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Results tagged with gap
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user 59303
GAP (Groups, Algorithms and Programming) is a system for computational discrete algebra, with particular emphasis on Computational Group Theory. It provides a programming language, a library of thousands of functions implementing algebraic algorithms, and large data libraries of algebraic objects.
3
votes
Accepted
Problem while multiplying under a set of relators
Therefore GAP will by default not reduce word expressions in finitely presented groups. … a, b*a*c*b, c^-1*a*c*b ]
gap> a:=G.1;;
gap> a^2;
<identity ...>
This however costs time and memory (and for large groups might not be able to succeed), and is not always necessary, thus it is not done …
- 1,210
2
votes
How do I find hyperbolic generating triples for a group using GAP?
First get the possible types:
gap> o:=Set(List(ConjugacyClasses(G),x->Order(Representative(x))));
[ 1, 2, 3, 4, 7 ]
gap> t:=Filtered(UnorderedTuples(o,3),x->1/x[1]+1/x[2]+1/x[3]<1);
[ [ 2, 3, 7 ], [ 2, … > mytup:=t[1];
[ 2, 3, 7 ]
gap> fp:=f/[f.1^mytup[1],f.2^mytup[2],(f.1*f.2)^mytup[3]];
<fp group on the generators [ x, y ]>
gap> q:=GQuotients(fp,G);
[ [ x, y ] -> [ (1,3)(2,5)(4,7)(6,8), (3,5,7)(4,6,8 …
- 1,210
6
votes
Accepted
A question about the possibilities of GAP
>List(r,x->Int(x)*One(rf))));;
gap> q:=Group(gens);
<matrix group with 5 generators>
gap> Size(q);
86016
gap> Size(GL(3,rf));
86016
gap> isop:=IsomorphismPermGroup(q);;
gap> p:=Image(isop);
We now construct … (Indeed this ought to be better, but it still beats hand-calculations.)
gap> bco:=[Br];;
gap> sub:=Group(bco);;
gap> FittingFreeLiftSetup(sub);;
gap> Size(sub);
512
gap> for i in bco do
> for j in GeneratorsOfGroup …
- 1,210
4
votes
Finding all submodules
The generic method for submodules would be to write down a matrix representation and to use MeatAxe tools -- in GAP there is e.g. a function MTX.BasesSubmodules. …
- 1,210