Difference between revisions of "ApCoCoA-1:GroupsToCheck"

From ApCoCoAWiki
Line 4: Line 4:
 
Braid Group
 
Braid Group
 
   Checked: No
 
   Checked: No
   Notes:
+
   Notes: --
  --
 
 
Cyclic Group
 
Cyclic Group
 
   Checked: No
 
   Checked: No
   Notes:
+
   Notes: --
  --
 
 
Dicyclic Group
 
Dicyclic Group
 
   Checked: No
 
   Checked: No
   Notes:
+
   Notes: I added two different implementations, one with explicit invers elements and one without. I think the
   --
+
   second one is the right one. The computation of the first implementation results in a GB with size 2812, the
 +
  second one with size 901.
 +
Dihedral Group
 +
  Checked: No
 +
  Notes: It follows, that a^{-1} = a^{2n-1} and that b^{4} = 1 (second equation) --> b^{-1} = b^{3}
 +
  My question is, do I have to implement the last equation with b^{3} instead of b^{-1} or should
 +
  I use 4 generators (a invers to c, b invers to d)?

Revision as of 10:04, 13 August 2013

Inserted Groups

Braid Group

 Checked: No
 Notes:  --

Cyclic Group

 Checked: No
 Notes:  --

Dicyclic Group

 Checked: No
 Notes:  I added two different implementations, one with explicit invers elements and one without. I think the
 second one is the right one. The computation of the first implementation results in a GB with size 2812, the
 second one with size 901.

Dihedral Group

 Checked: No
 Notes: It follows, that a^{-1} = a^{2n-1} and that b^{4} = 1 (second equation) --> b^{-1} = b^{3}
 My question is, do I have to implement the last equation with b^{3} instead of b^{-1} or should
 I use 4 generators (a invers to c, b invers to d)?