Questions on the group-theoretic functionality of Mathematica.
2
votes
1answer
66 views
What is the underlying algorithm for GroupElementToWord?
What algorithm is Mathematica 9 using for GroupElementToWord[group, g]?
2
votes
2answers
116 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 $L_i$ ($i=1,2,3$), ...
7
votes
2answers
154 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
240 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 ...
5
votes
2answers
172 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
278 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 = ...
10
votes
2answers
188 views
How can I compute the representation matrices of a point group under given basis functions?
Take the $C_{3v}$ point group for example:
...
6
votes
3answers
498 views
Find cycles of graphs with both directed and undirected edges
I need to enumerate all the simple cycles of a graph which has both directed and undirected edges, where we can treat the undirected edges as doubly directed. (Specifically, I am looking at the Cayley ...
4
votes
2answers
125 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 ...
2
votes
2answers
243 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 ...
9
votes
2answers
367 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 ...
19
votes
1answer
413 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 ...
