ApCoCoA-1:Free groups
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Revision as of 08:09, 16 August 2013 by F lorenz (talk | contribs) (New page: === <div id="Free_groups">Free groups</div> === ==== Description ==== F(n) = <a_{1},...,a_{n} | a_{i}a_{i}^{-1} = a_{i}^{-1}a_{i} = 1> (Reference:...)
Description
F(n) = <a_{1},...,a_{n} | a_{i}a_{i}^{-1} = a_{i}^{-1}a_{i} = 1>
(Reference: Kharlampovich, Olga; Myasnikov, Alexei (2006). "Elementary theory of free non-abelian groups". J. Algebra 302 (2): 451–552)
Computation
/*Use the ApCoCoA package ncpoly.*/
// Number of free group
MEMORY.N:=4;
Use ZZ/(2)[x[1..MEMORY.N],y[1..MEMORY.N]];
NC.SetOrdering("LLEX");
Define CreateRelationsFreeAbelian()
Relations:=[];
For Index1 := 1 To MEMORY.N Do
Append(Relations,[[x[Index1],y[Index1]],[1]]);
Append(Relations,[[y[Index1],x[Index1]],[1]]);
EndFor;
Return Relations;
EndDefine;
Relations:=CreateRelationsFreeAbelian();
Relations;
GB:=NC.GB(Relations);
GB;
