Difference between revisions of "ApCoCoA-1:Other13 groups"
From ApCoCoAWiki
(New page: === <div id="Other13_groups">Other groups</div> === ==== Description ==== This group has the following finite representation: G = <x,y | x^2 = xy^{...) |
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| Line 11: | Line 11: | ||
/*Use the ApCoCoA package ncpoly.*/ | /*Use the ApCoCoA package ncpoly.*/ | ||
| − | // Note that a,b >= 1 | + | // Note that a,b,c,d >= 1 |
MEMORY.A := 3; | MEMORY.A := 3; | ||
MEMORY.B := 3; | MEMORY.B := 3; | ||
MEMORY.C := 4; | MEMORY.C := 4; | ||
MEMORY.D := 5; | MEMORY.D := 5; | ||
| + | |||
// y is invers to z, the invers element of x follows directly from the relation x^2 = 1 | // y is invers to z, the invers element of x follows directly from the relation x^2 = 1 | ||
Use ZZ/(2)[x,y,z]; | Use ZZ/(2)[x,y,z]; | ||
| Line 31: | Line 32: | ||
// add the relation xy^{a}xy^{b}xy^{c}xy^{d} | // add the relation xy^{a}xy^{b}xy^{c}xy^{d} | ||
Append(Relations,[[x,y^(MEMORY.A),x,y^(MEMORY.B),x,y^(MEMORY.C),x,y^(MEMORY.D)],[1]]); | Append(Relations,[[x,y^(MEMORY.A),x,y^(MEMORY.B),x,y^(MEMORY.C),x,y^(MEMORY.D)],[1]]); | ||
| + | |||
Return Relations; | Return Relations; | ||
EndDefine; | EndDefine; | ||
Relations:=CreateRelationsOther13(); | Relations:=CreateRelationsOther13(); | ||
| − | + | Gb:=NC.GB(Relations,31,1,100,1000); | |
Revision as of 02:42, 24 September 2013
Description
This group has the following finite representation:
G = <x,y | x^2 = xy^{a}xy^{b}xy^{c}xy^{d} = 1>
Reference
No reference available
Computation
/*Use the ApCoCoA package ncpoly.*/
// Note that a,b,c,d >= 1
MEMORY.A := 3;
MEMORY.B := 3;
MEMORY.C := 4;
MEMORY.D := 5;
// y is invers to z, the invers element of x follows directly from the relation x^2 = 1
Use ZZ/(2)[x,y,z];
NC.SetOrdering("LLEX");
Define CreateRelationsOther13()
Relations:=[];
// add the relation of the invers elements yz = zy = 1
Append(Relations,[[y,z],[1]]);
Append(Relations,[[z,y],[1]]);
// add the relation x^2 = 1
Append(Relations,[[x,x],[1]]);
// add the relation xy^{a}xy^{b}xy^{c}xy^{d}
Append(Relations,[[x,y^(MEMORY.A),x,y^(MEMORY.B),x,y^(MEMORY.C),x,y^(MEMORY.D)],[1]]);
Return Relations;
EndDefine;
Relations:=CreateRelationsOther13();
Gb:=NC.GB(Relations,31,1,100,1000);
