Difference between revisions of "ApCoCoA-1:Other4 groups"

From ApCoCoAWiki
(New page: === <div id="Other4_groups">Other groups</div> === ==== Description ==== This group has the following representation: G = <a,b | a^2 = b^3 = (abab...)
 
Line 12: Line 12:
 
   Use ZZ/(2)[a,b];
 
   Use ZZ/(2)[a,b];
 
   NC.SetOrdering("LLEX");
 
   NC.SetOrdering("LLEX");
 +
 
   Define CreateRelationsOther4()
 
   Define CreateRelationsOther4()
 
     Relations:=[];
 
     Relations:=[];
 
      
 
      
 
     // add the relations a^2 = b^3 = 1
 
     // add the relations a^2 = b^3 = 1
     Append(Relations,[[a,a],[1]]);
+
     Append(Relations,[[a^2],[1]]);
     Append(Relations,[[b,b,b],[1]]);
+
     Append(Relations,[[b^3],[1]]);
 +
 
     // add the relation (ababab^{2})^{3} = 1
 
     // add the relation (ababab^{2})^{3} = 1
     Append(Relations,[[a,b,a,b,a,b,b,a,b,a,b,a,b,b,a,b,a,b,a,b,b],[1]]);
+
     Append(Relations,[[a,b,a,b,a,b^2,a,b,a,b,a,b^2,a,b,a,b,a,b^2],[1]]);
    Return Relations;
+
 
 +
  Return Relations;
 
   EndDefine;
 
   EndDefine;
 
    
 
    
 
   Relations:=CreateRelationsOther4();
 
   Relations:=CreateRelationsOther4();
   GB:=NC.GB(Relations);
+
   Gb:=NC.GB(Relations);
   Size(GB);
+
   Size(Gb);

Revision as of 10:15, 23 September 2013

Description

This group has the following representation:

 G = <a,b | a^2 = b^3 = (ababab^{2})^{3} = 1>

The number of elements of the Groebner-Basis is 111554.

Reference

No reference available

Computation

 /*Use the ApCoCoA package ncpoly.*/
 
 Use ZZ/(2)[a,b];
 NC.SetOrdering("LLEX");

 Define CreateRelationsOther4()
   Relations:=[];
   
   // add the relations a^2 = b^3 = 1
   Append(Relations,[[a^2],[1]]);
   Append(Relations,[[b^3],[1]]);

   // add the relation (ababab^{2})^{3} = 1
   Append(Relations,[[a,b,a,b,a,b^2,a,b,a,b,a,b^2,a,b,a,b,a,b^2],[1]]);
 
  Return Relations;
 EndDefine;
 
 Relations:=CreateRelationsOther4();
 Gb:=NC.GB(Relations);
 Size(Gb);