now. Although now I find myself wishing for filtered magmas...

jhpalmieri · 2015-10-26T18:59:00Z

comment:14

This looks okay to me.

jhpalmieri · 2015-10-26T18:59:00Z

Reviewer: John Palmieri

vbraun · 2015-10-27T00:01:41Z

comment:15

Doctests fail:

http://build.sagedev.org/release/builders/%20%20slow%20AIMS%20%20%28Debian%207%2064%20bit%29%20incremental/builds/152/steps/shell_4/logs/stdio

jhpalmieri · 2016-04-18T19:29:33Z

comment:41

I think there is a word ("when"?) missing in the "TODO" comment.

sagetrac-git · 2016-04-18T19:33:20Z

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

`068adf3`	`Trying to avoid infinite lists and adding a TODO comment.`

sagetrac-git · 2016-04-18T19:33:20Z

Changed commit from 6c0e7bd to 068adf3

tscrim · 2016-04-18T19:34:12Z

comment:43

Replying to @jhpalmieri:

I think there is a word ("when"?) missing in the "TODO" comment.

True. I also was able to make it so the text ended at the same position. :P FYI - I decided to amend my previous commit instead of a new one.

jhpalmieri · 2016-04-18T21:35:00Z

comment:44

Okay, I'm happy with this now. If you think it's not ready, revert my positive review.

tscrim · 2016-04-18T21:42:02Z

comment:45

It is good. Thank you. MRO issue is now #20460.

vbraun · 2016-04-19T16:24:43Z

comment:46

sage -t --long src/sage/categories/filtered_modules_with_basis.py
**********************************************************************
File "src/sage/categories/filtered_modules_with_basis.py", line 160, in sage.categories.filtered_modules_with_basis.FilteredModulesWithBasis.ParentMethods.basis
Failed example:
    A.basis(4)
Expected:
    Traceback (most recent call last):
    ...
    AttributeError: 'IndexedFreeAbelianMonoid_with_category' object has no attribute 'list'
Got:
    <BLANKLINE>
    Traceback (most recent call last):
      File "/mnt/disk/home/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 496, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/mnt/disk/home/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 858, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.categories.filtered_modules_with_basis.FilteredModulesWithBasis.ParentMethods.basis[5]>", line 1, in <module>
        A.basis(Integer(4))
      File "/mnt/disk/home/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/categories/filtered_modules_with_basis.py", line 186, in basis
        return self.homogeneous_component_basis(d)
      File "/mnt/disk/home/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/categories/filtered_modules_with_basis.py", line 215, in homogeneous_component_basis
        S = [i for i in list(self._indices) if self.degree_on_basis(i) == d]
      File "sage/structure/parent.pyx", line 1548, in sage.structure.parent.Parent.__len__ (/mnt/disk/home/buildslave-sage/slave/sage_git/build/src/build/cythonized/sage/structure/parent.c:12470)
        return len(self.list())
      File "/mnt/disk/home/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/sage/categories/infinite_enumerated_sets.py", line 76, in list
        raise NotImplementedError("infinite list")
    NotImplementedError: infinite list
**********************************************************************
1 item had failures:
   1 of  10 in sage.categories.filtered_modules_with_basis.FilteredModulesWithBasis.ParentMethods.basis
    [214 tests, 1 failure, 0.75 s]

jhpalmieri · 2016-04-19T16:56:31Z

comment:47

Volker, I don't see this failure when I run doctests or when I do it by hand, and I don't see it on the patchbots, either. Do you have any ideas why?

tscrim · 2016-04-19T17:32:11Z

comment:48

I also don't get the failure. Maybe something changed with the example implementation in another (already closed) ticket? I certainly can see why this failure might occur...and it is an easy enough fix...

sagetrac-git · 2016-04-23T02:20:55Z

Changed commit from 068adf3 to aa85da2

sagetrac-git · 2016-04-23T02:20:55Z

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

`13fee78`	`Merge branch 'public/categories/homogeneous_components-19397' of trac.sagemath.org:sage into public/categories/homogeneous_components-19397`
`aa85da2`	`Fixing change in error message and corresponding documentation.`

tscrim · 2016-04-23T02:24:42Z

comment:50

The problem occurred in beta5 (in fact, I believe I know exactly which ticket caused it...). I fixed the error message and the documentation (I am pretty sure a NotImplementedError will be more common with this change anyways...).

sagetrac-git · 2016-04-23T11:59:55Z

Changed commit from aa85da2 to f9aaad5

sagetrac-git · 2016-04-23T11:59:55Z

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

`f9aaad5`	`Fixing docstring (which should have been on the last commit).`

jhpalmieri · 2016-04-23T15:48:32Z

comment:52

Looks good to me. Passes all tests.

tscrim · 2016-04-23T20:16:46Z

comment:53

Replying to @jhpalmieri:

Looks good to me. Passes all tests.

Thank you.

vbraun · 2016-04-25T08:38:17Z

Changed branch from public/categories/homogeneous_components-19397 to f9aaad5

tscrim added this to the sage-6.10 milestone Oct 13, 2015

tscrim added c: categories labels Oct 13, 2015

tscrim assigned sagetrac-sage-combinat Oct 13, 2015

tscrim added the s: needs review label Oct 13, 2015

jhpalmieri added s: positive review and removed s: needs review labels Oct 26, 2015

vbraun added s: needs work and removed s: positive review labels Oct 27, 2015

jhpalmieri added s: positive review and removed s: needs review labels Apr 18, 2016

vbraun added s: needs work and removed s: positive review labels Apr 19, 2016

tscrim added s: needs review and removed s: needs work labels Apr 23, 2016

tscrim modified the milestones: sage-6.10, sage-7.2 Apr 23, 2016

jhpalmieri added s: positive review and removed s: needs review labels Apr 23, 2016

vbraun removed the s: positive review label Apr 25, 2016

vbraun closed this as completed in 9a46ec7 Apr 25, 2016

tscrim mentioned this issue Dec 29, 2022

Fix MRO issues with categories #20460

Open

Add support for homogeneous components of a filtered module #19397

Add support for homogeneous components of a filtered module #19397

Comments

tscrim commented Oct 13, 2015

tscrim commented Oct 13, 2015

tscrim commented Oct 13, 2015

tscrim commented Oct 13, 2015

jhpalmieri commented Oct 13, 2015

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jhpalmieri commented Oct 21, 2015

tscrim commented Oct 21, 2015

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darijgr commented Oct 24, 2015

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tscrim commented Oct 26, 2015

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tscrim commented Oct 26, 2015

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jhpalmieri commented Apr 18, 2016

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tscrim commented Apr 18, 2016

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