Difference between revisions of "ApCoCoA-1:VonDyck groups"
From ApCoCoAWiki
(New page: === <div id="VonDyck groups">Von Dyck groups</div> === ==== Description ==== D(l,m,n) = <x,y | x^{l} = y^{m} = (xy)^{n} = 1> (Reference: not f...) |
|||
| Line 10: | Line 10: | ||
/*Use the ApCoCoA package ncpoly.*/ | /*Use the ApCoCoA package ncpoly.*/ | ||
| − | // | + | // Parameters of von Dyck group |
| − | |||
| + | MEMORY.L:=3; | ||
| + | MEMORY.M:=5; | ||
| + | MEMORY.N:=2; | ||
| − | Use ZZ/(2)[ | + | Use ZZ/(2)[x,y]; |
NC.SetOrdering("LLEX"); | NC.SetOrdering("LLEX"); | ||
| − | Define | + | Define CreateRelationsVonDyck() |
Relations:=[]; | Relations:=[]; | ||
| − | |||
| − | |||
| − | |||
| − | // add the relation | + | // add the relation x^l = 1 |
| − | Append(Relations, [[ | + | BufferA:=[]; |
| + | Append(Relations,[[x^MEMORY.L],[1]]); | ||
| + | |||
| + | // add the relation y^m = 1 | ||
| + | Append(Relations,[[y^MEMORY.M],[1]]); | ||
| + | |||
| + | // add the relation (xy)^n = 1 | ||
| + | BufferXY:=[]; | ||
| + | For Index1 := 1 To MEMORY.N Do | ||
| + | Append(BufferXY,x); | ||
| + | Append(BufferXY,y); | ||
| + | EndFor; | ||
| + | |||
| + | Append(Relations,[BufferXY,[1]]); | ||
| − | |||
| − | |||
Return Relations; | Return Relations; | ||
EndDefine; | EndDefine; | ||
| − | Relations:= | + | Relations:=CreateRelationsVonDyck(); |
Relations; | Relations; | ||
GB:=NC.GB(Relations); | GB:=NC.GB(Relations); | ||
GB; | GB; | ||
Revision as of 10:12, 13 August 2013
Description
D(l,m,n) = <x,y | x^{l} = y^{m} = (xy)^{n} = 1>
(Reference: not found yet)
Computation
/*Use the ApCoCoA package ncpoly.*/
// Parameters of von Dyck group
MEMORY.L:=3;
MEMORY.M:=5;
MEMORY.N:=2;
Use ZZ/(2)[x,y];
NC.SetOrdering("LLEX");
Define CreateRelationsVonDyck()
Relations:=[];
// add the relation x^l = 1
BufferA:=[];
Append(Relations,[[x^MEMORY.L],[1]]);
// add the relation y^m = 1
Append(Relations,[[y^MEMORY.M],[1]]);
// add the relation (xy)^n = 1
BufferXY:=[];
For Index1 := 1 To MEMORY.N Do
Append(BufferXY,x);
Append(BufferXY,y);
EndFor;
Append(Relations,[BufferXY,[1]]);
Return Relations;
EndDefine;
Relations:=CreateRelationsVonDyck();
Relations;
GB:=NC.GB(Relations);
GB;
