Opened 9 months ago
Closed 3 months ago
#32505 closed enhancement (fixed)
Finitely presented graded modules over graded connected algebras
Reported by:  jhpalmieri  Owned by:  

Priority:  major  Milestone:  sage9.6 
Component:  algebra  Keywords:  
Cc:  ghsverre320, kvanwoerden, jhpalmieri, tscrim, ghrrbruner, cnassau  Merged in:  
Authors:  Bob Bruner, Michael Catanzaro, Sverre LunøeNielsen, Koen van Woerden, John Palmieri, Travis Scrimshaw  Reviewers:  John Palmieri, Travis Scrimshaw 
Report Upstream:  N/A  Work issues:  
Branch:  a1a9467 (Commits, GitHub, GitLab)  Commit:  a1a9467e95cd05a6439b4b2765e62c6aad6dc960 
Dependencies:  Stopgaps: 
Change History (90)
comment:1 Changed 9 months ago by
comment:2 Changed 9 months ago by
 Branch set to u/jhpalmieri/freegradedmodules
comment:3 Changed 9 months ago by
 Commit set to fa915966124a5e32b28a3a54538045d74858ed92
 Status changed from new to needs_review
This is not the final draft — I'd like to resolve at least some of the "TODO"s — but I'll mark it as "needs review".
New commits:
fa91596  trac 32505: finitely presented graded modules

comment:4 Changed 9 months ago by
Structurally, the starting place for a review perhaps should be the free_*
files; the others are built on top of those.
comment:5 Changed 9 months ago by
 Commit changed from fa915966124a5e32b28a3a54538045d74858ed92 to fd8545b771c670f6eda373b3fa5e4ea88d17b45d
Branch pushed to git repo; I updated commit sha1. New commits:
fd8545b  trac 32505: clear out __init__.py

comment:6 Changed 9 months ago by
In order to follow #32501, __init__.py
should be empty, so I changed it, moving the TODO list to module.py
.
comment:7 Changed 8 months ago by
Thank you for separating this ticket out. It will make it easier to focus on the general functionality here. I finally have gotten back around to this. Sorry it took so long (but I have now finally moved to Japan).
I think we should change the name FP_Element
and similar to FPElement
to match PEP8.
There are many places where TESTS:
should be TESTS::
.
Let's get rid of the is_FreeGradedModuleHomspace
and just replace it with the isinstance
call.
I don't like the name free_element()
. Perhaps free_module_representative()
?
The mathematical description does not quite seem to match the implementation. Your basis elements are not a basis over the F
algebra A
but over F
. This needs to be very carefully explained in the documentation.
I think more things should be using the category framework (unless this becomes a significant bottleneck in #30680) Mainly I am looking at degree()
by using degree_on_basis
, but there is a mismatch with what this is a module over. Actually, this is more like the cartesian_product
with some additional functionality. I might need to think a bit more about how this will all fit together.
comment:8 Changed 8 months ago by
 Commit changed from fd8545b771c670f6eda373b3fa5e4ea88d17b45d to 5153c6fab78b1a9869b67c76fbc6c1fff81862f7
comment:9 Changed 8 months ago by
Here are some of the changes: everything you suggested except for the category framework and changing the documentation to reflect what we mean by basis. (I thought I would take care of the easy things first.)
If you have more thoughts about how to use the category framework, I would be happy to hear them.
comment:10 Changed 8 months ago by
To utilize the degree()
from the category framework, we only need to implement a degree_on_basis()
method in the parent. This would mean less repeated code, although it might be slightly slower in the computation. Of course, the current version works and is fine to do things this way.
We also don't need the __nonzero__
anymore because __bool__
is Python3.
Right now, I feel like this is violating some internal assumptions of CFM
because of the basis mismatch. So it should not inherit from CFM
, but some other class, perhaps CombinatorialFreeModule_CartesianProduct
as we realize it as A
^{k} but are considering it to be an F
module from the implementation point of view. If we really want to think of it as an A
module, then internally we need to extract the F
basis coefficients from the values of the element dict
(and we might want to think a bit about how we name our methods). This should be fairly simple to do, but requires some minor refactoring.
Based upon the code and its intended use, you are converting things a lot to/from (dense) vectors in F
^{d}, so the Cartesian product approach with an entirely new element class might be the best option, where elements is stored as a dict of (degree, vector)
pairs. I guess it depends on how much time is spent doing element manipulations like this, but the caching suggests this is a timecritical operation.
comment:11 followup: ↓ 12 Changed 8 months ago by
First, FreeGradedModule
is indeed an honest free module, and I think it should be okay to use CombinatorialFreeModule
for it. The "basis" in this case is explicitly the basis as a module over algebra
; it is not a vector space basis. As a result, the degree_on_basis()
setup won't work, because it assumes that you're working with graded modules over an ungraded ring, and so it doesn't take into account the possible degree of the coefficients. At least that's my reading of the homogeneous_degree method in categories/filtered_modules_with_basis.py
.
I don't really see how using Cartesian products will help: A^{k} is just a free module, so we should be able to use the free module class for it. I don't think the code will use the projection and inclusion maps that are provided by the Cartesian product class.
FPModule
is trickier: it is not free as a module over algebra
, but of course it is free over the ground field. I don't know of a suitable class in Sage for it, but CombinatorialFreeModule
kind of works. One problem is that the basis keys correspond to the given choice of generators, and since the module need not be free, it need not be a basis. Another problem is that there is an actual vector space basis in each degree and we want to compute it, but we can't just deduce it from the "basis" for this CombinatorialFreeModule
.
It's a good idea to maybe cache dense_coefficient_list
for these elements, and maybe while we're at it, give the method for this class of elements a different name.
comment:12 in reply to: ↑ 11 ; followup: ↓ 14 Changed 8 months ago by
Replying to jhpalmieri:
First,
FreeGradedModule
is indeed an honest free module, and I think it should be okay to useCombinatorialFreeModule
for it. The "basis" in this case is explicitly the basis as a module overalgebra
; it is not a vector space basis. As a result, thedegree_on_basis()
setup won't work, because it assumes that you're working with graded modules over an ungraded ring, and so it doesn't take into account the possible degree of the coefficients. At least that's my reading of the homogeneous_degree method incategories/filtered_modules_with_basis.py
.
Ah, right, because we are considering it over a graded ring, which we do not have a mechanism to take that into account. That is a missing feature of the categories that probably needs to be addressed at some point. However, then the category of GradedModulesWithBasis(R)
is wrong, and instead it should be in GradedModules(R).WithBasis()
. These are not the same
sage: GradedModulesWithBasis(QQ) == GradedModules(QQ).WithBasis() False
as the latter is just saying there is a distinguished basis in a graded module, but not that the basis respects the grading. This allows us to circumvent this issue of the grading of the base ring (at least for now).
I don't really see how using Cartesian products will help: A^{k} is just a free module, so we should be able to use the free module class for it. I don't think the code will use the projection and inclusion maps that are provided by the Cartesian product class.
From the above, I agree that CFM
is fine. So we don't have to use this.
FPModule
is trickier: it is not free as a module overalgebra
, but of course it is free over the ground field. I don't know of a suitable class in Sage for it, butCombinatorialFreeModule
kind of works. One problem is that the basis keys correspond to the given choice of generators, and since the module need not be free, it need not be a basis. Another problem is that there is an actual vector space basis in each degree and we want to compute it, but we can't just deduce it from the "basis" for thisCombinatorialFreeModule
.
We can weaken this to be a subclass of IndexedGenerators
, Module
, and UniqueRepresentation
, which are the base classes of CFM
and has mos of the desired features. There might be some features we might want to abstract from CFM
to some intermediate ABC to also use in this class to remove code duplication. This will probably be the best way forward for FPModule
.
It's a good idea to maybe cache
dense_coefficient_list
for these elements, and maybe while we're at it, give the method for this class of elements a different name.
If we are going to cache it, then we might as well only store that and reimplement the module structure following my proposal at the end of in comment:10. IIRC, it is faster to go from the dense list to the indexed free module element than the other way around.
comment:13 Changed 8 months ago by
 Commit changed from 5153c6fab78b1a9869b67c76fbc6c1fff81862f7 to b3816f980e1fe37b0cacc16273e96b0f66e01017
Branch pushed to git repo; I updated commit sha1. New commits:
b3816f9  trac 32505: minor cleanup

comment:14 in reply to: ↑ 12 Changed 8 months ago by
Replying to tscrim:
Ah, right, because we are considering it over a graded ring, which we do not have a mechanism to take that into account. That is a missing feature of the categories that probably needs to be addressed at some point. However, then the category of
GradedModulesWithBasis(R)
is wrong, and instead it should be inGradedModules(R).WithBasis()
. These are not the samesage: GradedModulesWithBasis(QQ) == GradedModules(QQ).WithBasis() Falseas the latter is just saying there is a distinguished basis in a graded module, but not that the basis respects the grading. This allows us to circumvent this issue of the grading of the base ring (at least for now).
First, it is unfortunate that these are not the same, but that's not something to be fixed here. What differences does it make in this particular case to use GradedModules(algebra).WithBasis()
?
Re FPModule
:
We can weaken this to be a subclass of
IndexedGenerators
,Module
, andUniqueRepresentation
, which are the base classes ofCFM
and has mos of the desired features. There might be some features we might want to abstract fromCFM
to some intermediate ABC to also use in this class to remove code duplication. This will probably be the best way forward forFPModule
.
I'll work on this.
comment:15 Changed 8 months ago by
 Commit changed from b3816f980e1fe37b0cacc16273e96b0f66e01017 to ca45b2bfeb215d0d5e065daa3de1404c68467a85
comment:16 Changed 8 months ago by
Here are a bunch of changes in response to Travis' suggestions:
 use
__bool__
instead of__nonzero__
 change the category for free modules to
GradedModules(algebra).WithBasis()
. I have not tested whether this allows me to get away with just definingdegree_on_basis
.  change the class for
FPModule
to inherit fromIndexedGenerators
,Module
, andUniqueRepresentation
.
I still need to add some doctests for methods copied over from CombinatorialFreeModule
and other places, but this works as is. (So feel free to look at the changes, but I will be adding more doctests, if nothing else.) I have not created any intermediate classes in an attempt to remove any code duplication.
comment:17 Changed 8 months ago by
 Commit changed from ca45b2bfeb215d0d5e065daa3de1404c68467a85 to 46ef922ade27cd5223f64ae51238dc21813fa44a
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
46ef922  trac 32505: change inheritance for FPModule

comment:18 Changed 8 months ago by
Now including doctest coverage for everything.
comment:19 Changed 8 months ago by
I think this all works. We can use the suggestion at the end of comment:10 now or defer to another ticket. I think I would prefer to wait and see where the real bottlenecks are.
comment:20 Changed 7 months ago by
ping?
comment:21 Changed 7 months ago by
Sorry, I have been a bit busy with my move (Australia > Japan).
Before this goes to a positive review, there are a number of little code polishing things to take care of:
 Full doctest coverage (mainly
__init__
with adding aTestSuite(foo).run()
).  Pyflakes
 There are two
== None
>is None
needed.  I don't think we should have
0
be displayed as<>
. I know this is consistent with displaying the other elements, but I think it should just be0
.  The documentation of
degree()
is wrong with the output for0
.  Class docstrings shouldn't have an
OUTPUT:
.  Somewhere in the documentation needs to be stated that the module must be finite dimensional (over the algebra
A
). I think the category should also reflect this. It should be possible to remove this limitation, which shouldn't be too hard, but it is there currently. if len(self.generator_degrees()) == 0:
>if not self.generator_degrees():
 I am not sure we should use the name
basis_elements
as it is not giving basis elements overA
, but I can't think of a better name right now. It should be specified that these are basis elements over the base ringR
ofA
to make this clear. (Note that the direct sum is as additive groups (orR
modules), not asA
modules.  We probably want to state that this code only works for algebras that have a graded distinguished basis.
 I would want some of the key methods to have doctests that work for other graded algebras. Anything that is of the form
*Sym
is good; same withNilCoxeter
orExterior
(finite dimensional ones) orShuffle
.
I will probably also make a pass through this later for some code tweaks and improvements. However, before that, I want to talk a little bit more about the possible optimization in comment:10. Do we have any good ways to check the efficacy of such a change? Mainly, is there a computation that takes a few minutes that heavily uses this code? In terms of memory, it will likely be better because we are not storing the same information twice.
comment:22 Changed 6 months ago by
 Commit changed from 46ef922ade27cd5223f64ae51238dc21813fa44a to b5c789541fab53e4163c636e646d59e6caa2bbed
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
320be0d  trac 32505: finitely presented graded modules

fab508a  trac 32505: clear out __init__.py

c093016  trac 32505:

b595530  trac 32505: minor cleanup

9058e9a  trac 32505: change category for free modules

c0093e2  trac 32505: use __bool__ instead of __nonzero__

dfe2387  trac 32505: change inheritance for FPModule

b5c7895  trac 32505: add axiom "FinitelyPresented" for modules and use it.

comment:23 Changed 6 months ago by
Thanks, Travis. I've addressed most of these. I will add some doctests involving some other algebras like Exterior
. Regarding your list:
 I added test suites to the various
__init__
methods, and now I'm getting a doctest failure that I have yet to track down. I would be happy for help:File "src/sage/modules/fp_graded/module.py", line 156, in sage.modules.fp_graded.module.FPModule.__init__ Failed example: TestSuite(M).run() Expected nothing Got: Failure in _test_category: Traceback (most recent call last): File "/Users/palmieri/Desktop/Sage/git/sage/local/var/lib/sage/venvpython3.9/lib/python3.9/sitepackages/sage/misc/sage_unittest.py", line 297, in run test_method(tester=tester) File "sage/structure/element.pyx", line 722, in sage.structure.element.Element._test_category (build/cythonized/sage/structure/element.c:6825) tester.assertTrue(isinstance(self, self.parent().category().element_class)) File "/usr/local/Cellar/python@3.9/3.9.8/Frameworks/Python.framework/Versions/3.9/lib/python3.9/unittest/case.py", line 688, in assertTrue raise self.failureException(msg) AssertionError: False is not true  The following tests failed: _test_category Failure in _test_elements The following tests failed: _test_elements
When I actually run Sage and look at this, I think this is relevant information:sage: from sage.modules.fp_graded.module import FPModule sage: A3 = SteenrodAlgebra(profile=[4,3,2,1]) sage: M = FPModule(A3, [0,1], [[Sq(2), Sq(1)]]) sage: x = M.an_element() sage: x.parent().category().element_class <class 'sage.categories.category.JoinCategory.element_class'> sage: isinstance(x, x.parent().category().element_class) # _test_category asserts True False
 "Somewhere in the documentation needs to be stated that the module must be finite dimensional". We say "finitely presented" frequently already, but I've added a bit more. I also added a new category axiom, "FinitelyPresented".
Regarding comment:10 and optimization, I think the followup ticket #30680 will be a good testing ground, since it will use this code heavily.
comment:24 Changed 6 months ago by
Sorry (yet again) for taking so long to get to this. So as you are surmising, either the category or the element does not seem to be created correctly. I will need to look at this in more detail. As a quick workaround if we want to merge this quickly, we can just skip that particular test. However, this does seem to be a more serious but subtle issue that we should address.
comment:25 Changed 6 months ago by
 Commit changed from b5c789541fab53e4163c636e646d59e6caa2bbed to e8e4927b68ba5f762f4d1ce13525bff38b3ca2f0
Branch pushed to git repo; I updated commit sha1. New commits:
e8e4927  trac 32505: add a few examples using exterior algebras.

comment:26 followup: ↓ 42 Changed 6 months ago by
Here are a few examples with exterior algebras. Also in the previous version M.gen(0)
would work when M
was a free graded module but not a finitely presented module, so I've added gen
as an alias for generator
in the f.p. case, too. Same for gens
.
I also disabled the failing TestSuite
doctest. If we can figure out how to fix it, even better.
Finally, I am not happy with how elements are printed. Rather than <x, y>
, I would rather see x*g_0 + y*g_1
. Users should be allowed to name their generators, so you could also do
sage: M.<a,b,c> = FPModule(...) sage: x*a + y*b x*a + y*b
or
sage: M = FPModule(..., name='b', ...) # not sure about this syntax sage: x*M.gen(0) x*b_0
ghsverre320, kvanwoerden, ghrrbruner: any comments?
comment:27 followup: ↓ 38 Changed 6 months ago by
I know what the problem is. The TestSuite
is very useful:
element_class = FPElement +Element = FPElement
I will push a fix along with some other miscellaneous doc fixes one I make my way through all of the code.
One this that I do not like is submodule
returning a morphism. This is very counterintuitive to me. I propose we rename this submodule_inclusion
or submodule_embedding
(other names welcome). Same for kernel
. I know this is meant for homological algebra (+1 for that), but the method names should reflect their behavior IMO.
comment:28 followup: ↓ 31 Changed 6 months ago by
I am also +1 on changing the print (and latex) representation of elements to have user specified names. We can just use the framework of IndexedGenerators
to handle the printing. We can also add an option to retain the current printing (as it matches what FreeModule
does). John, what would (x + y)*a
, where x,y
are different basis elements of the algebra A
, print as? x*a + y*a
or (x + y)*a
? Should we add such an option too?
comment:29 followup: ↓ 39 Changed 6 months ago by
I also have some thoughts about the construction hooks. These do not necessarily need to be address on this ticket, but it might be good to do it here. I think we should have some method added to the category of GradedAlgebrasWithBasis
called free_graded_module
and possibly add FreeGradedModule
to the global namespace. This would serve as the main entry point.
Next, to construct a finitely presented module, I am thinking we should implement a quotient method or some other natural method to compute finitely presented modules as a 2step procedure. Of course, we can easily add a finitely_presented_graded_module()
or similar such method to allow a direct construction.
Thoughts?
comment:30 Changed 6 months ago by
 Branch changed from u/jhpalmieri/freegradedmodules to public/modules/free_graded_modules32505
 Commit changed from e8e4927b68ba5f762f4d1ce13525bff38b3ca2f0 to ded984f60dc7090448df317ec2b5104986ce1795
 Reviewers set to John Palmieri, Travis Scrimshaw
New commits:
ded984f  Reviewer changes with misc tweaks and fixes.

comment:31 in reply to: ↑ 28 Changed 6 months ago by
Replying to tscrim:
I am also +1 on changing the print (and latex) representation of elements to have user specified names. We can just use the framework of
IndexedGenerators
to handle the printing. We can also add an option to retain the current printing (as it matches whatFreeModule
does). John, what would(x + y)*a
, wherex,y
are different basis elements of the algebraA
, print as?x*a + y*a
or(x + y)*a
? Should we add such an option too?
I've been trying out using the default for IndexedFreeModuleElement
, and it uses parentheses: (x+y)*a + (y+z)*b
(no spaces around +
inside the parentheses). I would like to stick with the default. That means getting rid of _repr_
for the elements and adding _repr_term
for the parents.
By the way, the general switch from <a,b>
to a*g_{0} + b*g_{1}
is my preference, but it is also consistent with how Sage prints elements in algebraic structures more generally. My current implementation allows for
M = FreeGradedModule(A, (0, 2)) > generators are g_{0}, g_{2} M = FreeGradedModule(A, (0, 0, 2)) > generators are g_{0,0}, g_{0,1}, g_{2,0}: two indices since multiple generators in the same degree M = FreeGradedModule(A, (0, 0, 2), names='c') > use "c" instead of "g" M = FreeGradedModule(A, (0, 0, 2), names='a, b, c') > generators a, b, c: no subscripts M.<a0,b0,c2> = FreeGradedModule(A, (0, 0, 2)) > generators a0, b0, c2: no subscripts, also define a0, b0, c2
comment:32 Changed 6 months ago by
 Commit changed from ded984f60dc7090448df317ec2b5104986ce1795 to a12a8380fa33f8fb08c9c8b0cf9214c5a123861c
comment:33 Changed 6 months ago by
 Commit changed from a12a8380fa33f8fb08c9c8b0cf9214c5a123861c to 8529b6c0be23120ac6f087a5d9c04b805fdf008a
Branch pushed to git repo; I updated commit sha1. New commits:
8529b6c  trac 32505: add _latex_term

comment:34 Changed 6 months ago by
Here is a branch that uses the new print representation and adds a LaTeX representation. It also changes submodule
to submodule_inclusion
, kernel
> kernel_morphism
, cokernel
> cokernel_morphism
.
comment:35 Changed 6 months ago by
We can undo these changes if there are sound objections, of course.
comment:36 Changed 6 months ago by
 Commit changed from 8529b6c0be23120ac6f087a5d9c04b805fdf008a to 8e54829b2c315f9fd9bd696b82eef78c33510f09
Branch pushed to git repo; I updated commit sha1. New commits:
8e54829  trac 32505: typos

comment:37 Changed 6 months ago by
 Commit changed from 8e54829b2c315f9fd9bd696b82eef78c33510f09 to db79c13f71ab358d0d403db0903b57253110b53c
comment:38 in reply to: ↑ 27 Changed 6 months ago by
Replying to tscrim:
I know what the problem is. The
TestSuite
is very useful:element_class = FPElement +Element = FPElementI will push a fix along with some other miscellaneous doc fixes one I make my way through all of the code.
Thanks for figuring that out!
One this that I do not like is
submodule
returning a morphism. This is very counterintuitive to me. I propose we rename thissubmodule_inclusion
orsubmodule_embedding
(other names welcome). Same forkernel
. I know this is meant for homological algebra (+1 for that), but the method names should reflect their behavior IMO.
Fixed. I also suggested in a private email that another option would be to have a new class FpMorphismKernel
which would inherit from FPModule
but would also remember ambient module and the inclusion map. In the particular setting here, I think that the morphism is going to be used more than the kernel, so using f.kernel_inclusion()
and occasionally f.kernel_inclusion().domain()
looks better to me than f.kernel().inclusion()
and occasionally f.kernel()
.
comment:39 in reply to: ↑ 29 Changed 6 months ago by
Replying to tscrim:
I also have some thoughts about the construction hooks. These do not necessarily need to be address on this ticket, but it might be good to do it here. I think we should have some method added to the category of
GradedAlgebrasWithBasis
calledfree_graded_module
and possibly addFreeGradedModule
to the global namespace. This would serve as the main entry point.
This may require some other changes; in particular, every algebra (with basis? or every algebra?) should have a free_module
method, but the free_module
method for Clifford/exterior algebras just gives a rank 1 free module, the module underlying the algebra itself. Searching for free_module
methods suggests that some behave this way while some allow the user to specify a basis. We should probably have something like underlying_free_module(self)
and free_module(self, basis=...)
. The version in categories/rings.py
, which might be viewed as the default method, is a little strange, since it returns not just a free module V
over the ring R
but also maps R > V
and V > R
. Such maps are not particularly canonical, so I don't know why they are part of the structure. Actually, it looks like this may only return a free module of rank 1. I don't know why it doesn't just call CombinatorialFreeModule(R, basis, ...)
and allow for higher rank modules.
Maybe my point is, this looks messy enough that it should be deferred to another ticket. Alternatively we could ignore the mess and just add a free_graded_module
method as you suggest, and try to clean up the ungraded case later. It will be a little awkward if free_module
and graded_free_module
behave so differently.
Next, to construct a finitely presented module, I am thinking we should implement a quotient method or some other natural method to compute finitely presented modules as a 2step procedure. Of course, we can easily add a
finitely_presented_graded_module()
or similar such method to allow a direct construction.
The current code allows for the construction of a finitely presented module from a morphism between two free modules (mor.to_fp_module()
). That could also be turned into a method for free modules, accepting a morphism and returning an f.p. module.
comment:40 Changed 6 months ago by
 Commit changed from db79c13f71ab358d0d403db0903b57253110b53c to 2e9b692503d169c9e4f5fa0ee0c84ca5b7b6a863
Branch pushed to git repo; I updated commit sha1. New commits:
2e9b692  trac 32505: fix some comparisons to None

comment:41 Changed 6 months ago by
We could do this, for example:

src/sage/categories/graded_algebras_with_basis.py
diff git a/src/sage/categories/graded_algebras_with_basis.py b/src/sage/categories/graded_algebras_with_basis.py index e7ae68328e..8af922cd31 100644
a b class GradedAlgebrasWithBasis(GradedModulesCategory): 84 84 # Also, ``projection`` could be overridden by, well, a 85 85 # projection. 86 86 87 def free_graded_module(self, generator_degrees, names=None): 88 """ 89 Create a finitely generated free graded module over ``self`` 90 91 This is only implemented when the ground ring is a field. 92 93 INPUTS: 94 95  ``generator_degrees``  tuple of integers defining the 96 number of generators of the module, and their degrees 97 98  ``names``  optional, the names of the generators. If 99 ``names`` is a commaseparated string like ``'a, b, 100 c'``, then those will be the names. Otherwise, for 101 example if ``names`` is ``abc``, then the names will be 102 ``abc_{d,i}``. 103 104 By default, if all generators are in distinct degrees, 105 then the ``names`` of the generators will have the form 106 ``g_{d}`` where ``d`` is the degree of the generator. If 107 the degrees are not distinct, then the generators will be 108 called ``g_{d,i}`` where ``d`` is the degree and ``i`` is 109 its index in the list of generators in that degree. 110 111 See :mod:`sage.modules.fp_graded.free_module` for more 112 examples and details. 113 114 EXAMPLES:: 115 116 sage: Q = QuadraticForm(QQ, 3, [1,2,3,4,5,6]) 117 sage: Cl = CliffordAlgebra(Q) 118 sage: M = Cl.free_graded_module((0, 2, 3)) 119 sage: M.gens() 120 (g_{0}, g_{2}, g_{3}) 121 """ 122 from sage.modules.fp_graded.free_module import FreeGradedModule 123 return FreeGradedModule(self, generator_degrees, names) 124 125 87 126 class ElementMethods: 88 127 pass 89 128
comment:42 in reply to: ↑ 26 Changed 5 months ago by
Replying to jhpalmieri:
Finally, I am not happy with how elements are printed. Rather than
<x, y>
, I would rather seex*g_0 + y*g_1
. Users should be allowed to name their generators, so you could also dosage: M.<a,b,c> = FPModule(...) sage: x*a + y*b x*a + y*bor
sage: M = FPModule(..., name='b', ...) # not sure about this syntax sage: x*M.gen(0) x*b_0ghsverre320, kvanwoerden, ghrrbruner: any comments?
We like the printing and naming mechanism you propose, jhpalmieri!
comment:43 Changed 5 months ago by
 Milestone changed from sage9.5 to sage9.6
comment:44 Changed 5 months ago by
Sorry for being slow about this.
I like your idea in comment:41.
Now for something closer to bikeshedding. I think we should print the elements as, e.g., g[0]
following CFM. In addition, we could just pass everything off to IndexedGenerators
(via CFM) and let that handle everything. This makes it more customizable. In order to do so, we would extend that to support the names
option. How does this sound? I can take care of this if you want.
comment:45 Changed 5 months ago by
 Commit changed from 2e9b692503d169c9e4f5fa0ee0c84ca5b7b6a863 to c3bf4b88715dba4a2419e398cd30884b7f3f5fff
Branch pushed to git repo; I updated commit sha1. New commits:
c3bf4b8  trac 32505: add free_graded_module method to GradedAlgebrasWithBasis

comment:46 Changed 5 months ago by
Here is a branch with comment:41 incorporated. If you can push a branch with names
etc., that would be great!
comment:47 Changed 5 months ago by
 Commit changed from c3bf4b88715dba4a2419e398cd30884b7f3f5fff to 8435c780eea6a5d6749d80d914e20dc433301a1b
Branch pushed to git repo; I updated commit sha1. New commits:
8435c78  Reformatting output, simplifying basis construction, other misc changes.

comment:48 followups: ↓ 49 ↓ 53 Changed 5 months ago by
I have pushed the changes with names (we will want the patchbot to get around to it to see if there are other (almost certainly trivial) doctests breaking across Sage from the internal changes).
I also made a number of other changes and improvements. One important one is I changed the internal representation of basis elements to match the "generic" (i.e., no names
specified) printing indices. This is the most natural way to associate data to the basis element (IMO the only other natural way would just be to just use {0, ..., k} to index the basis elements). I also directly links the FP module to the free module's indices. This was also very useful for setting up the element printing.
I renamed the to_fp_module
to as_fp_module
for modules and fp_module
for morphisms. If it was to_fp_module
, I would expect some kind of map to be returned. I wanted the different names both to reflect the English and that modules and morphism are fundamentally different objects.
I have some design questions:
 I think we should have the
FPModule
construction be based on the morphism since that is the data that is actually stored. The__classcall_private__
would then preparse the input data as needed.  We should remove the
__contains__
ofFPModule
. I think this is suppressing an issue with comparing elements. Contrast this code withsage: Z4 = Zmod(4) sage: Z5 = Zmod(5) sage: Z5(3) in Z4 False sage: Z5(3) == Z4(3) False
which is using the generic__contains__
. Right now I can't provide any advice on how to fix this as I haven't looked at this too closely yet.
I also have some questions regarding the formatting that are easy enough to fix/change, but I wanted to be set on them before updating the remaining doctests (there will be some trivial failures in the added files):
 What do we want the default prefix to be? Previously it was
g
, but I was thinkingG
to reflect that it should be an element of the moduleG
. Pure bikeshedding, and I don't care. I just chose something that I thought was reasonable, but I should poll for other opinions before setting everything.  How do we want to print when the generator degrees? Right now the unique are
G[0]
and the nonunique areG(0, 0)
because that was the easiest to do. I can easily change the unique toG(0)
, and it is also relatively easy to changeG(0, 0)
to, e.g.,G[0,0]
.  I propose changing the morphism output to match that of ring morphisms:
sage: R.<x> = ZZ[] sage: S.<y> = ZZ[] sage: R.hom([y]) Ring morphism: From: Univariate Polynomial Ring in x over Integer Ring To: Univariate Polynomial Ring in y over Integer Ring Defn: x > y
This is better when there are a lot of elements, it is consistent with other parts of Sage, no tuplevslist printing issues, and we likely can take advantage of other morphism display code.
comment:49 in reply to: ↑ 48 Changed 4 months ago by
Replying to tscrim:
I have pushed the changes with names (we will want the patchbot to get around to it to see if there are other (almost certainly trivial) doctests breaking across Sage from the internal changes).
Great, thank you!
 I think we should have the
FPModule
construction be based on the morphism since that is the data that is actually stored. The__classcall_private__
would then preparse the input data as needed.
Sounds okay to me, but I don't a strong opinion about it.
 We should remove the
__contains__
ofFPModule
. I think this is suppressing an issue with comparing elements.
I'll try it and see what happens, then get back to you.
 What do we want the default prefix to be? Previously it was
g
, but I was thinkingG
to reflect that it should be an element of the moduleG
. Pure bikeshedding, and I don't care. I just chose something that I thought was reasonable, but I should poll for other opinions before setting everything.
I think lowercase is better: g[0]
looks more like an element to me than G[0]
.
 How do we want to print when the generator degrees? Right now the unique are
G[0]
and the nonunique areG(0, 0)
because that was the easiest to do. I can easily change the unique toG(0)
, and it is also relatively easy to changeG(0, 0)
to, e.g.,G[0,0]
.
I don't care too much, but I have a slight preference for uniformity: square brackets in both cases?
 I propose changing the morphism output to match that of ring morphisms:
Yes, sounds good.
comment:50 Changed 4 months ago by
 Commit changed from 8435c780eea6a5d6749d80d914e20dc433301a1b to d745357be5294371512684d2a23614d358c43a7b
comment:51 Changed 4 months ago by
I changed G[0]
to g[0]
but also changed G(0, 0)
to g(0, 0)
— it wasn't clear how to get brackets in the second case. I also changed the print representation for morphisms. I think I fixed all of the doctests, too.
comment:52 Changed 4 months ago by
 Commit changed from d745357be5294371512684d2a23614d358c43a7b to a73519c9f03e4b9d5f2461a55619ee8b6a09c7fb
Branch pushed to git repo; I updated commit sha1. New commits:
a73519c  trac 32505: delete the method "__contains__" for FPModules

comment:53 in reply to: ↑ 48 ; followup: ↓ 58 Changed 4 months ago by
Replying to tscrim:
 I think we should have the
FPModule
construction be based on the morphism since that is the data that is actually stored. The__classcall_private__
would then preparse the input data as needed.
I would be happy for you to take care of this. I ran into problems because I want to use generators and relations as arguments (as is currently done) but then have __classcall_private__
convert to a morphism and pass that to __init__
, and I couldn't figure out a clean way to do that. I didn't try that hard, but it seems that __classcall_private__
and __init__
should have the same arguments, so they both need morphism
, generators
, and relations
? I guess we could switch to using a factory to construct these modules instead, but I didn't try that.
I removed the __contains__
method, but I didn't know what you were referring to with "I think this is suppressing an issue with comparing elements."
With elements, it's easy for me to switch to g(0)
and keep the current g(0, 0)
, but I can't figure out how to instead switch the second one to g[0, 0]
.
Otherwise, I'm happy with this.
comment:54 Changed 4 months ago by
 Commit changed from a73519c9f03e4b9d5f2461a55619ee8b6a09c7fb to ebcae245641d773e9a3961702345143fe757b16a
Branch pushed to git repo; I updated commit sha1. New commits:
ebcae24  trac 32505: fix a doctest

comment:55 Changed 4 months ago by
Sorry, I have been busy this past week. I should be able to do this today. It is simply a matter of adding a layer in the _repr_term
method to convert the input to a list and then passing it up. Although I am thinking a better (long term) solution is to add another hook in IndexedGenerators
for more broadly handling iterable input and use the general mechanics (so if someone wants to change the brackets to, say, {
, it becomes a simple changing of the print options). This should also be quick to do.
comment:56 Changed 4 months ago by
 Commit changed from ebcae245641d773e9a3961702345143fe757b16a to 6b840715fc73c0fc528a6d48e2020dc86c682bef
Branch pushed to git repo; I updated commit sha1. New commits:
4599fb5  Merge branch 'develop' into public/modules/free_graded_modules32505

7d6bdf9  Merge branch 'public/modules/free_graded_modules32505' of git://trac.sagemath.org/sage into public/modules/free_graded_modules32505

6b84071  Adding additional print option to IndexedGenerators for iterating through keys.

comment:57 Changed 4 months ago by
 Commit changed from 6b840715fc73c0fc528a6d48e2020dc86c682bef to d6f67cfe115757c2415c7c4755a10e6a096ae649
Branch pushed to git repo; I updated commit sha1. New commits:
d6f67cf  Fix containment issues and add some more doctests.

comment:58 in reply to: ↑ 53 Changed 4 months ago by
Replying to jhpalmieri:
Replying to tscrim:
 I think we should have the
FPModule
construction be based on the morphism since that is the data that is actually stored. The__classcall_private__
would then preparse the input data as needed.I would be happy for you to take care of this. I ran into problems because I want to use generators and relations as arguments (as is currently done) but then have
__classcall_private__
convert to a morphism and pass that to__init__
, and I couldn't figure out a clean way to do that. I didn't try that hard, but it seems that__classcall_private__
and__init__
should have the same arguments, so they both needmorphism
,generators
, andrelations
? I guess we could switch to using a factory to construct these modules instead, but I didn't try that.
A factory is overkill. The only thing needed is checking if the __classcall_private__
input is a morphism or not. Well, I am feeling lazy (forgive me!) and don't really care too much to simplify the input as the current version works albeit somewhat inefficiently since it converts from the morphism data and then reconstructs said morphism. Anyways, this isn't anything that needs to be done right now. If you want to do this, please go ahead.
I removed the
__contains__
method, but I didn't know what you were referring to with "I think this is suppressing an issue with comparing elements."
I was getting errors for those doctest you removed. Using the default containment, you get this:
sage: from sage.modules.fp_graded.module import FPModule sage: M = FPModule(SteenrodAlgebra(2), [0,1], [[Sq(4), Sq(3)]]) sage: N = FPModule(SteenrodAlgebra(2), [0], [[Sq(2)]]) sage: y = Sq(2) * N.generator(0) sage: y in M True
which I think is wrong as it is checking this:
sage: M(y) == y True
So either it is the equality or the conversion that has a bug (possibly both). Taking another look, the _element_constructor_
was too permissive in how it was handling elements. I have fixed this, and it seems to resolve other issues I found with testing for this.
With elements, it's easy for me to switch to
g(0)
and keep the currentg(0, 0)
, but I can't figure out how to instead switch the second one tog[0, 0]
.
I have done this following what I sketched in comment:55.
Otherwise, I'm happy with this.
I am too if my changes are good.
comment:59 Changed 4 months ago by
 Commit changed from d6f67cfe115757c2415c7c4755a10e6a096ae649 to f5ec2c1b87b21f4af85c95ca48d43a6c68301419
Branch pushed to git repo; I updated commit sha1. New commits:
f5ec2c1  trac 32505: do not use __class__(...), instead explicitly name the class

comment:60 Changed 4 months ago by
I tried to modify __classcall_private__
to allow a morphism as input, but I ran into problems, which I have now mostly fixed. One minor problem is that the class is often initialized with the explicit keyword generator_degrees
(as in FPModule(..., generator_degrees=...)
), but it doesn't make sense to use that name for the argument anymore, so I removed those. Now we can easily change the name of the argument. Another problem is that some objects were constructed by calling self.__class__(...)
, and this usage seems to bypass __classcall_private__
and go straight to __init__
. It seems like a bad idea anyway, so I changed those to just use FPModule(...)
.
I may try later to implement a morphism as input, but this will do for now.
comment:61 Changed 4 months ago by
 Commit changed from f5ec2c1b87b21f4af85c95ca48d43a6c68301419 to ca9cdf08d263d417566d20f86387c69512408034
Branch pushed to git repo; I updated commit sha1. New commits:
ca9cdf0  trac 32505: fix one doctest

comment:62 Changed 4 months ago by
This passes all tests for me now. Let's not worry about allowing a morphism as input to the FPModule
constructor. I'd like to be able to move on to #30680. Travis, I'm happy with all of your work on this; thank you. Any objections to my most recent changes?
comment:63 Changed 4 months ago by
 Commit changed from ca9cdf08d263d417566d20f86387c69512408034 to 7dc91398f34cd0f21a3a4922e8330f596454ea4d
Branch pushed to git repo; I updated commit sha1. New commits:
7dc9139  trac 32505: remove an unneeded import

comment:64 Changed 4 months ago by
 Commit changed from 7dc91398f34cd0f21a3a4922e8330f596454ea4d to b7f9179ccb50b17cf867e5b11009594a5ba6d155
Branch pushed to git repo; I updated commit sha1. New commits:
b7f9179  Adding support for morphism input.

comment:65 followup: ↓ 66 Changed 4 months ago by
I got out of my laziness and added support for taking a morphism input.
I also changed the FPModule.j
parameter to the hidden _j
.
Although looking again at the code, I have a few more questions (sorry!):
 With allowing both input formats, do we need the
from_free_module*
methods? They seem more like clutter to me. I propose to remove them.
 Related, I don't see why we want to create a free
FPModule
(instead ofFreeGradedModule
) inresolution()
. Likely this is related to having different APIs, where methods likely just need to be added to the free version or perhaps some ABC needs to be created. We might want to even have the__classcall_private__
redirect to the free module where appropriate.
 Should the
FPModule
belong to the category ofModulesWithBasis
? I don't think this is guaranteed (over the base algebra). See also the comment below.
 I don't agree with the comment before
FPModule
"vector spaces" is illdefined (in particular, we don't require the base ring of the base algebra to be a field). This can be corrected fairly easily. However, I propose removing this as it doesn't contribute anything to (understanding) the code.
comment:66 in reply to: ↑ 65 Changed 4 months ago by
Replying to tscrim:
I got out of my laziness and added support for taking a morphism input.
Great, thanks! I also added code to allow a free module as input, in which case it would return a finitely presented module with no relations. We can revisit this based on how we want to handle your question below about resolution
.
I also changed the
FPModule.j
parameter to the hidden_j
.
Good, makes sense.
 With allowing both input formats, do we need the
from_free_module*
methods? They seem more like clutter to me. I propose to remove them.
Done.
 Related, I don't see why we want to create a free
FPModule
(instead ofFreeGradedModule
) inresolution()
. Likely this is related to having different APIs, where methods likely just need to be added to the free version or perhaps some ABC needs to be created. We might want to even have the__classcall_private__
redirect to the free module where appropriate.
Good question. Comments from the original authors? Why not just use free modules in resolution
?
 Should the
FPModule
belong to the category ofModulesWithBasis
? I don't think this is guaranteed (over the base algebra). See also the comment below.
I deleted this.
 I don't agree with the comment before
FPModule
"vector spaces" is illdefined (in particular, we don't require the base ring of the base algebra to be a field). This can be corrected fairly easily. However, I propose removing this as it doesn't contribute anything to (understanding) the code.
I replaced it with another comment, pointing out that some of the methods assume that there is a vector space structure and a chosen basis.
comment:67 Changed 4 months ago by
 Commit changed from b7f9179ccb50b17cf867e5b11009594a5ba6d155 to 5c242e73c2685630cea27fda10d1b14632c179da
Branch pushed to git repo; I updated commit sha1. New commits:
5c242e7  trac 32505: remove from_free_module, from_free_module_morphism

comment:68 Changed 4 months ago by
 Commit changed from 5c242e73c2685630cea27fda10d1b14632c179da to 5e021535eb5917c9b65036db7c018b66729063e3
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
5e02153  trac 32505: remove from_free_module, from_free_module_morphism

comment:69 Changed 4 months ago by
 Commit changed from 5e021535eb5917c9b65036db7c018b66729063e3 to f253e83ccaed4b920b62147878c65cb8a0c1e61b
Branch pushed to git repo; I updated commit sha1. New commits:
f253e83  trac 32505: allow the resolution to be made up of maps between

comment:70 Changed 4 months ago by
 Commit changed from f253e83ccaed4b920b62147878c65cb8a0c1e61b to 11b37258a9c3fa8989f0e7c42bd839b643014a2a
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
11b3725  trac 32505: allow the resolution to be made up of maps between

comment:71 Changed 4 months ago by
This now allows for the possibility of the terms in the resolution being instances of FreeGradedModuleMorphism
(except for the initial map, which has codomain the original module). I've also added a (slow) method which will compute the top dimension of a finitedimensional algebra, for use in determining when to stop computing the resolution. I've also added a computation of a free resolution of a trivial module over an exterior algebra.
comment:72 Changed 4 months ago by
So maybe the choice for resolution
was because the initial map has codomain M
which is likely not free. With the new as_free=True
option, the later maps are all converted to type FreeGradedModuleMorphism
, and you could just omit the 0th term to get an honest (graded) free resolution out of it.
Maybe now we're done?
comment:73 Changed 4 months ago by
 Commit changed from 11b37258a9c3fa8989f0e7c42bd839b643014a2a to 6c1ab8dc9a5f2a932297bf5256dab88dbb5f27e1
Branch pushed to git repo; I updated commit sha1. New commits:
6c1ab8d  trac 32505: more fixes

comment:74 Changed 4 months ago by
Fixed a few more things: the free_graded_module
method for algebras with basis wasn't handling the names
argument correctly, and a few doctests were failing. I changed some of the documentation, too.
comment:75 Changed 4 months ago by
I was just running into that problem in comment:74 and about to fix it. Thanks. I will be pushing a bunch of changes shortly too.
comment:76 Changed 4 months ago by
 Commit changed from 6c1ab8dc9a5f2a932297bf5256dab88dbb5f27e1 to 50744642c4c07b3987729988501d7347b5286b9d
Branch pushed to git repo; I updated commit sha1. New commits:
72e455e  We do not require the base algebra's base ring to be a field.

fcce24d  Merge branch 'public/modules/free_graded_modules32505' of git://trac.sagemath.org/sage into public/modules/free_graded_modules32505

2e0518f  Using free modules where possible and improved compatibility.

6cf6d14  Merge branch 'public/modules/free_graded_modules32505' of git://trac.sagemath.org/sage into public/modules/free_graded_modules32505

5074464  Some last fixes and removing redundancy.

comment:77 Changed 4 months ago by
I took this a bit further and made everything in the resolution a FreeGradedModule
. As I suspected, there were some compatibility issues to sort out, but I took care of all of the ones that came up in doctests (and a few others I saw along the way). There might be a few others (which will show up as missing methods), but we can fix them as we come across them.
Towards this, I made the free module morphism/homspace a subclass of the respective nonfree version. This required some slight workaround, but the code is much cleaner IMO because there are no duplicated methods and the subclassing makes mathematical sense.
I tweaked the documentation to say "free module" basically everywhere we use "vector space" because we are not using the field properties AFAICS.
As of right now, I am happy with the code. Please check my changes. If they are good, then go ahead and set a positive review.
comment:78 followup: ↓ 81 Changed 4 months ago by
I saw that you replaced PlusInfinity()
with infinity
, so I made the same change a few other places. I also removed a "todo" about dealing with finite dimensionality rather than just finiteness, handling it the same way we did elsewhere in the code. If someone gets motivated (on another ticket), they can try to handle the case where self.base_ring().dimension()
is not defined.
comment:79 Changed 4 months ago by
 Commit changed from 50744642c4c07b3987729988501d7347b5286b9d to ffe7179490704efe9157a6796cdbf2ae68f27c46
Branch pushed to git repo; I updated commit sha1. New commits:
ffe7179  trac 32505: replace "PlusInfinity()" with "infinity"

comment:80 Changed 4 months ago by
 Status changed from needs_review to positive_review
comment:81 in reply to: ↑ 78 Changed 4 months ago by
Replying to jhpalmieri:
I saw that you replaced
PlusInfinity()
withinfinity
, so I made the same change a few other places.
Indeed, this is a microoptimization since they are the same object, but infinity
is already created (and nailed in memory).
I also removed a "todo" about dealing with finite dimensionality rather than just finiteness, handling it the same way we did elsewhere in the code.
Thank you. I had made that note for myself, but I forgot about it.
If someone gets motivated (on another ticket), they can try to handle the case where
self.base_ring().dimension()
is not defined.
I concur.
Thank you.
comment:82 Changed 4 months ago by
Good question. Comments from the original authors? Why not just use free modules in resolution?
In the original version, the free module class was not intended for public use.
comment:83 Changed 4 months ago by
 Status changed from positive_review to needs_work
[sagemath_doc_htmlnone] [modules ] The inventory files are in local/share/doc/sage/inventory/en/reference/modules. [sagemath_doc_htmlnone] Error building the documentation. [sagemath_doc_htmlnone] Traceback (most recent call last): [sagemath_doc_htmlnone] File "/home/release/Sage/local/var/lib/sage/venvpython3.9.9/lib/python3.9/runpy.py", line 197, in _run_module_as_main [sagemath_doc_htmlnone] return _run_code(code, main_globals, None, [sagemath_doc_htmlnone] File "/home/release/Sage/local/var/lib/sage/venvpython3.9.9/lib/python3.9/runpy.py", line 87, in _run_code [sagemath_doc_htmlnone] exec(code, run_globals) [sagemath_doc_htmlnone] File "/home/release/Sage/local/var/lib/sage/venvpython3.9.9/lib/python3.9/sitepackages/sage_docbuild/__main__.py", line 2, in <module> [sagemath_doc_htmlnone] main() [sagemath_doc_htmlnone] File "/home/release/Sage/local/var/lib/sage/venvpython3.9.9/lib/python3.9/sitepackages/sage_docbuild/__init__.py", line 1731, in main [sagemath_doc_htmlnone] builder() [sagemath_doc_htmlnone] File "/home/release/Sage/local/var/lib/sage/venvpython3.9.9/lib/python3.9/sitepackages/sage_docbuild/__init__.py", line 776, in _wrapper [sagemath_doc_htmlnone] getattr(DocBuilder, build_type)(self, *args, **kwds) [sagemath_doc_htmlnone] File "/home/release/Sage/local/var/lib/sage/venvpython3.9.9/lib/python3.9/sitepackages/sage_docbuild/__init__.py", line 136, in f [sagemath_doc_htmlnone] runsphinx() [sagemath_doc_htmlnone] File "/home/release/Sage/local/var/lib/sage/venvpython3.9.9/lib/python3.9/sitepackages/sage_docbuild/sphinxbuild.py", line 323, in runsphinx [sagemath_doc_htmlnone] sys.stderr.raise_errors() [sagemath_doc_htmlnone] File "/home/release/Sage/local/var/lib/sage/venvpython3.9.9/lib/python3.9/sitepackages/sage_docbuild/sphinxbuild.py", line 258, in raise_errors [sagemath_doc_htmlnone] raise OSError(self._error) [sagemath_doc_htmlnone] OSError: /home/release/Sage/local/var/lib/sage/venvpython3.9.9/lib/python3.9/sitepackages/sage/modules/fp_graded/free_homspace.py:docstring of sage.modules.fp_graded.free_homspace.FreeGradedModuleHomspace.identity:4: WARNING: Literal block expected; none found. [sagemath_doc_htmlnone] [sagemath_doc_htmlnone] Note: incremental documentation builds sometimes cause spurious [sagemath_doc_htmlnone] error messages. To be certain that these are real errors, run [sagemath_doc_htmlnone] "make docclean docuninstall" first and try again.
comment:84 followup: ↓ 85 Changed 4 months ago by
Travis, was your intention to delete the identity
method from free_homspace
? Perhaps also remove zero
?
comment:85 in reply to: ↑ 84 Changed 4 months ago by
Replying to jhpalmieri:
Travis, was your intention to delete the
identity
method fromfree_homspace
? Perhaps also removezero
?
Yes it was. They are now inherited as they had (effectively) the same code as the notnecessarilyfree homspace.
comment:86 Changed 4 months ago by
 Commit changed from ffe7179490704efe9157a6796cdbf2ae68f27c46 to a1a9467e95cd05a6439b4b2765e62c6aad6dc960
Branch pushed to git repo; I updated commit sha1. New commits:
a1a9467  trac 32505: remove redundant "zero" and "identity" methods

comment:87 Changed 4 months ago by
 Status changed from needs_work to positive_review
comment:88 Changed 4 months ago by
Thank you.
comment:89 Changed 4 months ago by
Followup in #33275.
comment:90 Changed 3 months ago by
 Branch changed from public/modules/free_graded_modules32505 to a1a9467e95cd05a6439b4b2765e62c6aad6dc960
 Resolution set to fixed
 Status changed from positive_review to closed
I will quote from the TODO list in the forthcoming
__init__.py
:__bool__
and__eq__
in element.py? They should be taken care of automatically, once we define__nonzero__
.In
__classcall__/__init__
for FP_Modules, allow as input a free module or a morphism of free modules? Or just leave it as is, with methods inFP_Modules
, morphisms, and free modules for these constructions. (See the preexistingFP_Modules.from_free_module
etc., and also new methodsmorphism.to_fp_module()
andfree_module.to_fp_module()
.)Question 1 is bugging me the most: I get doctest failures if I don't define
__bool__
and__eq__
, but according tostructure/element.pyx
, I shouldn't have to do this: the documentation there for__nonzero__
says:which really sounds like I shouldn't have to define
__bool__
.