ApCoCoA-1:Ikosaeder group
From ApCoCoAWiki
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
Description
The Ikosaeder group has the following representation:
I = <a,b | a^2 = b^3 = (ab)^5 = 1>
Reference
Eric W. Weisstein: Math World, Icosahedral Group
Computation
/*Use the ApCoCoA package ncpoly.*/
Use ZZ/(2)[a,b];
NC.SetOrdering("LLEX");
Define CreateRelationsIkosaeder()
Relations:=[];
// add the relation a^2 = 1
Append(Relations,[[a^2],[1]]);
// add the relation b^3 = 1
Append(Relations,[[b^3],[1]]);
// add the relation (ab)^5 = 1
Append(Relations,[[a,b,a,b,a,b,a,b,a,b],[1]]);
Return Relations;
EndDefine;
Relations:=CreateRelationsIkosaeder();
Gb:=NC.GB(Relations);
Example in Symbolic Data Format
<FREEALGEBRA createdAt="2014-01-20" createdBy="strohmeier"> <vars>a,b</vars> <basis> <ncpoly>a*a-1</ncpoly> <ncpoly>b*b*b-1</ncpoly> <ncpoly>a*b*a*b*a*b*a*b*a*b-1</ncpoly> </basis> <Comment>Ikosaeder_group</Comment> </FREEALGEBRA>
