Implement basic multivariate polynomial species #38446

Newtech66 · 2024-07-29T17:59:44Z

Related to #30727.

We implement basic functionality for multivariate polynomial species, using its representation as a pair of a permutation group and a mapping between the domain of the permutation group and some variables. We provide addition, multiplication, and (partitional) composition (for some special cases). We also allow it to be constructed as a group action (or a sequence thereof). Atomic and molecular decompositions are automatically computed thanks to #38371.

📝 Checklist

The title is concise and informative.
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 and checked the documentation preview.

…groups Also added various miscellaneous functions

Co-authored-by: Martin Rubey <axiomize@yahoo.de>

Also some fixes to _element_constructor_ ConjugacyClassesOfSubgroups

…).WithBasis()

Added _repr_ for ConjugacyClassesOfSubgroups I now output B[(gens or name if available)] as _repr_ for generators, for example B[1] + 2*B[(2,3,4)]

…y and doctest updates

…r changes

…bgroups

…ial case in construct_element

mantepse · 2024-11-04T17:27:18Z

src/sage/rings/species.py

+    def __classcall__(cls, *args, **kwds):
+        """
+        Normalize the arguments.
+
+        EXAMPLES::
+
+            sage: from sage.rings.species import MolecularSpecies
+            sage: MolecularSpecies("X,Y") is MolecularSpecies(["X", "Y"])
+            True
+
+            sage: MolecularSpecies("X,Y") == MolecularSpecies(["X", "Z"])
+            False
+        """
+        if isinstance(args[0], AtomicSpecies):
+            indices = args[0]
+        else:
+            assert "names" not in kwds or kwds["names"] is None
+            indices = AtomicSpecies(args[0])
+        category = Monoids().Commutative() & SetsWithGrading().Infinite()
+        return super().__classcall__(cls, indices,
+                                     prefix='', bracket=False,
+                                     category=category)


This looks actually fishy to me. I really would like to have MolecularSpecies only accept names as argument. However, if I understand correctly, MolecularSpecies.__init__ has to have the same signature, but apparently it must also have the same signature as IndexedFreeAbelianMonoid.__classcall__ (or __init__?).

No, you can explicitly skip that __classcall__ and go to its base class's one through UniqueRepresentation.__classcall__(cls, names). The __init__ and __classcall__ signatures (which can be different) only need to be able to take as input the final key/signature that is given to the UniqueRepresentation.

mantepse · 2024-11-05T13:08:17Z

I think that I adressed all other comments, please let me know if this is not the case. Most importantly: many thanks for the thorough review, I appreciate it!

tscrim

Essentially this is good to go modulo one doc detail and one potential change for you.

src/sage/rings/species.py

tscrim · 2024-11-07T16:24:56Z

src/sage/rings/species.py

+    def __classcall__(cls, *args, **kwds):
+        """
+        Normalize the arguments.
+
+        EXAMPLES::
+
+            sage: from sage.rings.species import MolecularSpecies
+            sage: MolecularSpecies("X,Y") is MolecularSpecies(["X", "Y"])
+            True
+
+            sage: MolecularSpecies("X,Y") == MolecularSpecies(["X", "Z"])
+            False
+        """
+        if isinstance(args[0], AtomicSpecies):
+            indices = args[0]
+        else:
+            assert "names" not in kwds or kwds["names"] is None
+            indices = AtomicSpecies(args[0])
+        category = Monoids().Commutative() & SetsWithGrading().Infinite()
+        return super().__classcall__(cls, indices,
+                                     prefix='', bracket=False,
+                                     category=category)


No, you can explicitly skip that __classcall__ and go to its base class's one through UniqueRepresentation.__classcall__(cls, names). The __init__ and __classcall__ signatures (which can be different) only need to be able to take as input the final key/signature that is given to the UniqueRepresentation.

src/sage/rings/species.py

mantepse · 2024-11-07T20:04:10Z

No, you can explicitly skip that __classcall__ and go to its base class's one through UniqueRepresentation.__classcall__(cls, names). The __init__ and __classcall__ signatures (which can be different) only need to be able to take as input the final key/signature that is given to the UniqueRepresentation.

Cool, that worked and looks much better! Thank you!

src/sage/rings/species.py

tscrim · 2024-11-07T23:06:33Z

src/sage/rings/species.py

+        INPUT:
+
+        - ``dis`` -- a directly indecomposable permutation group
+        - ``domain_partition`` -- a `k`-tuple of ``frozenset``s,


Suggested change

- ``domain_partition`` -- a `k`-tuple of ``frozenset``s,

- ``domain_partition`` -- a `k`-tuple of ``frozenset`` entries,

This will not format properly.

Actually, should all of this information should be moved to the (public facing) class level?

Co-authored-by: Travis Scrimshaw <clfrngrown@aol.com>

tscrim · 2024-11-08T04:59:55Z

src/sage/rings/species.py

+        H = _stabilizer_subgroups(S, X, a)
+        if len(H) > 1:
+            raise ValueError("action is not transitive")
+        return self(H[0], pi, check=check)


Suggested change

return self(H[0], pi, check=check)

return self._element_constructor_(H[0], pi, check=check)

This is where you expect it to always end up (without any coercion being done), right?

Indeed. I reorganized so that recursion is avoided, because it is a pain when debugging.

Also, the error message was (mathematically) wrong.

src/sage/rings/species.py

Co-authored-by: Travis Scrimshaw <clfrngrown@aol.com>

mantepse · 2024-11-08T08:09:55Z

Thank you for being careful, I especially like that we caught the wrong error message!

tscrim · 2024-11-08T09:13:55Z

Thank you for all the changes. If the bot comes back (morally) green, then you can set a positive review.

mantepse

Approved via tscrim

mantepse · 2024-11-08T10:56:41Z

yippie!

Related to sagemath#30727. We implement basic functionality for multivariate polynomial species, using its representation as a pair of a permutation group and a mapping between the domain of the permutation group and some variables. We provide addition, multiplication, and (partitional) composition (for some special cases). We also allow it to be constructed as a group action (or a sequence thereof). Atomic and molecular decompositions are automatically computed thanks to sagemath#38371. ### 📝 Checklist - [x] The title is concise and informative. - [x] The description explains in detail what this PR is about. - [x] I have linked a relevant issue or discussion. - [ ] I have created tests covering the changes. - [ ] I have updated the documentation and checked the documentation preview. URL: sagemath#38446 Reported by: Mainak Roy Reviewer(s): Mainak Roy, Martin Rubey, Travis Scrimshaw

Newtech66 and others added 30 commits May 12, 2024 19:59

Initial commit

8a5f1db

Added _add_, _mul_, _element_constructor_ for group action input

ce7c87f

Fixed bugs with caching and _mul_

2ae5497

Improved repr output and added a way to name conjugacy classes of sub…

663b422

…groups Also added various miscellaneous functions

Merge branch 'develop' into burnside_ring

b3f16ba

Update src/sage/rings/burnside.py

6f9cac4

Co-authored-by: Martin Rubey <axiomize@yahoo.de>

Doctest updates

bec9b0b

Added ConjugacyClassesOfSubgroups

476218f

Burnside ring now inherits from CombinatorialFreeModule

3d2a730

Also some fixes to _element_constructor_ ConjugacyClassesOfSubgroups

Changed category of Burnside ring to Algebras(base_ring).Commutative(…

d49eb76

…).WithBasis()

Implemented monomial() and one_basis()

bf76e0d

Added _repr_ for ConjugacyClassesOfSubgroups I now output B[(gens or name if available)] as _repr_ for generators, for example B[1] + 2*B[(2,3,4)]

Add rename_gen

dc1d95d

Add construct_from_action

c271e60

Add _from_dict

1453c90

Add product_on_basis and monomial_coefficients

fa8b9f5

Remove ConjugacyClassesOfSubgroups from import

be11997

Make indexes for generators use ConjugacyClassesOfSubgroups internall…

f39807c

…y and doctest updates

Add __eq__ for ConjugacyClassOfSubgroups so we can use it as dict key

d4af3fc

Removed BurnsideRingElement and refactored code

de3ccbc

Add __getitem__, minor doctest fix

d9e5aab

Add __eq__ and minor fix in _normalize and set_name

1a377f5

Implemented all suggested changes

45361c3

Doctest additions

b8da0e6

Doctest updates

ac4bb20

Run doctest fixer

8ecf26d

Small change

f617657

Draft implementation of PolynomialMolecularDecomposition + other mino…

6ecbe83

…r changes

Added PolynomialMolecularDecomposition to imports

bd55d15

Fixed __iter__ and added subset in ConjugacyClassesOfSymmetricGroupSu…

2ce14a5

…bgroups

Refactor conjugacy classes of subgroups of symmetric groups, add spec…

04ac9e9

…ial case in construct_element

mantepse added 3 commits November 4, 2024 17:50

remove superfluous __init__ as spotted by tscrim

0bc0224

sort cover relations as str

580a5c2

more replacements of parent == self to parent is self

0ca9a5b

mantepse reviewed Nov 4, 2024

View reviewed changes

tscrim approved these changes Nov 7, 2024

View reviewed changes

mantepse added 2 commits November 7, 2024 18:56

make MolecularSpecies.__classcall__ sane

4598eda

improve documentation

ade63cc

tscrim reviewed Nov 7, 2024

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mantepse and others added 2 commits November 8, 2024 02:30

Update src/sage/rings/species.py

727d4d2

Co-authored-by: Travis Scrimshaw <clfrngrown@aol.com>

Update src/sage/rings/species.py

ff604c8

Co-authored-by: Travis Scrimshaw <clfrngrown@aol.com>

tscrim reviewed Nov 8, 2024

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mantepse and others added 3 commits November 8, 2024 08:30

Apply suggestions from code review

8d7ab18

Co-authored-by: Travis Scrimshaw <clfrngrown@aol.com>

docfixes

622d08e

avoid recursion in _element_constructor_

9ef4cdb

mantepse approved these changes Nov 8, 2024

View reviewed changes

mantepse added s: positive review and removed s: needs review labels Nov 8, 2024

vbraun merged commit 4817e52 into sagemath:develop Nov 16, 2024
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Implement basic multivariate polynomial species #38446

Implement basic multivariate polynomial species #38446

Newtech66 commented Jul 29, 2024 •

edited by mantepse

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mantepse commented Nov 8, 2024

	- ``domain_partition`` -- a `k`-tuple of ``frozenset``s,
	- ``domain_partition`` -- a `k`-tuple of ``frozenset`` entries,

	return self(H[0], pi, check=check)
	return self._element_constructor_(H[0], pi, check=check)

Implement basic multivariate polynomial species #38446

Implement basic multivariate polynomial species #38446

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Newtech66 commented Jul 29, 2024 • edited by mantepse Loading

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Newtech66 commented Jul 29, 2024 •

edited by mantepse

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