Hmm, that means you can transform an operation involving the monads /: \: |. on permutations into an isomorphic operation using the monads j. + - on complex vectors.
The relationship to complex numbers was not mentioned in the introductory abstract algebra course that I took many years ago. Perhaps it is "obvious". ----- Original Message ----- From: John Randall <[EMAIL PROTECTED]> Date: Wednesday, July 12, 2006 6:21 am Subject: Re: [Jprogramming] Musings on permutation vectors > R&S HUI wrote: > > Another treatment of /: and \: can be found in the > > following J Wiki page: > > > > http://www.jsoftware.com/jwiki/Essays/Symmetries_of_the_Square > > Here is another approach to symmetries of the square that relates > elementary identities of the complex plane to permutations. > > p=:1j0 0j1 _1j0 0j_1 > P=:1 : 'p i. u p' > j. P > 1 2 3 0 > + P > 0 3 2 1 > ] P > 0 1 2 3 > > j. and + are generators for an action of the dihedral group on the > complex plane. The adverb P gives a direct permutation representation > of the transformation of the orbit p. Then we have for example > > (- P)-:(j.^:2 P) > 1 > (j.^:[EMAIL PROTECTED] P)-:([EMAIL PROTECTED] P) > 1 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
