Difference between revisions of "ApCoCoA-1:Hecke groups"
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(New page: === <div id="Hecke_groups">Hecke groups</div> === ==== Description ==== The Hecke groups has the following representation: H(lambda_q) = <x,y | x^...) |
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Use ZZ/(2)[x,y,z]; | Use ZZ/(2)[x,y,z]; | ||
NC.SetOrdering("LLEX"); | NC.SetOrdering("LLEX"); | ||
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Define CreateRelationsHecke() | Define CreateRelationsHecke() | ||
Relations:=[]; | Relations:=[]; | ||
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Relations:=CreateRelationsHecke(); | Relations:=CreateRelationsHecke(); | ||
| − | + | Gb:=NC.GB(Relations); | |
Revision as of 03:32, 22 September 2013
Description
The Hecke groups has the following representation:
H(lambda_q) = <x,y | x^2=(xy)^q=1, for q >= 3>
Reference
GROWTH IN HECKE GROUPS, MARTIN KREUZER AND GERHARD ROSENBERGER
Computation
/*Use the ApCoCoA package ncpoly.*/
// Define the variable q of the Hecke group
MEMORY.Q := 4;
// y is invers to z, x is invers to itself (that follows directly from the first relation)
Use ZZ/(2)[x,y,z];
NC.SetOrdering("LLEX");
Define CreateRelationsHecke()
Relations:=[];
// add the invers relation of y and z
Append(Relations,[[y,z],[1]]);
Append(Relations,[[z,y],[1]]);
// add the relation x^2 = 1
Append(Relations,[[x,x],[1]]);
// add the relation (xy)^q = 1
RelationBuffer1:=[];
For Index0 := 1 To MEMORY.Q Do
Append(RelationBuffer1,x);
Append(RelationBuffer1,y);
EndFor;
Append(Relations,[RelationBuffer1,[1]]);
Return Relations;
EndDefine;
Relations:=CreateRelationsHecke();
Gb:=NC.GB(Relations);
