Difference between revisions of "ApCoCoA-1:Modular group"
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(New page: === <div id="Modular_group">Modular group</div> === ==== Description ==== The Modular group has the following representation: PSL(2,Z) = <a,b | a...) |
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| − | === <div id="Modular_group">[[:ApCoCoA:Symbolic data#Modular_group|Modular | + | === <div id="Modular_group">[[:ApCoCoA:Symbolic data#Modular_group|Modular Group]]</div> === |
==== Description ==== | ==== Description ==== | ||
The Modular group has the following representation: | The Modular group has the following representation: | ||
| Line 30: | Line 30: | ||
Relations:=CreateRelationsModular(); | Relations:=CreateRelationsModular(); | ||
GB:=NC.GB(Relations); | GB:=NC.GB(Relations); | ||
| + | ====Example in Symbolic Data Format==== | ||
| + | <FREEALGEBRA createdAt="2014-01-24" createdBy="strohmeier"> | ||
| + | <vars>a,b,d</vars> | ||
| + | <basis> | ||
| + | <ncpoly>b*d-1</ncpoly> | ||
| + | <ncpoly>d*b-1</ncpoly> | ||
| + | <ncpoly>a*a-1</ncpoly> | ||
| + | <ncpoly>(a*b)^3-1</ncpoly> | ||
| + | </basis> | ||
| + | <Comment>Modular_group</Comment> | ||
| + | </FREEALGEBRA> | ||
Latest revision as of 21:04, 22 April 2014
Description
The Modular group has the following representation:
PSL(2,Z) = <a,b | a^2 = (ab)^3 = 1 >
Reference
Platonic tilings of Riemann surfaces: The Modular Group, Gerard Westendorp
Computation
/*Use the ApCoCoA package ncpoly.*/
// a^{-1} is a and b is invers to d
Use ZZ/(2)[a,b,d];
NC.SetOrdering("LLEX");
Define CreateRelationsModular()
Relations:=[];
// add the invers relations
Append(Relations,[[b,d],[1]]);
Append(Relations,[[d,b],[1]]);
// add the relation a^2 = 1
Append(Relations,[[a^2],[1]]);
// add the relation (ab)^3 = 1
Append(Relations,[[a,b,a,b,a,b],[1]]);
Return Relations;
EndDefine;
Relations:=CreateRelationsModular();
GB:=NC.GB(Relations);
Example in Symbolic Data Format
<FREEALGEBRA createdAt="2014-01-24" createdBy="strohmeier"> <vars>a,b,d</vars> <basis> <ncpoly>b*d-1</ncpoly> <ncpoly>d*b-1</ncpoly> <ncpoly>a*a-1</ncpoly> <ncpoly>(a*b)^3-1</ncpoly> </basis> <Comment>Modular_group</Comment> </FREEALGEBRA>
