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...)
 
 
(3 intermediate revisions by 2 users not shown)
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=== <div id="Other4_groups">[[:ApCoCoA:Symbolic data#Other_groups|Other groups]]</div> ===
+
=== <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,a],[1]]);
+
     Append(Relations,[[a^2],[1]]);
     Append(Relations,[[b,b,b],[1]]);
+
     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,b,a,b,a,b,a,b,b,a,b,a,b,a,b,b],[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;
+
 
 +
  Return Relations;
 
   EndDefine;
 
   EndDefine;
 
    
 
    
 
   Relations:=CreateRelationsOther4();
 
   Relations:=CreateRelationsOther4();
   GB:=NC.GB(Relations);
+
   Gb:=NC.GB(Relations);
   Size(GB);
+
   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>