https://www.speedsolving.com/wiki/api.php?action=feedcontributions&feedformat=atom&user=Tasguitar7 2026-10-30T14:19:23Z User contributions MediaWiki 1.43.8 https://www.speedsolving.com/wiki/index.php?title=Commutators_and_Conjugates&diff=16502 2011-11-25T16:58:46Z

<p>Tasguitar7: /* External Links */</p> <hr /> <div>== Introduction ==<br /> A Commutator is an algorithm of the form A B A' B', and a conjugate is an algorithm of the form A B A', where A and B denote arbitrary algorithms on a puzzle, and A', B' denote their respective inverses. They are formal versions of the simple, intuitive idea of &quot;do something to set up another task which does something useful, and undo the setup.&quot; Commutators can be used to generate algorithms that only modify specifics portion of a cube, and are intuitive derivable. Many puzzle solutions are heavily or fully based on commutators.<br /> <br /> == Commutator and Conjugate Notation ==<br /> <br /> [A, B] is a commonly used notation to represent the sequence A B A' B'.<br /> [A: B] is a well-accepted representation of the conjugate A B A'.<br /> <br /> Since commutators and conjugates are often nested together, Lucas Garron has proposed the following system for compact notation: Brackets denote an entire algorithm, and within these, the comma delimits a commutator, and a colon or a semicolon a conjugate. The symbols are given order of precedence: colon, comma, semicolon. For example, [A; B, C: D] represents A ( B (C D C') B' (C D' C')) A'.<br /> <br /> == See Also ==<br /> * [[Niklas]]<br /> * [[Fewest Moves Techniques]]<br /> * [[BH]]<br /> <br /> == External Links ==<br /> * [http://www.ryanheise.com/cube/commutators.html RyanHeise.com] has a page on commutators. Also notice all kinds of other useful sections on his website on the left. He has a lot of group theory related content, and other things that will really help you understand how algorithms work, and how you can create your own.<br /> * [http://www.youtube.com/watch?v=54SGrZbLcoE Commutators and Conjugates - The Ultimate Instructional Video] - The title says it all, pay attention, take your time and make sure you have set some time aside before clicking play.<br /> * Youtube: [http://ca.youtube.com/watch?v=7yZoDi_B1lI YouTube tutorial] by badmephisto on Commutators and their uses<br /> * Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?t=169 Post from Speedsolving] on Commutators<br /> <br /> <br /> [[Category:Puzzle Theory]]</div>

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