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...) |
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| 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 | + | Append(Relations,[[a^2],[1]]); |
| − | Append(Relations,[[b | + | 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 | + | 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; | EndDefine; | ||
Relations:=CreateRelationsOther4(); | Relations:=CreateRelationsOther4(); | ||
| − | + | Gb:=NC.GB(Relations); | |
| − | Size( | + | 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);
