MatrixSpace: Support constructing Hom(CombinatorialFreeModule)
#37514
Conversation
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Ready to go? |
…s row/column keys
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It's checked for consistency, and errors are raised if there's a mismatch |
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Yes, I can add more doctests for that. If there are specific ones that you'd like to see, let me know |
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Just doctests testing the compatibility, such as Also, your |
It's intended as the name of a positional-only argument.
No, I disagree, it should be rejected as a case of "duplicate argument" nrows. |
Ah, sorry I missed it in the long list of arguments. Now there are more compatibility tests to be done as you have to mix with the
It isn't a duplication per se. I could see it being used as a sanity check by a user. I would be a bit confused by this resulting in an error because of course it has 4 rows and 2 columns and the 4 is a shorthand for the index set [0, 1, 2, 3] in this setting. Also, I believe this is true but I would like confirmation, the values that can be converted to |
Well, there's a clear distinction between passing 4 and passing range(4). |
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I have added the doctests (and input checking code), please take a look |
No, |
If both of the arguments were integers, then I would agree. However, because one of the inputs is a list, passing |
That didn't exactly answer my question. I don't know what limits Python has imposed on the |
No, there's no such mechanism. It constructs a morphism between a Edit: I'll add that many of these homsets are not fully implemented, but that's outside of the scope of this PR. I have added some |
I don't understand what you mean. What limits are you talking about? |
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Okay, I've checked, in Python3, |
Ah I see. This is acceptable then. Although now I notice another issue. I don't quite like how, e.g., setting I am treating the |
That's a bug. |
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Fixed now |
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Documentation preview for this PR (built with commit d26b9c8; changes) is ready! 🎉 |
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Any more comments or can we merge it? |
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Thanks! |
…ialFreeModule)`
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The `FreeModule` constructor was recently generalized so that it can
create `CombinatorialFreeModule` objects. In particular,
```
sage: ZZ^3
Ambient free module of rank 3 over the principal ideal domain Integer
Ring
sage: ZZ^['a','b','c']
Free module generated by {'a', 'b', 'c'} over Integer Ring
```
Here as a follow-up, we extend `MatrixSpace` in a similar way: When
lists or enumerated sets of row indices and column indices are given, it
constructs `CombinatorialFreeModule`s whose bases are indexed by these
index sets, and then returns the homset. In particular,
```
sage: ZZ^(2, 3)
Full MatrixSpace of 2 by 3 dense matrices over Integer Ring
sage: ZZ^(['x','y'], ['a', 'b', 'c'])
Set of Morphisms from Free module generated by {'a', 'b', 'c'} over
Integer Ring to Free module generated by {'x', 'y'} over Integer Ring in
Category of finite dimensional modules with basis over Integer Ring
```
Follow-up PRs:
- extend `matrix` likewise; guiding application: adjacency / incidence
"matrices" of graphs, where rows/columns are indexed by nodes and edges
- see also sagemath#35801
### 📝 Checklist
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### ⌛ Dependencies
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<!-- - sagemath#12345: short description why this is a dependency -->
<!-- - sagemath#34567: ... -->
URL: sagemath#37514
Reported by: Matthias Köppe
Reviewer(s): Frédéric Chapoton, gmou3, Matthias Köppe, Travis Scrimshaw
…representation`: Support constructing `Hom(CombinatorialFreeModule)` elements
<!-- ^ Please provide a concise and informative title. -->
<!-- ^ Don't put issue numbers in the title, do this in the PR
description below. -->
<!-- ^ For example, instead of "Fixes sagemath#12345" use "Introduce new method
to calculate 1 + 2". -->
<!-- v Describe your changes below in detail. -->
<!-- v Why is this change required? What problem does it solve? -->
<!-- v If this PR resolves an open issue, please link to it here. For
example, "Fixes sagemath#12345". -->
We use morphisms of `CombinatorialFreeModule`s (each of which has a
distinguished finite or enumerated basis indexed by arbitrary objects)
as matrices whose rows and columns are indexed by arbitrary objects
(`row_keys`, `column_keys`).
Example:
```
sage: M = matrix([[1,2,3], [4,5,6]],
....: column_keys=['a','b','c'], row_keys=['u','v']);
M
Generic morphism:
From: Free module generated by {'a', 'b', 'c'} over Integer
Ring
To: Free module generated by {'u', 'v'} over Integer Ring
```
Example application done here on the PR: The incidence matrix of a graph
or digraph. Returning it as a morphism instead of a matrix has the
benefit of keeping the vertices and edges with the result. This new
behavior is activated by special values for the existing parameters
`vertices` and `edges`.
```
sage: D12 = posets.DivisorLattice(12).hasse_diagram()
sage: phi_VE = D12.incidence_matrix(vertices=True,
edges=True); phi_VE
Generic morphism:
From: Free module generated by
{(1, 2), (1, 3), (2, 4), (2, 6), (3, 6), (4, 12),
(6, 12)}
over Integer Ring
To: Free module generated by {1, 2, 3, 4, 6, 12} over
Integer Ring
sage: print(phi_VE._unicode_art_matrix())
(1, 2) (1, 3) (2, 4) (2, 6) (3, 6) (4, 12)
(6, 12)
1⎛ -1 -1 0 0 0 0
0⎞
2⎜ 1 0 -1 -1 0 0
0⎟
3⎜ 0 1 0 0 -1 0
0⎟
4⎜ 0 0 1 0 0 -1
0⎟
6⎜ 0 0 0 1 1 0
-1⎟
12⎝ 0 0 0 0 0 1
1⎠
```
### 📝 Checklist
<!-- Put an `x` in all the boxes that apply. -->
- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation accordingly.
### ⌛ Dependencies
<!-- List all open PRs that this PR logically depends on. For example,
-->
<!-- - sagemath#12345: short description why this is a dependency -->
<!-- - sagemath#34567: ... -->
- Depends on sagemath#37607
- Depends on sagemath#37514
- Depends on sagemath#37606
- Depends on sagemath#37646
URL: sagemath#37692
Reported by: Matthias Köppe
Reviewer(s): gmou3
…representation`: Support constructing `Hom(CombinatorialFreeModule)` elements
<!-- ^ Please provide a concise and informative title. -->
<!-- ^ Don't put issue numbers in the title, do this in the PR
description below. -->
<!-- ^ For example, instead of "Fixes sagemath#12345" use "Introduce new method
to calculate 1 + 2". -->
<!-- v Describe your changes below in detail. -->
<!-- v Why is this change required? What problem does it solve? -->
<!-- v If this PR resolves an open issue, please link to it here. For
example, "Fixes sagemath#12345". -->
We use morphisms of `CombinatorialFreeModule`s (each of which has a
distinguished finite or enumerated basis indexed by arbitrary objects)
as matrices whose rows and columns are indexed by arbitrary objects
(`row_keys`, `column_keys`).
Example:
```
sage: M = matrix([[1,2,3], [4,5,6]],
....: column_keys=['a','b','c'], row_keys=['u','v']);
M
Generic morphism:
From: Free module generated by {'a', 'b', 'c'} over Integer
Ring
To: Free module generated by {'u', 'v'} over Integer Ring
```
Example application done here on the PR: The incidence matrix of a graph
or digraph. Returning it as a morphism instead of a matrix has the
benefit of keeping the vertices and edges with the result. This new
behavior is activated by special values for the existing parameters
`vertices` and `edges`.
```
sage: D12 = posets.DivisorLattice(12).hasse_diagram()
sage: phi_VE = D12.incidence_matrix(vertices=True,
edges=True); phi_VE
Generic morphism:
From: Free module generated by
{(1, 2), (1, 3), (2, 4), (2, 6), (3, 6), (4, 12),
(6, 12)}
over Integer Ring
To: Free module generated by {1, 2, 3, 4, 6, 12} over
Integer Ring
sage: print(phi_VE._unicode_art_matrix())
(1, 2) (1, 3) (2, 4) (2, 6) (3, 6) (4, 12)
(6, 12)
1⎛ -1 -1 0 0 0 0
0⎞
2⎜ 1 0 -1 -1 0 0
0⎟
3⎜ 0 1 0 0 -1 0
0⎟
4⎜ 0 0 1 0 0 -1
0⎟
6⎜ 0 0 0 1 1 0
-1⎟
12⎝ 0 0 0 0 0 1
1⎠
```
### 📝 Checklist
<!-- Put an `x` in all the boxes that apply. -->
- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation accordingly.
### ⌛ Dependencies
<!-- List all open PRs that this PR logically depends on. For example,
-->
<!-- - sagemath#12345: short description why this is a dependency -->
<!-- - sagemath#34567: ... -->
- Depends on sagemath#37607
- Depends on sagemath#37514
- Depends on sagemath#37606
- Depends on sagemath#37646
URL: sagemath#37692
Reported by: Matthias Köppe
Reviewer(s): gmou3
The
FreeModuleconstructor was recently generalized so that it can createCombinatorialFreeModuleobjects. In particular,Here as a follow-up, we extend
MatrixSpacein a similar way: When lists or enumerated sets of row indices and column indices are given, it constructsCombinatorialFreeModules whose bases are indexed by these index sets, and then returns the homset. In particular,Follow-up PRs:
matrixlikewise; guiding application: adjacency / incidence "matrices" of graphs, where rows/columns are indexed by nodes and edgescmr(Combinatorial Matrix Recognition library) and Cython interface #35801📝 Checklist
⌛ Dependencies