Questions on the group-theoretic functionality of Mathematica.

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7
votes
0answers
90 views

Mathematica package for explicit matrix representations of group generators?

While there are several packages that are capable of working with weights and roots (for example LieArt), I couldn't find any package that spits out explicit matrices for the generators, for example ...
5
votes
0answers
48 views

Counting automorphisms that preserve a group action

Note: the math, I believe, is not the problem here. The issue is not that I get the wrong answer, just that my code does not terminate. So, if you do not feel comfortable with the problem below, I do ...
5
votes
0answers
65 views

Displaying elements of $\mathbb{Z}/n\mathbb{Z}$

When I want to display the elements of the cyclic group $\mathbb{Z}/9\mathbb{Z}$, I get the output in cycle form like this: Is there a way I can display the group elements like this: $\{0,1,2,3,4,5,...
3
votes
0answers
52 views

Generation of Space Representation of non-crystallographic Point Groups

In Mathematica the command FiniteGroupData[{"CrystallographicPointGroup",<group number>}, "SpaceRepresentation"] yields the space representation (...
2
votes
0answers
36 views

How to find the optimum word length of a group element?

I have a (large, finite, permutation) group, and a group element that I know is a product of length=20 of the generators. But when I ConvertGroupElementToWord, I get a word of length=118. Other, ...
1
vote
0answers
62 views

Calculating in the group ring $Q[GL_n(Z)]$

I am trying to use Mathematica to check some identities in the group ring $Q[GL_n(Z)]$. Is there a package/function of Mathematica to do this? Thanks a lot in advance!
1
vote
0answers
40 views

Does “FiniteRingData” or something like that exists?

I want to find a function like FiniteGroupData but for finite rings. Does something like that exists?