Questions on the group-theoretic functionality of Mathematica.

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12
votes
4answers
2k views

Finding elementary cycles of (directed) graphs

I need to enumerate all the simple cycles (i.e. elementary cycles where no vertex is repeated other than the starting) of a graph which has both directed and undirected edges, where we can treat the ...
6
votes
2answers
421 views

Plotting All Possible Points Belonging to a Group Orbit

Given that $$X = \{(x,y,z) \in \mathbb{R}^3 |\, x^2 + y^2 + z^2 - 2(xy + xz + yz) = k\}\,,$$ where $k$ is a constant. Also given that a group $G$ is represented by $$\langle g_1,g_2,g_3|\, g_1^2 = ...
4
votes
2answers
2k views

Defining a non-commutative operator algebra in Mathematica

I am trying to develop a function(s) to do some commutator algebra to compute the enveloping algebra and ideals of a Lie algebra. For example if I have $SU(2)$ algebra generated by $L_i$ ($i=1,2,3$), ...
3
votes
2answers
375 views

What is the command to find function invariant?

What is the command to find function invariant? http://demonstrations.wolfram.com/AFunctionInvariantUnderAGroupOfTransformations/ what is algorithm it use to calculate this? Edit there is a book ...
6
votes
6answers
335 views

Total by a criteria

I am developing a weighted KNN algorithm. In a step, I need to do the sum of weights of each class. For example: ...
9
votes
1answer
216 views

$3\times 3 = 6 + \bar{3}$ in Mathematica?

Can Mathematica handle this type of algebra, which is used very frequently in e.g. particle/nuclear physics? That is, I want to decompose a product of representations (in $SU(N)$ say) into irreducible ...
8
votes
2answers
638 views

How to generate a matrix group?

I have three $7\times 7$ matrices (with real entries, lots of zeros) and I'd like to check if they generate a finite group (or, more precisely, if the group they generate is of precise order). Would ...
0
votes
0answers
34 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 ...