Fix cardinality of special linear group #36881

RuchitJagodara · 2023-12-14T15:33:09Z

Fixed infinite recursion of the cardinality and order functions
Improved pycodestyle
Add more doctests to cover all cases

This patch fixes #36876 and fixes #35490. In this PR, I have implemented a method to fix the
answer given by cardinality function for finite special linear groups
(before it was going into infinite recursion). This also fixes the answer given by is_finite()
function for finite special linear groups.

📝 Checklist

The title is concise, informative, and self-explanatory.
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.

⌛ Dependencies

None

RuchitJagodara · 2023-12-23T06:33:39Z

@dimpase, @jukkakohonen and @videlec can you please review this PR ?

src/sage/categories/finite_groups.py

mantepse · 2023-12-25T11:31:32Z

Have you located the reason for the infinite recursion?

RuchitJagodara · 2023-12-25T16:39:05Z

Yes, the is_finite() function is calling this cardinality function, and it seems that it is calling the order function (Considering that other classes have their own order function). I didn't find any special function that calculates the cardinality of these special linear groups. So, maybe it is not implemented yet, so it is calling the order function of some class from which it is derived, but that function is calling back this cardinality function.

dimpase · 2023-12-25T17:31:15Z

Orders of special linear groups over fields are known, you can just implement formulae.

Less sure for more general cases

RuchitJagodara · 2023-12-27T14:05:42Z

Orders of special linear groups over fields are known, you can just implement formulae.

I checked and found that order function is implemented only for gap-based groups and there is only one function available for other groups which is going in infinite recursion. Here below is a example of a gap-based special linear group which is working perfect.

sage: F = FiniteField(3)
sage: SL(2,F).order()
24

But when it comes to other groups which are not gap-based then it is going in infinite recursion like below

sage: q = 7
....: FqT.<T> = GF(q)[]
....: N = T^2+1
....: FqTN = QuotientRing(FqT, N*FqT)
....: S = SL(2,FqTN)
....: S.order()
---------------------------------------------------------------------------
RecursionError                            Traceback (most recent call last)
...

This is happening because in below code it is first trying to make an object of LinearMatrixGroup_gap but if it fails then it is simply making an object of LinearMatrixGroup_generic and that class does not have properties of gap and because of that it is not able to calculate order/cardinality of the gorup.

sage/src/sage/groups/matrix_gps/linear.py

Lines 308 to 316 in 879ac37

    
               try: 
        
                   cmd = 'SL({0}, {1})'.format(degree, ring._gap_init_()) 
        
                   return LinearMatrixGroup_gap(degree, ring, True, name, ltx, cmd, 
        
                                                category=cat) 
        
               except ValueError: 
        
                   pass 
        
           return LinearMatrixGroup_generic(degree, ring, True, name, ltx, 
        
                                            category=cat)

mantepse · 2023-12-27T17:08:02Z

But when it comes to other groups which are not gap-based then it is going in infinite recursion like below
sage: q = 7
....: FqT.<T> = GF(q)[]
....: N = T^2+1
....: FqTN = QuotientRing(FqT, N*FqT)
....: S = SL(2,FqTN)

Should we be able to iterate over such a group?

dimpase · 2023-12-27T22:47:03Z

There should be a special .order() method for SL. For finite fields $\mathbb{F}_q$ one has

$|SL(n,q)|={\frac{1}{q-1}} \Pi_{k=0}^{n-1} (q^n-q^k).$

Here FqTN is isomorphic to $\mathbb{F}_{49}$, so just use the forrmula, with $n=2$, $q=49$.

RuchitJagodara · 2024-01-29T12:59:42Z

I have implemented the order function for linear matrix groups. I discovered that GAP does not support linear matrix groups over the rational field (and some other fields), which was the main cause of the error. Consequently, I attempted to address this issue in GAP, but it proved to be very non-trivial. Therefore, I implemented the function in Sage. Additionally, I have another question: Why do we use functions from GAP when we can implement all of those functions from scratch in Sage as well? In this case, we would have the flexibility to construct functions according to our needs. I understand it may take considerable time, but we can proceed step by step. The same can be applied to Magma, which was also causing some errors, as can be found in the Discussion and in issue #36841.

RuchitJagodara · 2024-02-08T06:15:55Z

@dimpase and @mantepse, can you please review this pr...

src/sage/groups/matrix_gps/linear.py

In this commit, I have fixed the :trac:`36876` and :trac:`35490`. And I have also added some doc tests covering this changes.

Added more doctests.

Corrected the error of previous commit.

RuchitJagodara · 2024-02-09T09:43:37Z

I have also included a documentation change in this pr only because it is a very small change. Is it okay ?

github-actions · 2024-02-09T10:14:52Z

Documentation preview for this PR (built with commit baa3b50; changes) is ready! 🎉

mantepse

Thank you!

grhkm21 · 2024-02-13T21:17:31Z

src/sage/groups/matrix_gps/linear.py

+            q = self.base_ring().order()
+            ord = prod(q**n - q**i for i in range(n))
+            if self._special:
+                return ord / (q-1)


This should be //.

Possibly yes, but it doesn't look serious to me. Since this ticket is about to be merged, please open a new one!

Yes but also no, rational numbers behave weirdly, e.g. is_prime(7 / 1) is False. But I will open a new PR

@grhkm21, have you made another PR for the changes you suggested? If not then, should I create a new PR for this?

sagemathgh-37980: Fix order computation for linear groups GL(n, R) and SL(n, R) sagemath#36881 introduced some wrong results for orders of linear groups since it did not check whether the base ring is a field. We add the necessary checks as well as formulas for some further cases, namely $\mathbb{Z}$ and $\mathbb{Z}/q\mathbb{Z}.$ Finally, we add a `NotImplementedError` for the cases that are not supported. The formula for the general linear group over $\mathbb{Z}/q\mathbb{Z}$ is taken from https://math.stackexchange.com/a/2044571, and for the order of the special linear group we use the group isomorphism induced by the determinant. Fixes sagemath#37934. URL: sagemath#37980 Reported by: Sebastian A. Spindler Reviewer(s): Travis Scrimshaw

RuchitJagodara force-pushed the cardinality_fot_small_spelcial_groups branch from 9cb6027 to 7a28d2f Compare December 17, 2023 18:45

RuchitJagodara changed the title ~~Implement method to find correct cardinality of special linear group~~ Fix cardinality of special linear group Dec 23, 2023

dimpase reviewed Dec 23, 2023

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RuchitJagodara marked this pull request as draft December 25, 2023 09:10

RuchitJagodara marked this pull request as ready for review January 29, 2024 14:35

RuchitJagodara requested review from dimpase and mantepse January 30, 2024 06:51

mantepse reviewed Feb 8, 2024

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RuchitJagodara added 10 commits February 9, 2024 15:10

Fixed infinite recursion of the cardinality and order functions

a9e2b74

In this commit, I have fixed the :trac:`36876` and :trac:`35490`. And I have also added some doc tests covering this changes.

Add more doctests to cover all cases

0101a8d

Added more doctests.

Corrected lint error

b0f3988

Remove unnecessary comments

2dc4a32

Correct the error in finding cardinality of special linear group

d4eb8ed

Corrected the error of previous commit.

Revert all the changes

df64b41

Add a new order method for linear matrix groups

d15eb8f

Corrected a linting error

e2840ed

Fixed a doctest

84077dc

Fixed few linting errors

a13d56a

RuchitJagodara added 2 commits February 9, 2024 15:10

Improved coding style

1781ad3

Shifted the position of import statements

4b7bac3

RuchitJagodara force-pushed the cardinality_fot_small_spelcial_groups branch from 91ec122 to baa3b50 Compare February 9, 2024 09:41

Fixed documentation of minimal_normal_subgroups function

baa3b50

mantepse approved these changes Feb 9, 2024

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mantepse added s: positive review c: group theory labels Feb 9, 2024

grhkm21 reviewed Feb 13, 2024

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vbraun merged commit 6ad8584 into sagemath:develop Feb 13, 2024
23 checks passed

github-actions bot removed the s: positive review label Feb 14, 2024

mkoeppe added this to the sage-10.3 milestone Mar 7, 2024

This was referenced May 10, 2024

Wrong order of finite matrix groups #37934

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Fix order computation for linear groups GL(n, R) and SL(n, R) #37980

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Fix cardinality of special linear group #36881

Fix cardinality of special linear group #36881

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Fix cardinality of special linear group #36881

Fix cardinality of special linear group #36881

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