All Questions
Tagged with computational-group-theory computer-algebra
8 questions
10
votes
1
answer
639
views
Computing homology groups with GAP
I’m studying the homology groups of arithmetic groups such as $SL(5,\mathbb{Z})$. I saw in the answer to this post that we can use GAP to compute some of the homology groups for $SL(3,\mathbb{Z})$. Is ...
- 545
0
votes
0
answers
274
views
Algorithm to compute automorphism group of a finite group
Is there an algorithm to compute automorphism group of a finite group?
GAP has a function to do this, but while perusing their GitHub repo, I could not find an implementation. I'm struggling to find ...
2
votes
1
answer
191
views
programming to compute kernel quotient image of a $\mathbb{Z}$-module endomorphism
Let the integers $n\geq 2$, $k\geq 1$, $v=0$ or $1$ and $n_1,\cdots,n_k\geq 1$ such that
$$
\sum_{i=1}^k n_i+v=n.
$$
Define $P_a^b=0$ if both $a,b$ are odd and $P_a^b={{[a/2]}\choose {[(a+b)/2]}}$ ...
- 1,990
0
votes
1
answer
330
views
Computational Algebra and Symbolic Computation - Where? [closed]
Following the line of this question, I'm in my last year of M.Sc., and I'm looking for a place where I can start my PHD. Since that question has been asked 4 years ago, I thought it may be wise to ask ...
- 201
6
votes
1
answer
517
views
Using math software to show that the following groups are infinite?
I would like to show that the following finitely presented group in 3 generators $P, Q, R$ is infinite in certain cases:
$$P^p, Q^q, R^r, (PQ)^2, (QR)^2, (PQR)^2, (QR^{r/2+1})^a (RQR^{r/2})^b$$
For ...
- 656
15
votes
4
answers
4k
views
Program for computing group cohomology
Is there any computer program with which I can compute the group cohomology H^n(G,V) for a group G acting linearly on a vector space?
I mainly care about infinite groups.
- 151
22
votes
4
answers
1k
views
Is there a way of canonically labelling permutation groups?
When working with large numbers of graphs, a canonical labelling routine is essential as, after the initial cost of canonically labelling each graph, it permits isomorphism checks to be replaced with ...
- 12.7k
8
votes
4
answers
7k
views
Computational algebra: where?
I'm on my last semester of a math B.Sc. and about to start studying for a math M.Sc in the same institute.
It now seems like a good time to start thinking of a PhD.
I'm interested in both algebra and ...