#18066 closed enhancement (fixed)
Cleanup of ModulesWithBasis and friends
Reported by:  tscrim  Owned by:  tscrim 

Priority:  major  Milestone:  sage6.10 
Component:  categories  Keywords:  
Cc:  nthiery, darij, aschilling, zabrocki, jhpalmieri  Merged in:  
Authors:  Travis Scrimshaw  Reviewers:  Darij Grinberg 
Report Upstream:  N/A  Work issues:  
Branch:  96004df (Commits)  Commit:  
Dependencies:  Stopgaps: 
Description
Currently ModulesWithBasis
requires its implementations to behave like CombinatorialFreeModule
, along with having an indexing set for the basis which is comparable. The aim of this ticket is to move various methods from CombintorialFreeModule
and it's element class to ModulesWithBasis
. This ticket will also give better generic functionality, such as a default implementation of support
.
Change History (27)
comment:1 Changed 5 years ago by
 Branch set to public/categories/cleanup_CFM_modules_wBasis18066
 Commit set to f8bd45183a2894e9260073209ecd8b93b957f6c4
 Milestone changed from sage6.6 to sage6.10
 Status changed from new to needs_review
comment:2 followup: ↓ 8 Changed 5 years ago by
Also a question mostly for Nicolas, do we still need _apply_module_morphism
? Is it just a method so that we don't have to create a full morphism object?
comment:3 followups: ↓ 6 ↓ 7 Changed 5 years ago by
+1! This is the way to go, and thanks for doing it.
However, one thing I'm still missing is an explicit explanation of what methods one needs to implement in order to inherit from ModulesWithBasis
. I suspect this is no longer uptodate:
# To implement a module_with_basis you need to implement either # basis() or an _indices attribute and monomial().
(as in, we probably need more now), right?
Coercion of coefficients into the base ring needs to be carefully thought over. As of now, I am not sure if it works correctly. For instance, term
does no coercion, but __invert__
does self.parent().term(one, ~mcs[one])
, although the inversion operator ~
might produce an element of a bigger ring (for example, ~(ZZ(2))
returns 1/2
).
One more thing, which is probably not your fault but just caught my eyes. The docstring of module_morphism
says:
 ``matrix``  a matrix of size `\dim X \times \dim Y` or `\dim Y \times \dim X`
I don't see why the "or" is here. The doctests show that \dim Y \times \dim X
works, but does \dim X \times \dim Y
work too? And if so, *should* it? I think checking whether the matrix has the "wrong" dimensions, and then trying to fix them by transposing it, would be a brittle paradigm.
Also, could we have doctests proving that the monomial_coefficients
method works correctly (including not mutating the dictionary unless explicitly required) on various instances of ModulesWithBasis
(e.g., vector spaces)? Thank you!
comment:4 Changed 5 years ago by
 Commit changed from f8bd45183a2894e9260073209ecd8b93b957f6c4 to aa444d2681187c178d9eca7c410468056a14bb3d
Branch pushed to git repo; I updated commit sha1. New commits:
aa444d2  Fixing doctests, trying to improve compatibility, and some changes.

comment:5 Changed 5 years ago by
 Commit changed from aa444d2681187c178d9eca7c410468056a14bb3d to 954e3542ccc00ef3cc294f19019da3608d87a5a8
Branch pushed to git repo; I updated commit sha1. New commits:
954e354  Added a test Darij requested.

comment:6 in reply to: ↑ 3 Changed 5 years ago by
 Cc aschilling zabrocki jhpalmieri added
So in my latest commit I fixed doctests. Some were trivial due to support
no longer being ordered (and hence changes to the kschur book tests and the cc of Anne and Mike), some were more substantial:
ChainComplexes
when passed a field saidVectorSpaces
, and so it did not consider itself as having a distinguished basis. However, if you give it a ring (likeZZ
), then it became inModulesWithBasis
(=FreeModules
), which it currently does not live from what I saw. Since there wasn't anything using this extra functionality (any attempt to use it was likely broken), I opted to downgrade the category to justModules
. (John, I cc'ed you to let you know.)
 I added a
dense_coefficient_list
for finite dimensional modules with basis so that you could get an ordered list of coefficients including 0's. This was needed for hyperplane arrangements. I'm open to different names.
 I made the linear expression code be in finite dimensional modules with basis.
Replying to darij:
However, one thing I'm still missing is an explicit explanation of what methods one needs to implement in order to inherit from
ModulesWithBasis
. I suspect this is no longer uptodate:# To implement a module_with_basis you need to implement either # basis() or an _indices attribute and monomial().(as in, we probably need more now), right?
I put that in there because that is all that should be required. However, how the code breaks and the traceback tells you everything you need to know as far as what to implement.
Coercion of coefficients into the base ring needs to be carefully thought over. As of now, I am not sure if it works correctly. For instance,
term
does no coercion, but__invert__
doesself.parent().term(one, ~mcs[one])
, although the inversion operator~
might produce an element of a bigger ring (for example,~(ZZ(2))
returns1/2
).
Actually my generic implementation should handle this with grace as it is coeff * self.monomial(index)
. However, CFM currently does not do any coercion as indicated in the docstring, but that is a discussion for another ticket.
One more thing, which is probably not your fault but just caught my eyes. The docstring of
module_morphism
says: ``matrix``  a matrix of size `\dim X \times \dim Y` or `\dim Y \times \dim X`I don't see why the "or" is here. The doctests show that
\dim Y \times \dim X
works, but does\dim X \times \dim Y
work too? And if so, *should* it? I think checking whether the matrix has the "wrong" dimensions, and then trying to fix them by transposing it, would be a brittle paradigm.
I don't know and I don't really care as that is outside of the scope of this ticket.
Also, could we have doctests proving that the
monomial_coefficients
method works correctly (including not mutating the dictionary unless explicitly required) on various instances ofModulesWithBasis
(e.g., vector spaces)?
Added.
comment:7 in reply to: ↑ 3 ; followup: ↓ 11 Changed 5 years ago by
Replying to darij:
One more thing, which is probably not your fault but just caught my eyes. The docstring of
module_morphism
says: ``matrix``  a matrix of size `\dim X \times \dim Y` or `\dim Y \times \dim X`I don't see why the "or" is here. The doctests show that
\dim Y \times \dim X
works, but does\dim X \times \dim Y
work too? And if so, *should* it? I think checking whether the matrix has the "wrong" dimensions, and then trying to fix them by transposing it, would be a brittle paradigm.
Which of the two it is depends on the value of the optional side
argument. No worry, there is no attempt at "fixing" things by transposition.
comment:8 in reply to: ↑ 2 ; followup: ↓ 10 Changed 5 years ago by
Replying to tscrim:
Also a question mostly for Nicolas, do we still need
_apply_module_morphism
? Is it just a method so that we don't have to create a full morphism object?
As far as I know, that was indeed the motivation when Mike H implemented it. I imagine it can make sense in certain cases where many different morphisms are applied. But I don't have a strong opinion either.
comment:9 Changed 5 years ago by
Thanks for the progress on that btw!
comment:10 in reply to: ↑ 8 Changed 5 years ago by
Replying to nthiery:
Replying to tscrim:
Also a question mostly for Nicolas, do we still need
_apply_module_morphism
? Is it just a method so that we don't have to create a full morphism object?As far as I know, that was indeed the motivation when Mike H implemented it. I imagine it can make sense in certain cases where many different morphisms are applied. But I don't have a strong opinion either.
I ended up doing something for diagram algebras where I found this to be useful (although I could have used a full morphism to work around it), so I'm happy enough to keep it around for now.
comment:11 in reply to: ↑ 7 Changed 5 years ago by
Replying to nthiery:
Replying to darij:
One more thing, which is probably not your fault but just caught my eyes. The docstring of
module_morphism
says: ``matrix``  a matrix of size `\dim X \times \dim Y` or `\dim Y \times \dim X`I don't see why the "or" is here. The doctests show that
\dim Y \times \dim X
works, but does\dim X \times \dim Y
work too? And if so, *should* it? I think checking whether the matrix has the "wrong" dimensions, and then trying to fix them by transposing it, would be a brittle paradigm.Which of the two it is depends on the value of the optional
side
argument. No worry, there is no attempt at "fixing" things by transposition.
Ah, thank you! I didn't see this, as the argument is hidden inside the **keywords
.
comment:12 Changed 5 years ago by
 Commit changed from 954e3542ccc00ef3cc294f19019da3608d87a5a8 to 2a935f54705b998469f68f54cc8af77c440fb1f7
Branch pushed to git repo; I updated commit sha1. New commits:
2a935f5  Made FreeModules in the category of finite dimensional free modules with basis.

comment:13 Changed 5 years ago by
 Commit changed from 2a935f54705b998469f68f54cc8af77c440fb1f7 to 7c0223af13ccb7e92191eea50431b3ebc477dbc7
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
570bc49  Merge branch 'public/categories/super_categories18044' into 6.9.b1

b91cd82  trac #18044 correct one typo in the doc

7fd1df2  Merge branch 'public/categories/super_categories18044' of trac.sagemath.org:sage into public/categories/super_categories18044

0579337  Some reviewer tweaks and doc additions.

aec22cc  Added one more test.

4b2046f  Merge branch 'public/categories/super_categories18044' into public/categories/filtered_algebras17096

3f67b6b  Fixing trivial doctest due to changes in category heirarchy.

fa476dd  Fixing doublecolon in INPUT block.

6cc8b84  Reviewer changes with Darij.

7c0223a  Merge branch 'public/categories/filtered_algebras17096' of trac.sagemath.org:sage into public/categories/cleanup_CFM_modules_wBasis18066

comment:14 Changed 5 years ago by
It wasn't letting me post this comment:
To fix the failing doctests, I made the free modules be in the category of finite dimensional modules with basis, which I believe they should have been awhile ago. I also merged in the filtered algebras patch.
comment:15 Changed 5 years ago by
 Commit changed from 7c0223af13ccb7e92191eea50431b3ebc477dbc7 to c504110a3d44de5381b3ed33ed5d9765e2b060a9
comment:16 Changed 5 years ago by
 Commit changed from c504110a3d44de5381b3ed33ed5d9765e2b060a9 to 913a0c14f45142e5f80579c58147174daa18f27b
Branch pushed to git repo; I updated commit sha1. New commits:
913a0c1  Fixing doctest/tab issues from merge.

comment:17 Changed 5 years ago by
 Commit changed from 913a0c14f45142e5f80579c58147174daa18f27b to b32e479bffac439f3cfb561027dfebc871d01528
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
07cc001  18411: Fixed unused import

7c103df  18411: cleanup spacing for optional arguments

a35ef8a  18411: proofreading

22f8b77  18411: proofreading

4a9fd81  Trac 18411: merge Sage 6.10.beta0

525d038  Trac 18411: Fix doctest in colored_permutations.py

41af762  Trac 18411: pass keywords in __call__

6e27dde  Trac 18411: merge sage6.10.beta1

b21396c  Merge branch '18411' into HEAD

b32e479  further changes (mostly doc)

comment:18 Changed 5 years ago by
 Commit changed from b32e479bffac439f3cfb561027dfebc871d01528 to e2fb14a393beb5e40519df8cf7ae06b077a398b0
comment:19 Changed 5 years ago by
Great job, Travis. If you are fine with my edits and the doctests agree, this is a positive_review.
I am somewhat unhappy about the fact that submodules of free modules don't play nicely with monomial_coefficients
(if M
is a submodule of R^n
given as the span of some vectors, then m.monomial_coefficients
for m \in M
gives me the monomial coefficients of m
with respect to the standard basis of R^n
, not with respect to any basis of M
), but this is hardly a flaw of this particular ticket.
comment:20 Changed 5 years ago by
 Status changed from needs_review to positive_review
comment:21 Changed 5 years ago by
 Reviewers set to Darij Grinberg
comment:22 Changed 5 years ago by
 Status changed from positive_review to needs_work
How about running the tests before setting something to positive review?
sage t long src/sage/geometry/linear_expression.py ********************************************************************** File "src/sage/geometry/linear_expression.py", line 183, in sage.geometry.linear_expression.LinearExpression.monomial_coefficients Failed example: sorted(linear.monomial_coefficients().items() Exception raised: Traceback (most recent call last): File "/mnt/disk/home/buildslavesage/slave/sage_git/build/local/lib/python2.7/sitepackages/sage/doctest/forker.py", line 496, in _run self.compile_and_execute(example, compiler, test.globs) File "/mnt/disk/home/buildslavesage/slave/sage_git/build/local/lib/python2.7/sitepackages/sage/doctest/forker.py", line 856, in compile_and_execute compiled = compiler(example) File "/mnt/disk/home/buildslavesage/slave/sage_git/build/local/lib/python2.7/sitepackages/sage/doctest/forker.py", line 494, in <lambda> example.source, filename, "single", compileflags, 1) File "<doctest sage.geometry.linear_expression.LinearExpression.monomial_coefficients[3]>", line 1 sorted(linear.monomial_coefficients().items() ^ SyntaxError: unexpected EOF while parsing ********************************************************************** 1 item had failures: 1 of 5 in sage.geometry.linear_expression.LinearExpression.monomial_coefficients [165 tests, 1 failure, 1.47 s]
comment:23 Changed 5 years ago by
 Commit changed from e2fb14a393beb5e40519df8cf7ae06b077a398b0 to 96004dfa8a3368fe4f2fe122268744d9f6e4bf79
Branch pushed to git repo; I updated commit sha1. New commits:
96004df  Darij...

comment:24 Changed 5 years ago by
 Status changed from needs_work to positive_review
comment:25 Changed 5 years ago by
Thanks Travis! (I've just fired up my virtual machine a few minutes ago to deal with this...)
Note to self: do test sage/geometry...
comment:26 Changed 5 years ago by
 Branch changed from public/categories/cleanup_CFM_modules_wBasis18066 to 96004dfa8a3368fe4f2fe122268744d9f6e4bf79
 Resolution set to fixed
 Status changed from positive_review to closed
comment:27 Changed 18 months ago by
 Commit 96004dfa8a3368fe4f2fe122268744d9f6e4bf79 deleted
in src/sage/categories/modules_with_basis.py
one still sees
Once :trac:`18066` is merged
namely here:
9bc28fd5fdb (Travis Scrimshaw 20150326 23:33:19 0700 129) This category currently requires an implementation of an 6cc8b8460df (Travis Scrimshaw 20151004 16:20:51 0500 130) element method ``support``. Once :trac:`18066` is merged, an 6cc8b8460df (Travis Scrimshaw 20151004 16:20:51 0500 131) implementation of an ``items`` method will be required.
Okay, I figured this was the best starting point for trying to see if the quack of a free module echoes. For this ticket, I moved many methods up and was able to generalize them. There were only minimal changes needed to remove the ordering on
support
(only the Macdonald basis ofSym
) and makemonomial_coefficients()
an abstract method. I added thecopy
parameter to monomial coefficients for both speed anddict
in the usual free modules has this API. Most of the other changes are trivial changes to doctest output.The next thing to do would be to check to see if #10672 becomes invalid because of this ticket (execpt perhaps the iteration issue). After that, then move onto either merging CFM and (sparse?) free modules #10671 or rebasing and finalizing #18310.
New commits:
Moving code up from CFM to modules_with_basis.