# Questions tagged [group-theory]

Questions on the group-theoretic functionality of Mathematica.

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### How to evaluate an expression [closed]

I have a 3-dimensional array of numbers say A. I want to evaluate the following expression. $\displaystyle\sum_{\sigma,\tau \in S_6}(\Pi_{i=1}^6A(i,\sigma(i),\tau(i)))$. $S_6$ is the symmetric group ...
42 views

### What is the cycle index polynomial for the trivial group

CycleIndexPolynomial[Cycles[{}], {Subscript[x, 1]}] returns 1. I was expecting ...
88 views

297 views

### Defining an Arbitrary Group

I learned today, while doing my homework, that Mathematica can understand group theory. Combing through the documentation though just gave the examples of permutation groups. I would like to know how ...
64 views

### $GL(n,C)$ as a Lie group [closed]

I understand that $SO(3)$, $SU(3)$ are Lie groups since they are associated with rotations (The S excludes reflection). Why is $GL(n,C)$ also a Lie group?
66 views

### Wreath products of groups in Mathematica?

Looking online, I found this external package that can compute e.g. the CycleIndexPolynomial of wreath products of symmetry groups. Considering that this package is ...
154 views

### Generate all dihedral transformations of a matrix?

Given a matrix, e.g. matrix = Table[a[i, j], {i, 1, 3}, {j, 1, 3}]; I would like to have a function that takes matrix as ...
55 views

### Unified class of an object type “Group”?

Does Mathematica support an unified class for "group-type" objects? Or, less general, for groups with a fixed defined representation in Mathematica? For example: ...
771 views

### Is there concise code for the list operation I want to perform?

Is there any concise syntax for the following partitioning of a list. Given {1, 2, 3, 4}, I want to get the output as shown below. I have tried various function ...
187 views

### Fox Calculus/Fox Derivative

Is there a way to compute the Fox derivative in Mathematica? I know there are some methods to do it in Sage, but I'd like to use Mathematica instead. Any suggestions?
143 views

### How can I output list of permutation products?

I have A = Permutations[{1, 2, 3, 4}]. And c = Cycles[{{1, 2, 3, 4}}]. And I need to output for all \$a \in A: a \cdot с \cdot a^{...
How can I display the elements (polynomials) of the ring $$\mathbb Z_3[x]/\langle x^3+2x^2+1\rangle$$ Is there a built-in function that displays them?