Questions on the group-theoretic functionality of Mathematica.

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-1
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1answer
61 views

how to get a constant value by mathematica?

I'm anew user of mathematica ,, forgive me A.B - B.A = 2Ιf C and c = {{0, 0, 0}, {0, 0, -Ι}, {0, Ι, 0}}; I is imaginary number, f is a constant and equal (1/2) How to get the value of f by ...
5
votes
0answers
41 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
1answer
70 views

Generating abstract group from direct product of two abstract groups

In group theory one can calculate some abstract groups through the direct product of two other abstract groups. An example for such a generation is the product $A_5\times Z_2$ with order 120, or ...
0
votes
1answer
52 views

Filter pattern from a list

I have group elements, that I'd like to condense down according to group rules. Take the modular group. This has generators $S,T$ that satisfy the groups relations $S^2 = I, (ST)^3 = I$. So given a ...
3
votes
0answers
77 views
3
votes
0answers
43 views

Generation of Space Representation of non-crystallographic Point Groups

In Mathematica the command FiniteGroupData[{"CrystallographicPointGroup",<group number>}, "SpaceRepresentation"] yields the space representation ...
5
votes
2answers
148 views

How to make pairs of Young diagrams appear?

I have the following Young diagrams {{{0}, {2}}, {{0}, {1, 1}}, {{1}, {1}}, {{2}, {0}}, {{1, 1}, {0}}} where you can interpret each pair as following: For ...
0
votes
1answer
91 views

How to construct Cayley Table when only few entries are known?

Let $A$ be a set consisting of 25 elements, that is, $a$, $b$, $c$, $d$ and so on..., and $*$ be a binary operation defined on $A$. If I know the value of only a few compositions, like for instance ...
1
vote
1answer
33 views

Normal subgroups, Group order, Automorphisms

I am a beginner at Mathematica and have a few problems. Find all normal subgroups of the Alternating Group A[4]. Find the order of a group Aut(U[8]). Find the group Aut(S[3]). I've been trying to ...
1
vote
0answers
58 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!
6
votes
2answers
164 views

Generating $\mathbb{Z}^*_n$

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 ...
5
votes
0answers
53 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: ...
6
votes
1answer
96 views

Can Mathematica return the order of an element in $S_n$

I want to input an element like Cycles[{{1, 2}, {3, 4, 5}}] and I want Mathematica to return 6, the order of this element in $S_5$.
2
votes
0answers
35 views

How do I specify the size of the domain of action in the function CycleIndexPolynomial? [closed]

If I input CycleIndexPolynomial[{1, 2, 3, 4, 5}, Table[Subscript[x, i], {i, 1, 5}]] Mathematica returns 1; I was hoping for $x_1^5$. If I input ...
4
votes
1answer
66 views

How can I “permute” an ordered pair over all the permutations of say $S_4$?

I want to make an action table of the symmetric group (say $S_4$) acting on the set of unordered pairs of distinct vertices of a square. I have the list of such pairs: ...
4
votes
1answer
216 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 ...
5
votes
1answer
85 views

How to transform abstract finite group to permutation group?

It seems that Mathematica only has group functionality for permutation groups? Then there is a step to transform the abstract finite one to a permutation one. As an example, consider the following ...
5
votes
1answer
106 views

How to get a new list by exchanging some elements?

Let's begin with a simple example. Now, we have a list, list0=Range[4]; k1 and k2 are some elements of the list0. If |k1-k2|==2, then the elements k1 and k2 can ...
4
votes
3answers
331 views

How to find a quotient group?

Given a normal subgroup H of a (large, finite permutation) group G, knowing a set of generators for each of H and G, how to find a subgroup K of G that is isomorphic to G/H? (Using Mathematica.)
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, ...
6
votes
0answers
75 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
2answers
218 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 ...
4
votes
4answers
152 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: ...
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?
6
votes
6answers
358 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: ...
1
vote
1answer
55 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 ...
9
votes
1answer
260 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 ...
3
votes
1answer
100 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 ...
1
vote
2answers
89 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.
5
votes
1answer
199 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 ...
2
votes
2answers
128 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?
3
votes
1answer
126 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 + ...
0
votes
1answer
76 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?
7
votes
2answers
293 views

What is the underlying algorithm for GroupElementToWord?

What algorithm is Mathematica 9 using for GroupElementToWord[group, g]?
5
votes
2answers
769 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 ...
2
votes
1answer
82 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 ...
3
votes
1answer
76 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 ...
13
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 ...
5
votes
2answers
3k 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 $L_i$ ($i=1,2,3$), ...
9
votes
2answers
855 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 ...
3
votes
2answers
423 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
2answers
637 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
486 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
194 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 ...
3
votes
2answers
726 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 ...
13
votes
2answers
845 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 ...
24
votes
1answer
978 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 ...