Questions tagged [group-theory]

Questions on the group-theoretic functionality of Mathematica.

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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 ...
M-Askman's user avatar
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7 votes
2 answers
8k 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 $L_i$ ($i=1,2,3$), ...
Bilentor's user avatar
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14 votes
4 answers
4k 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 ...
Jimeree's user avatar
  • 549
19 votes
4 answers
3k 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 those,...
Cameron Smith's user avatar
7 votes
6 answers
491 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: ...
BetterEnglish's user avatar
10 votes
2 answers
3k 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 ...
mathdonk's user avatar
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10 votes
1 answer
277 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 ...
van abel's user avatar
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8 votes
2 answers
796 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 = g_2^...
Markeur's user avatar
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6 votes
2 answers
3k 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 ...
KoObO's user avatar
  • 81
5 votes
3 answers
275 views

How the solve the parameter of the conjugate permutations

As we know the definition of conjugate permutations is: $$\exists p \quad p^{-1} \alpha p=\beta$$ When I have an alpha=Cycles[{{1,4},{2,5,6,3}}] and a ...
yode's user avatar
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Mathematica 11 Symmetry Packages

Are there any symmetry finding packages (for differential equations) that work with Mathematica 11.1? I've tried MathLie but from looking at the documentation it had instructions for Windows 95... I ...
Pythonista's user avatar
4 votes
2 answers
441 views

How to use Mathematica to prove that isotropic materials have only two independent parameters

Posts on related issues can be found from here or here. Index symmetries: A stiffness tensor $C$ is a fourth-order tensor with components $c_{ijkl}$ which maps symmetric second-order tensors into ...
A little mouse on the pampas's user avatar
14 votes
2 answers
776 views

How can I compute the representation matrices of a point group under given basis functions?

Take the $C_{3v}$ point group for example: ...
goodluck's user avatar
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9 votes
1 answer
1k views

Definition of WignerD function?

On Wikipedia, elements of Wigner's D-matrix are defined as $$D_{m'm}^{j}(\alpha,\beta,\gamma)=\langle jm'|e^{-i\alpha J_z}e^{-i\beta J_y}e^{-i\gamma J_z}|jm\rangle=e^{-im'\alpha}d_{m'm}^j (\beta)e^{-...
Semiclassical's user avatar
8 votes
1 answer
567 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 $Z_4\...
Rainer's user avatar
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7 votes
2 answers
626 views

Listing all subgroups

Here's how to show all subgroups of $S_4$ in GAP: ...
dharmatech's user avatar
6 votes
1 answer
1k views

Irreducible representations for the symmetry group $T_d$

I am trying to get the explicit two dimensional irreducible representation matrices for the symmetry group $T_d$. I need the matrix representation for each element in the group. Are there any ...
Dsb's user avatar
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5 votes
3 answers
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How to know the Galois Group of a polynomial is a solvable group?

ResourceFunction["StauduharGaloisGroup"][2 x^5+3 x^4+10 x^3+15 x^2+8 x+12,x]["GaloisGroup"] ...
yode's user avatar
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4 votes
3 answers
165 views

How to list all subgroups of symmetry group S_6?

I learned from https://oeis.org/A005432 that $S_6$ has $1455$ subgroups, how can I list them all in mathematica? As the comment says, the direct approach cannot solve the problem.
lapcal's user avatar
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4 votes
1 answer
168 views

Calculating Rubiks $ 2 \times 2 \times 2 $ Permutation using Cycles

The help page of PermutationGroup shows a neat example on calculating the permutations of a $3\times 3\times 3$: ...
Tino 's user avatar
  • 219
4 votes
1 answer
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LieArt --- 3 different 8 dimensional irreducible representation of $\mathrm{SO}(8)$ and their decompositions

I am using the LieArt which you can download freely online https://arxiv.org/pdf/1206.6379.pdf There are three different 8 dimensional $\mathrm{SO}(8)$ irreducible representations, formally it is ...
annie marie cœur's user avatar
4 votes
1 answer
138 views

How can I remove the redundant generators in PermutationGroup?

Consider: ...
yode's user avatar
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4 votes
2 answers
398 views

How to correctly enumerate all the schemes of this cube coloring problem?

This problem is the fifth question of 1996 Chinese High School Mathematics League or Chinese Mathematical Olympiad in Senior: Choose several colors from the given six different colors to dye six faces ...
A little mouse on the pampas's user avatar
4 votes
1 answer
2k views

Hadamard Lemma and commutators algebra

I would like to implement the following formula, which goes under the name of Hadamard Lemma: $ e^A \, B \, e^{-A} = \sum_{k=0}^{+\infty} \frac{1}{k!} [A,B]_k $ where $ [A,B]_0 = B , \...
AndreaPaco's user avatar
3 votes
1 answer
215 views

How to draw a cycle graph of a group?

MMA can plot a Cayley graph by CayleyGraph directly, which can help us to visualize the group: ...
yode's user avatar
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3 votes
3 answers
199 views

How to delete duplicate graphics of the same kind?

A054247: Number of n X n binary matrices under action of dihedral group of the square D_4. ...
A little mouse on the pampas's user avatar
3 votes
0 answers
178 views

Reducing to Irreducible Representations

Group Theory Background / Utilities Suppose I give you a list G of matrices which represent some group, in that the matrices are closed under multiplication. In ...
evanb's user avatar
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2 votes
1 answer
75 views

Relabeling and matching variables (in MultiplicationTable)

Suppose we have a set of data given here as the multiplication table of 8 elements labeled {1,2,3,4,9,10,11,12}: $$ \begin{array}{cccccccc} 1 & 2 & 3 & 4 & 9 & 10 & 11 & ...
wonderich's user avatar
  • 923
2 votes
1 answer
181 views

How to determine if a group H is a normal subgroup of group G?

A subgroup $H$ of the group $G$ is normal group in $G$ if and only if $\displaystyle ghg^{-1}\in H$ for all $\displaystyle g\in G$ and $\displaystyle h\in H$. How to use MMA to know the group $H$ is a ...
yode's user avatar
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2 votes
1 answer
156 views

How to generate addition table for ring $\mathbb Z_{15}$?

How do I generate an addition table for ring R such that $R = \mathbb{Z}_{15}$ or generally speaking, how to generate an addition table for any polynomial ring <...
Heisenberg's user avatar
1 vote
1 answer
239 views

Function that Generates all Normal Subgroups of a Group

I am trying to create a function which, given a group structure, generates a list of all the normal subgroups contained within it. But I am not sure how to proceed. For now, I have the following: <...
Omari Celestine's user avatar
1 vote
1 answer
452 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 ...
user27584's user avatar
0 votes
1 answer
67 views

Relabeling/matching variables of big data (in MultiplicationTable)

Let A and B be two sets of tables (from multiplication tables of a group, 24 by 24 as rows by columns), how can we effectively (and possibly also efficiently) find a way to map between them, if two ...
wonderich's user avatar
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