ApCoCoA-1:Ikosaeder group: Difference between revisions
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New page: === <div id="Ikosaeder group">Ikosaeder group</div> === ==== Description ==== The Ikosaeder group has the following representation: I = <a,b |... |
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=== <div id="Ikosaeder group">[[:ApCoCoA:Symbolic data#Ikosaeder_group|Ikosaeder | === <div id="Ikosaeder group">[[:ApCoCoA:Symbolic data#Ikosaeder_group|Ikosaeder Group]]</div> === | ||
==== Description ==== | ==== Description ==== | ||
The Ikosaeder group has the following representation: | The Ikosaeder group has the following representation: | ||
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// add the relation (ab)^5 = 1 | // add the relation (ab)^5 = 1 | ||
Append(Relations,[[a,b,a,b,a,b,a,b],[1]]); | Append(Relations,[[a,b,a,b,a,b,a,b,a,b],[1]]); | ||
Return Relations; | Return Relations; | ||
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Relations:=CreateRelationsIkosaeder(); | Relations:=CreateRelationsIkosaeder(); | ||
Gb:=NC.GB(Relations); | 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> | |||
Latest revision as of 21:00, 22 April 2014
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>
