Difference between revisions of "ApCoCoA-1:Other12 groups"
From ApCoCoAWiki
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MEMORY.B := 3; | MEMORY.B := 3; | ||
MEMORY.N := 4; | MEMORY.N := 4; | ||
| + | |||
// x is invers to z, t has an implicit invers (Relation: t^{n} = 1) | // x is invers to z, t has an implicit invers (Relation: t^{n} = 1) | ||
Use ZZ/(2)[x,t,z]; | Use ZZ/(2)[x,t,z]; | ||
NC.SetOrdering("LLEX"); | NC.SetOrdering("LLEX"); | ||
| + | |||
Define CreateRelationsOther12() | Define CreateRelationsOther12() | ||
Relations:=[]; | Relations:=[]; | ||
| Line 39: | Line 41: | ||
Append(RelationBuffer1,t^(MEMORY.N-1)); | Append(RelationBuffer1,t^(MEMORY.N-1)); | ||
Append(Relations,[RelationBuffer1,[x^MEMORY.B]]); | Append(Relations,[RelationBuffer1,[x^MEMORY.B]]); | ||
| + | |||
Return Relations; | Return Relations; | ||
EndDefine; | EndDefine; | ||
Relations:=CreateRelationsOther12(); | Relations:=CreateRelationsOther12(); | ||
| − | + | Gb:=NC.GB(Relations,31,1,100,1000); | |
Revision as of 02:38, 24 September 2013
Description
This group has the following finite representation:
G = <x,t | tx^{a}t^{-1} = x^{b},t^{n} = 1>
for a,b >= 1 and n >= 2.
Reference
No reference available
Computation
/*Use the ApCoCoA package ncpoly.*/
// Note that a,b >= 1 and n >= 2
MEMORY.A := 3;
MEMORY.B := 3;
MEMORY.N := 4;
// x is invers to z, t has an implicit invers (Relation: t^{n} = 1)
Use ZZ/(2)[x,t,z];
NC.SetOrdering("LLEX");
Define CreateRelationsOther12()
Relations:=[];
// add the invers relations xz = zx = 1
Append(Relations,[[x,z],[1]]);
Append(Relations,[[z,x],[1]]);
// add the relation t^{n} = 1
RelationBuffer0:=[];
For Index0:=1 To MEMORY.N Do
Append(RelationBuffer0,t);
EndFor;
Append(Relations,[RelationBuffer0,[1]]);
// add the relation tx^{a}t^{-1} = x^{b}
RelationBuffer1:=[];
Append(RelationBuffer1,t);
Append(RelationBuffer1,x^(MEMORY.A));
Append(RelationBuffer1,t^(MEMORY.N-1));
Append(Relations,[RelationBuffer1,[x^MEMORY.B]]);
Return Relations;
EndDefine;
Relations:=CreateRelationsOther12();
Gb:=NC.GB(Relations,31,1,100,1000);
