Questions tagged [group-theory]
Questions on the group-theoretic functionality of Mathematica.
160
questions
2
votes
2
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Unstable work of PolynomialMod
I tried to use PolynomialMod for my calculation and i need some help on working with it, because i'll need to use it several hundred times.
I made such a request
...
- 23
1
vote
1
answer
92
views
The central product and the permutation representation of the Pauli group of order 16
I am interested in obtaining a permutation representation of the Pauli Group $G_1 = \langle X, Y, Z \rangle$. I think this would be easy enough as a "Regular representation" but then I learn ...
- 349
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vote
0
answers
55
views
Why is SymmetrizedArray taking so much memory?
The context is: I take the tensor product of 2 totally symmetric tensors of rank 8, in 2 dimensions(in this case there are only 9 independent components):
...
- 609
1
vote
0
answers
34
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Efficient chain rule implementation
(there is a fair amount of context here) I am implementing a generalized chain rule to do some work, say for order 3 in derivatives ($\partial_i = \partial/\partial x_i$):
\begin{align}
\partial_i \...
- 609
5
votes
3
answers
182
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Calculating the basis set of quotient spaces
Having a polynomial $f(x,y)$, I would like to compute the following quantity
\begin{equation*}
{\mathbb C}[X,Y,Z]/\langle f_{x}, f_{y}, f_{z} \rangle,
\end{equation*}
where $f_{x},f_{y},f_{z}$ are, ...
- 1,043
2
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1
answer
49
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By what criteria does Mathematica generate the list of group elements in `GroupElements[group]`?
I ask because aside from always giving the identity element first, I have found a "pattern" associated with the list given by GroupElements[group]. This &...
- 349
3
votes
2
answers
71
views
Bug in Point Group Conjugacy Class Data
I noticed that in $Version == "13.2.0 for Mac OS X x86 (64-bit) (November 18, 2022)" Mathematica has conflicting ...
- 6,276
0
votes
0
answers
47
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Defining function through a formula
I would like to define a cocycle on a group that maps into the unit circle. That is, I want to be able to define a function $f:G\times G\to\mathbb{T}$ such that $f(e_G,a)=f(a,e_G)=1$ for all $a\in G$ ...
- 1
1
vote
1
answer
93
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Elements of a group that send one element to another
If I have a permutation group, say $S_{10}$, how do I get all the permutations that send the set {1, 2, 3} to {5, 6, 7}? I know ...
- 21
4
votes
3
answers
212
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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.
- 531
4
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2
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83
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How to find a set of generators with the smallest number of elements in a permutation group?
Given a permutation group with many generators
...
- 531
4
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2
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391
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How to generate all permutation matrices for 4 qubits?
In quantum mechanics, a qubit can be understood as a 2 by 1 vector denoted by Dirac notation as $$|0\rangle \equiv \left( \begin{array}{c}
1\\
0\\
\end{array} \right) ,|1\rangle \equiv \left( \...
- 381
3
votes
1
answer
130
views
Why am I having issues working with large group multiplication tables?
My mathematica running on Wolfram Cloud seems to break down if I use a SymmetricGroup greater than 6. As a basic example, when I run,
...
- 31
3
votes
2
answers
218
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Cayley for SL group
In this paper, they are using an expander graph. It seems like it's just a Cayley graph for $SL(2,Z_p)$, where $P$ is a prime number.
How do I go about making a Cayley graph as shown in the first of ...
- 717
4
votes
1
answer
264
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How to convert a polynomial into monic form of a polynomial
The function ResourceFunction["StauduharGaloisGroup"] can get a Galois Group about a monic irreducible integer polynomial. But I want to know the Galois ...
- 26.9k