Difference between revisions of "ApCoCoA-1:Other4 groups"
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(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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| − | === <div id="Other4_groups">[[:ApCoCoA:Symbolic data#Other_groups|Other | + | === <div id="Other4_groups">[[:ApCoCoA:Symbolic data#Other_groups|Other Groups]]</div> === |
==== Description ==== | ==== Description ==== | ||
This group has the following representation: | This group has the following representation: | ||
| 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); |
| + | ====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*b)^3-1</ncpoly> | ||
| + | <Comment>relation:(ababab^{2})^{3} = 1 </Comment> | ||
| + | </basis> | ||
| + | <Comment>Other_groups4</Comment> | ||
| + | </FREEALGEBRA> | ||
Latest revision as of 21:08, 22 April 2014
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);
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*b)^3-1</ncpoly>
<Comment>relation:(ababab^{2})^{3} = 1 </Comment>
</basis>
<Comment>Other_groups4</Comment>
</FREEALGEBRA>
