add is_trivial method for groups #36873

mantepse · 2023-12-13T07:39:55Z

We add a method to check whether a permutation group is trivial, that is, consists only of the identity element.

The title is concise, informative, and self-explanatory.
The description explains in detail what this PR is about.
I have created tests covering the changes.

jukkakohonen · 2023-12-13T08:10:33Z

src/sage/groups/perm_gps/permgroup.py

+        Return ``True`` if this group is the trivial group.
+
+        A permutation group is trivial, if it consists only of the
+        identity element, that is, if it has no generators.


This method is a very welcome addition, thanks. The code is good as far as I understand. A small complaint about the docstring: In Sage a trivial group may in fact have a (trivial) generator. To my surprise, here we specify no generators but end up having one generator anyway:

sage: PermutationGroup([],domain=[1,2]).gens() ((),)

If the docstring mentions generators (and I think it is a good idea, since it clarifies to the user what the code will actually be checking), it should mention this surprising possibility.

(I believe/hope it is not possible to make a group with several trivial generators, at least not easily. If that is a possibility, we would need to check that all generators are trivial.)

It is, actually.

Oh well, it is possible and not that difficult...

sage: P=PermutationGroup([(),()], canonicalize=False) sage: P.gens() ((), ()) sage: P.order() 1

A human would likely not create such a group on purpose, but I imagine some code might. Anyway it is possible. Mathematically of course this is a trivial group, so Sage should recognize it as one.

Looks good now!

videlec · 2023-12-13T08:55:28Z

Why is this new method restricted to permutation groups and not made available for groups in general? To my mind, such code would better be in the Groups or possibly Monoids category.

mantepse · 2023-12-13T09:28:36Z

Why is this new method restricted to permutation groups and not made available for groups in general? To my mind, such code would better be in the Groups or possibly Monoids category.

We certainly need finitely generated for this code, although, we can certainly use cardinality for a generic implementation.

It seems that the same code might work well for MatrixGroup, I can add it there, if you want to.

I don't know the category code well enough to add generic code, but if you help me, I'd do it.

jukkakohonen · 2023-12-13T09:54:19Z

we can certainly use cardinality for a generic implementation.

Interestingly, cardinality can fail in some corner cases, e.g. a special linear group of degree 1:

sage: SL(1, QQ).cardinality()
...
RecursionError: maximum recursion depth exceeded

(Should probably file an issue on this.)

dimpase · 2023-12-13T10:01:39Z

we can certainly use cardinality for a generic implementation.

Interestingly, cardinality can fail in some corner cases, e.g. a special linear group of degree 1:
sage: SL(1, QQ).cardinality()
...
RecursionError: maximum recursion depth exceeded
(Should probably file an issue on this.)

yes, this is definitely a bug (it should return NotImplementedError I think). Please file an issue

jukkakohonen · 2023-12-13T10:24:25Z

Please file an issue

#36876

mantepse · 2023-12-13T11:24:48Z

I am not sure what to do in the case of finitely presented group. Being trivial is undecidable (https://en.wikipedia.org/wiki/Adian%E2%80%93Rabin_theorem), but of course we can (and should) attempt to decide it. Computing the cardinality seems to be wasteful, however.

dimpase · 2023-12-13T11:28:36Z

I am not sure what to do in the case of finitely presented group. Being trivial is undecidable (https://en.wikipedia.org/wiki/Adian%E2%80%93Rabin_theorem), but of course we can (and should) attempt to decide it. Computing the cardinality seems to be wasteful, however.

Throw NotImplementedError ?

mantepse · 2023-12-13T11:32:41Z

I am not sure what to do in the case of finitely presented group. Being trivial is undecidable (https://en.wikipedia.org/wiki/Adian%E2%80%93Rabin_theorem), but of course we can (and should) attempt to decide it. Computing the cardinality seems to be wasteful, however.

Throw NotImplementedError ?

Isn't that worse to checking cardinality?

mantepse · 2023-12-13T12:07:27Z

Done, please review.

dimpase · 2023-12-13T12:31:33Z

It appears that automatic actions triggering is working for you. So it is possible that you not seeing the "Approve and run" button on other PRs is due to your browser/auth, not the setup on GitHub.

dimpase · 2023-12-13T12:32:53Z

It appears that automatic actions triggering is working for you. So it is possible that you not seeing the "Approve and run" button on other PRs is due to your browser/auth, not the setup on GitHub.

unless someone pushed "Approve and run" button here. It was not me, anyone else?

dimpase · 2023-12-14T16:30:09Z

For solvable groups the world problem is decidable. OK, we can talk about this somewhere later

dimpase

lgtm

…ationGroup # Fast cardinality method for IntegerVectorsModPermutationGroup This patch fixes sagemath#36787 by implementing a `cardinality` method for `IntegerVectorsModPermutationGroup_with_constraints`. The method calculates the cardinality using the the [Polya enumeration theorem](https://en.wikipedia.org/wiki/P%C3%B3lya_enumeration_theorem) (also known as the cycle index theorem). It is faster than the the default implementation, which iterates through the full set to find the cardinality. Incidentally this PR fixes also sagemath#36681 so that cardinality and iter no longer crash in empty-domain situations. ### 📝 Checklist     - [x] The title is concise, informative, and self-explanatory. - [x] The description explains in detail what this PR is about. - [x] I have linked a relevant issue or discussion. - [x] I have created tests covering the changes. - [x] I have updated the documentation accordingly. ### ⌛ Dependencies - sagemath#36873: we can use `is_trivial` from that PR   URL: sagemath#36814 Reported by: Jukka Kohonen Reviewer(s): Dima Pasechnik, Jukka Kohonen, Martin Rubey, Travis Scrimshaw

mantepse · 2023-12-18T12:29:40Z

sorry, I pressed the wrong button

github-actions · 2023-12-18T13:04:03Z

Documentation preview for this PR (built with commit 1ef1380; changes) is ready! 🎉

mantepse changed the title ~~add is_trivial method~~ add is_trivial method for permutation groups Dec 13, 2023

mantepse added s: needs review c: group theory labels Dec 13, 2023

mantepse requested review from dcoudert, dimpase and jukkakohonen December 13, 2023 07:51

mantepse mentioned this pull request Dec 13, 2023

Fast cardinality method for IntegerVectorsModPermutationGroup #36814

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mantepse changed the title ~~add is_trivial method for permutation groups~~ add is_trivial method for groups Dec 13, 2023

mantepse added 5 commits December 14, 2023 16:27

add is_trivial method

bcac6d4

further clarify docstring

aa0ba80

allow non-canonicalized generators

4092ca9

is_trivial for matrix groups

9222df6

is_trivial for generic groups

1ef1380

dimpase force-pushed the perm_gps/is_trivial branch from 6455956 to 1ef1380 Compare December 14, 2023 16:27

dimpase approved these changes Dec 14, 2023

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dimpase added s: positive review and removed s: needs review labels Dec 14, 2023

mantepse closed this Dec 18, 2023

mantepse deleted the perm_gps/is_trivial branch December 18, 2023 12:28

mantepse restored the perm_gps/is_trivial branch December 18, 2023 12:28

mantepse reopened this Dec 18, 2023

vbraun merged commit 2343c20 into sagemath:develop Dec 19, 2023
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mkoeppe added this to the sage-10.3 milestone Dec 19, 2023

github-actions bot removed the s: positive review label Dec 19, 2023

mantepse deleted the perm_gps/is_trivial branch January 27, 2024 11:02

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add is_trivial method for groups #36873

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add is_trivial method for groups #36873

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