Difference between revisions of "ApCoCoA-1:Extended Hecke groups"
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==== Computation ==== | ==== Computation ==== | ||
| + | /*Use the ApCoCoA package ncpoly.*/ | ||
| + | |||
| + | // Define the variable p of the extended Hecke group | ||
| + | MEMORY.P := 3; | ||
| + | |||
| + | Use ZZ/(2)[r,x,y]; | ||
| + | NC.SetOrdering("LLEX"); | ||
| + | |||
| + | Define CreateRelationsExtendedHeckegroup() | ||
| + | Relations:=[]; | ||
| + | |||
| + | //add the relation r^2 = 1 | ||
| + | Append(Relations,[[r,r],[1]]); | ||
| + | |||
| + | //add the relation x^2 = 1 | ||
| + | Append(Relations,[[x,x],[1]]); | ||
| + | |||
| + | //add the relation y^p = 1 | ||
| + | Append(Relations,[[y^MEMORY.P],[1]]); | ||
| + | |||
| + | //add the relation (rx)^2 = 1 | ||
| + | Append(Relations,[[r,x,r,x],[1]]); | ||
| + | |||
| + | // add the relation (yr)^2 = 1 | ||
| + | Append(Relations,[[y,r,y,r],[1]]); | ||
| + | Return Relations; | ||
| + | EndDefine; | ||
| + | |||
| + | Relations:=CreateRelationsExtendedHeckegroup(); | ||
| + | Relations; | ||
| + | |||
| + | Gb:=NC.GB(Relations,31,1,100,1000); | ||
| + | Gb; | ||
====Examples in Symbolic Data Format==== | ====Examples in Symbolic Data Format==== | ||
Revision as of 09:10, 20 July 2014
Description
Reference
Ma. Louise Antonette N. De Las Peñas, Ma. Carlota B. Decena and Glenn R. Laigo, ON THE SUBGROUPS OF THE EXTENDED HECKE, HECKE AND PICARD GROUPS, Proceedings of the 5th Asian Mathematical Conference, Malaysia 2009.
Computation
/*Use the ApCoCoA package ncpoly.*/
// Define the variable p of the extended Hecke group
MEMORY.P := 3;
Use ZZ/(2)[r,x,y];
NC.SetOrdering("LLEX");
Define CreateRelationsExtendedHeckegroup()
Relations:=[];
//add the relation r^2 = 1
Append(Relations,[[r,r],[1]]);
//add the relation x^2 = 1
Append(Relations,[[x,x],[1]]);
//add the relation y^p = 1
Append(Relations,[[y^MEMORY.P],[1]]);
//add the relation (rx)^2 = 1
Append(Relations,[[r,x,r,x],[1]]);
// add the relation (yr)^2 = 1
Append(Relations,[[y,r,y,r],[1]]);
Return Relations;
EndDefine;
Relations:=CreateRelationsExtendedHeckegroup();
Relations;
Gb:=NC.GB(Relations,31,1,100,1000);
Gb;
