added method exponent for permutation group #18888

mohitacecode · 2020-03-17T10:03:24Z

References to other Issues or PRs

Brief description of what is fixed or changed

A method is added to calculate the exponent of a permutation group

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Release Notes

combinatorics
- Added method exponent in perm_groups.py.

sympy-bot · 2020-03-17T10:03:35Z

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combinatorics
- Added method exponent in perm_groups.py. (#18888 by @mohitacecode)

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#### Brief description of what is fixed or changed
A method is added to calculate the exponent of a permutation group

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- combinatorics
    - Added method `exponent` in `perm_groups.py`.
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mohitacecode · 2020-03-17T10:03:58Z

Please review @jksuom

codecov · 2020-03-17T11:42:19Z

Codecov Report

Merging #18888 into master will decrease coverage by 0.014%.
The diff coverage is 100%.

@@              Coverage Diff              @@
##            master    #18888       +/-   ##
=============================================
- Coverage   75.668%   75.653%   -0.015%     
=============================================
  Files          647       647               
  Lines       168520    168524        +4     
  Branches     39709     39710        +1     
=============================================
- Hits        127516    127495       -21     
- Misses       35448     35471       +23     
- Partials      5556      5558        +2

divyanshu132 · 2020-03-17T15:29:30Z

sympy/combinatorics/perm_groups.py

+        """
+            Returns the exponent of a group
+
+            The exponent e of a group G is the lcm of the orders of its elements,


There is an existing method in sympy to compute lcm.

exp = 1 for g in self.generators: exp = lcm(exp, g.order())

Okay I will change it.

Can you dedent the docstrings?

I am not sure do we need to do it for docstring too?

It’s only for the code convention

Smit-create · 2020-03-17T18:25:52Z

sympy/combinatorics/tests/test_perm_groups.py

+    assert A.exponent() == 12
+
+    c = Permutation(1,2,3,4,5,6)(2,3,4)(5,6,7)(8,9)(10,11,12)
+    A = PermutationGroup([a,b,c])


I think you should add spacing around commas

This line should have [a, b, c] but I think that the previous line can be left as it is. Otherwise it will grow in size unreasonably.

Okay I have changed it.

jksuom · 2020-03-18T08:33:08Z

The orders of all elements are needed for the exponent, generators alone do not suffice.

>>> from sympy.combinatorics import *
>>> s = Permutation(0, 1)
>>> t = Permutation(0, 2)
>>> G = PermutationGroup([s, t])
>>> G.exponent()
2
>>> (s*t).order()
3

mohitacecode · 2020-03-18T08:49:08Z

The orders of all elements are needed for the exponent, generators alone do not suffice.

Yes right I have done the changes.

mohitacecode · 2020-03-18T08:50:31Z

sympy/combinatorics/tests/test_perm_groups.py

+    assert A.exponent() == 12
+
+    c = Permutation(1,2,3,4,5,6)(2,3,4)(5,6,7)(8,9)(10,11,12)
+    A = PermutationGroup([a, b, c])


Should I change this too its order is to large to be used for test?

>>> A.order() 15120

mohitacecode · 2020-03-18T12:04:50Z

why is it failing? it is passing on my system.

jksuom · 2020-03-18T13:02:36Z

I think that this is not a practical method. It should not be necessary to compute all elements and their orders. What does GAP do?

mohitacecode · 2020-03-18T16:02:23Z

they calculate the prime divisor of the order of G and then for every prime they compute the sylow subgroup and find it's exponent.

something like:

P = primedivisor(order(G))
exp=1
for p in P:
  exp = exp * Exponent(sylowsubgroup(G,p))
return exp

jksuom · 2020-03-18T16:52:20Z

That seems a reasonable method. The exponent of a finite group is the product of the exponents of its Sylow subgroups.

mohitacecode · 2020-03-18T19:31:45Z

In case when G = sylow_subgroup(p) do we have to go for normal method of lcm otherwise it will get into infinite loop.?
for example:

>>> A = PermutationGroup([Permutation(1,2,3)])
>>> A.sylow_subgroup(3)
PermutationGroup([
    (1 2 3)])
>>> A
PermutationGroup([
    (1 2 3)])

divyanshu132 · 2020-03-20T04:37:19Z

If that is the case perhaps, you can have a set having all the sylow-p subgroups to terminate the loop you can probably use break statement if the resultant subgroup is already there in the set.

mohitacecode · 2020-03-20T12:08:07Z

I have done the changes.

Please look will they suffice.

mohitacecode · 2020-03-21T09:52:55Z

Please review the changes.

jksuom · 2020-03-21T11:01:45Z

Does GAP use a special method for computing the exponent of a p-group?

mohitacecode · 2020-03-21T11:19:26Z

Ahh... I did't find any they have a special method for finite abelian group where they calculate the lcm of order of the generators of group.

jksuom · 2020-03-21T12:28:47Z

Maybe for solvable groups. p-groups a solvable, even nilpotent.

mohitacecode · 2020-03-21T13:44:56Z

sry I again did'nt find any :( I searched extensively
but I saw they have only two method one generic and one special for finite abelian group and after that they uses RedispatchOnCondition method which usually means taking some properties and finding the method accordingly .

mohitacecode · 2020-03-21T16:20:52Z

maybe It can be improved more by applying the following property:

1.)the exponent of a cyclic group is it's order(|G|).
2.)For abelian group the exponent is equal to the largest order of its element.

mohitacecode · 2020-03-22T18:32:28Z

Hello @jksuom ,
I finally found a method that gap uses. They use a method for p-group named ExponentOfPGroupAndElm which they have in grppc.gi file.
I am exploring it now but from the overview it looks that it will require some other methods too.

After edit : -
That would require the computation of specialpcgs.

jksuom · 2020-03-23T11:45:47Z

sympy/combinatorics/perm_groups.py

+            if sylow_p_subgroup not in sylow_groups:
+                elements = list(sylow_p_subgroup.elements)
+                exp_p = elements[0].order()
+                for i in range(1, len(elements)):


This looks inefficient. len(elements) may be very big.

Okay, got it
I looked at the gap implementation that method will require the computation of many other methods too such Leedham-Green series and special pcgs and many others too.

should I go ahead and implement those in new pr's and after that jump to this pr again?

It seems that something like that will be needed. If there are no algorithms in the Handbook, then those method may be hard to implement.

Yes you are right It can be hard probably I can take help of gap implementation (as of now they look possible to implement to me but there need to be too many implemented) but implementing these may take too much time so first I will try to open a pr on which I have already worked and they are on my system.

oscarbenjamin · 2020-04-26T00:35:37Z

@mohitacecode this has merge conflicts now

czgdp1807 · 2020-05-02T17:44:34Z

@mohitacecode Please resolve the conflicts. Thanks for your contributions.

added method exponent

0489641

mohitacecode changed the title ~~added method exponent for permuatation group~~ added method exponent for permutation group Mar 17, 2020

remove unicode character

f125b14

divyanshu132 reviewed Mar 17, 2020

View reviewed changes

Mohit Gupta added 2 commits March 17, 2020 21:55

using sympy lcm

7bf2c58

added test case

2130e0a

Smit-create reviewed Mar 17, 2020

View reviewed changes

czgdp1807 added the combinatorics label Mar 17, 2020

improved spacing inbetween variables

eb76f3e

using elements

889cdad

mohitacecode commented Mar 18, 2020

View reviewed changes

changes test

e4535dd

improved version using sylow_groups

ca6134b

Mohit Gupta added 2 commits March 20, 2020 19:21

removed exp_p = 1 initialisation

6c3afe0

converted to Integer

1397686

mohitacecode requested a review from jksuom March 23, 2020 10:08

jksuom reviewed Mar 23, 2020

View reviewed changes

czgdp1807 added the Please take over label Jan 2, 2021

github-actions bot added the Merge conflict label Oct 26, 2022

added method exponent for permutation group #18888

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mohitacecode commented Mar 17, 2020

References to other Issues or PRs

Brief description of what is fixed or changed

Other comments

Release Notes

sympy-bot commented Mar 17, 2020

mohitacecode commented Mar 17, 2020

codecov bot commented Mar 17, 2020 • edited

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jksuom commented Mar 18, 2020

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