Difference between revisions of "File:COMM Effects section Example.jpg"

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[http://alg.garron.us/?alg=B-_D_B_U-_B-_D-_B_U_&scheme=brogwy Applet of commutator used in this image.]
 
[http://alg.garron.us/?alg=B-_D_B_U-_B-_D-_B_U_&scheme=brogwy Applet of commutator used in this image.]
  
Referring to the image above, the sequence A changes the pieces at a set of locations we will call '''J'''. The sequence B changes the pieces at a set of locations we will call '''K'''. We will call the intersection of '''J''' and '''K''', '''N'''.  If, as in the image when '''J''' and '''K''' have an intersection , A and B do not commute and the cube, as a result, is changed by the commutator.
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Referring to the image above, the sequence A changes the pieces at a set of locations we will call '''J'''. The sequence B changes the pieces at a set of locations we will call '''K'''. We will call the intersection of '''J''' and '''K''', '''N'''.  If, as in the image, when '''J''' and '''K''' do have an intersection, A and B do not commute and the cube, as a result, is changed by the commutator. Note that the inner workings of this particular commutator are rather difficult to understand.
  
 
Pieces that are brought into the intersection by A will be called '''N'''A'. This name is appropriate because the pieces can be identified by applying the inverse of A to the locations '''N'''. Pieces that are brought into the intersection by B are called '''N'''B'.
 
Pieces that are brought into the intersection by A will be called '''N'''A'. This name is appropriate because the pieces can be identified by applying the inverse of A to the locations '''N'''. Pieces that are brought into the intersection by B are called '''N'''B'.
  
The only pieces that are affected by the commutator [A, B] = A B A' B' are located in the union of '''N''', '''N'''A' and '''N'''B'. In other words, pieces that are affected by a commutator are those who are at the intersection of both moves, or are brought into the intersection by A or B. Other pieces, even if they are temporarily mixed up after sequences A and B are performed, will be put back at their original locations with sequences A' and B'. This restoration of all the pieces that are not in the union of '''N''', '''N'''A' and '''N'''B' is the reason the commutator is such a powerful tool.
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The only pieces that are affected by any commutator are the ones located in the union of '''N''', '''N'''A' and '''N'''B'. In other words, pieces that are affected by a commutator are those who are at the intersection of both moves, or are brought into the intersection by A or B. Other pieces, even if they are temporarily mixed up after the sequences A and B are performed, will be put back into their original locations with sequences A' and B'. This restoration of all the pieces that are not in the union of '''N''', '''N'''A' and '''N'''B' is the reason the commutator is such a powerful tool.
  
 
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Revision as of 14:50, 9 April 2013

Applet of commutator used in this image.

Referring to the image above, the sequence A changes the pieces at a set of locations we will call J. The sequence B changes the pieces at a set of locations we will call K. We will call the intersection of J and K, N. If, as in the image, when J and K do have an intersection, A and B do not commute and the cube, as a result, is changed by the commutator. Note that the inner workings of this particular commutator are rather difficult to understand.

Pieces that are brought into the intersection by A will be called NA'. This name is appropriate because the pieces can be identified by applying the inverse of A to the locations N. Pieces that are brought into the intersection by B are called NB'.

The only pieces that are affected by any commutator are the ones located in the union of N, NA' and NB'. In other words, pieces that are affected by a commutator are those who are at the intersection of both moves, or are brought into the intersection by A or B. Other pieces, even if they are temporarily mixed up after the sequences A and B are performed, will be put back into their original locations with sequences A' and B'. This restoration of all the pieces that are not in the union of N, NA' and NB' is the reason the commutator is such a powerful tool.

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx This JPG image was created for the speedsolving.com wiki page Commutators (www.speedsolving.com/wiki/index.php/Commutator) . It is an example that helps understand the terms J, K, N, NA’,NB’ used to describe how the commutator works.

It is PNG version of a SVG image. (Presently (2013 04 10) the Wiki does not support SVG images) It was created using the free opensource program Inkscape. If there is an error or something needs to be changed contact Dave3457.

Colors used White: 5% Grey F2F2F2 (242,242,242) Red: BB0000 (187,0,0) L=94 Blue: 000077 (0, 0, 119) L=60 Green: 005500 (0,85,0) L=43 Orange: DD6000 (255,68,0) L=128 Yellow: FFCC00 (255,204,0) L=128 (same) Light grey: 808080 (128,128,128) L=128 Dark grey: 404040 (64,64,64) L=64

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Date/TimeThumbnailDimensionsUserComment
current14:15, 9 April 2013Thumbnail for version as of 14:15, 9 April 20132,500 × 1,575 (896 KB)Dave3457 (talk | contribs)
21:37, 8 April 2013Thumbnail for version as of 21:37, 8 April 20131,500 × 2,470 (869 KB)Dave3457 (talk | contribs)This JPG image was created for the speedsolving.com wiki page Commutators (www.speedsolving.com/wiki/index.php/Commutator) . It is an example that helps understand the terms J, K, N, NA’,NB’ used to describe how the commutator works. It is PNG ve...

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