Difference between revisions of "Conjugate"

From Speedsolving.com Wiki
m (→‎Effect: grammar)
m (→‎Effect: link word)
Line 13: Line 13:
 
In A B A', the sequence A is the setup move or sequence and A' puts the cube in its original state. In between, there is an embedded sequence B. Alone, this sequence would affect some set of locations on the cube L. Because of the conjugation, the affected pieces will be A' L, which means that the locations will be transformed by the inverse of A.
 
In A B A', the sequence A is the setup move or sequence and A' puts the cube in its original state. In between, there is an embedded sequence B. Alone, this sequence would affect some set of locations on the cube L. Because of the conjugation, the affected pieces will be A' L, which means that the locations will be transformed by the inverse of A.
  
So the sequence B will be applied on a cube which space has been modified by A. The sequence B is supposed to change some pieces in the locations L, A consists in bringing the piece you want to change to the location L. Once you've done the sequence B, you bring those pieces back with A'.
+
Indeed the sequence B will be applied on a cube which space has been modified by A. The sequence B is supposed to change some pieces in the locations L and A consists in bringing the piece you want to change to the location L. Once you've done the sequence B, you bring those pieces back with A'.
  
 
=== Special case ===
 
=== Special case ===

Revision as of 07:55, 25 October 2012

A conjugate is a sequence of moves that consists in doing a sequence A, then a sequence B, and finally the inverse of the sequence A. In other words, a conjugate is an algorithm like A B A', where A and B can be any sequence of moves. In intuitive terms, it means: do something to set up another task which does something useful, and undo the setup.

Mathematical definition

Given a group, a conjguate is an element of the form ghg', where g and h are elements of the group with inverses g' and h'.

Cube notation is very close : A B A'

It is sometimes written as [A: B] = A B A'

Effect

In A B A', the sequence A is the setup move or sequence and A' puts the cube in its original state. In between, there is an embedded sequence B. Alone, this sequence would affect some set of locations on the cube L. Because of the conjugation, the affected pieces will be A' L, which means that the locations will be transformed by the inverse of A.

Indeed the sequence B will be applied on a cube which space has been modified by A. The sequence B is supposed to change some pieces in the locations L and A consists in bringing the piece you want to change to the location L. Once you've done the sequence B, you bring those pieces back with A'.

Special case

If the set of locations L is not modified by A, then the conjugation does not change anything, and A B A' = B.

See also