Questions on the group-theoretic functionality of Mathematica.

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22
votes
1answer
851 views

Visualizing Rubik's Graph

After the August 2010 discovery that the diameter of the Rubik graph is 20, I wanted to make a way to visualize Rubik's graph. Since there are about $4.3 \times 10^{19}$ vertices in this graph, it is ...
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 ...
10
votes
2answers
696 views

How to create a group action table with Mathematica?

Background: I want to explain the Sylow Theorems as detailed as possible, therefore I am rewriting the proof using concrete examples. Since the answers to my questions ( about Mathematica ) have ...
10
votes
2answers
248 views
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
637 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 ...
7
votes
2answers
275 views

What is the underlying algorithm for GroupElementToWord?

What algorithm is Mathematica 9 using for GroupElementToWord[group, g]?
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: ...
6
votes
2answers
480 views

Symmetry-finding packages

Where can I find the most up-to-date or whatever you consider to be the most useful symmetry-finding package for differential equations? I do not intend to restrict to, but would like to include ...
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 = ...
5
votes
1answer
115 views

Create group from multiplication table

Suppose I have a multiplication table for a group. For example, m = {{1, 2, 3, 4}, {2, 3, 4, 1}, {3, 4, 1, 2}, {4, 1, 2, 3}} I would like to create a group from ...
4
votes
2answers
175 views

Standardizing a coset table via matrix manipulation

Suppose we have a group $G$ and a subgroup $H$. A coset table encodes the permutation representation of $G$ on the right cosets of $H$. When we want to use these coset tables in calculations, it is ...
4
votes
4answers
127 views

Express block matrix in terms of matrix basis

I'm trying to construct a function that returns the multiplication table of a matrix Lie algebra. Assuming a basis of matrices, my definitions: ...
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
570 views

decompose a number (less than 255) in a sum of powers of 2

Is there a built in function that would take a number and decompose it into a sum of powers of 2? The numbers will be non negative less than 256. For what it's worth I'm trying to understand a paper ...
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 ...
3
votes
2answers
108 views

Generating Z^*_n

I'm using Mathematica to illustrate basic number theory concepts in a graduate cryptography class. To generate elements of the multiplicative group of integers modulo $n$, i.e. $\mathbb{Z}^*_n$, I can ...
3
votes
2answers
473 views

Package for representation of groups (group theory)

I wanted to know if there is a package which allows to compute representations of a group like the definition representation, adjoint and so on (for example the Pauli matrix for $SU(2)$ if I specify ...
3
votes
1answer
127 views

Test for group isomorphism and construct automorphism groups

MMA has some support for group theory, allowing representation of any finite group as a subgroup of $S_n$. It does not seem to have a function for testing whether two finite groups are isomorphic. Is ...
3
votes
1answer
108 views

Rewrite an expression as a sum of $SU(2)$ characters?

I have an expression of the form $$q^{-3/2} t^{-7/2}[4qt^2(t + q t^2) + t^2 (q + t) (1 + q t (1 + q t))],$$ I can factor it and write it as $4((qt)^{1/2} + (qt)^{-1/2}) + (qt+1 + ...
3
votes
1answer
62 views

Change group generators?

I want to make Cayley graphs for the same group, but with different generators. Is there any way to represent a group, besides a cumbersome permutation representation or using the default Mathematica ...
3
votes
1answer
66 views

How does GroupActionBase affect the order of elements in a group?

Related (math.SE): How does the base of a group determine the “sort” of the elements in the group The help page for GroupActionBase says: A base of a group ...
2
votes
2answers
96 views

Creating a Cayley's table of square

I'm interested in creating a Cayley's table of square using Mathematica. I'm not a programmer but occasionally resort to using Mathematica to simplify my work insofar as the programming doesn't take ...
2
votes
2answers
114 views

Counting the permuted forms of a list with repeated members under a permutation group

DeleteDuplicates[Permute[{g, g, g, g, g, e, r}, AlternatingGroup[7]]] How to count number of lists automatically?
2
votes
1answer
69 views

How to distribute PermutationProduct over the sum

Assuming I have two elements of the permutation group algebra $a_1$, $a_2$ such that $a_i=\sum_{p\in S_n}\alpha_pp$, I want to define a linear product $\odot$ that distributes over the sum and pulls ...
1
vote
1answer
42 views

Symmetric group action on polynomials

I am working with polynomials in several variables with the obvious action of $S_n$. That is, given a polynomial $f$ in the variables $x_1, \dots, x_n$, a permutation $\sigma \in S_n$ acts on $f$ by ...
1
vote
0answers
34 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
2answers
65 views

I need to make and manipulate a group ( the quaternion)

I am trying to define a group and use it to defined its classes, its character table, and irreducible representations. I am having trouble finding code to define a group and use it.
0
votes
1answer
70 views

Any command for group products?

Is there any Mathematica command or well known technique to take the direct product between two symmetric/permutation groups?
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 ...
0
votes
0answers
97 views

Group theory - symmetry inequivalent sqaure matrices with PBC

I would like to obtain the symmetry inequivalent possible occupations of indistinguishable objects in a square lattice with periodic boundary conditions. Examples: 1 object in a 4 by 4 square ...