Questions on the group-theoretic functionality of Mathematica.

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6
votes
0answers
67 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 ...
4
votes
0answers
44 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: ...
2
votes
0answers
35 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
30 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
52 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
39 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?
0
votes
0answers
54 views

Can Mathematica rewrite irreps given in Dynkin Coeffs in tensor form?

Apparently, it is possible to do Young Tableaux calculations with mathematica (see the Susyno and LieART packages). A natural follow up question is then, given that one has decomposed a direct product ...