http://code.jsoftware.com/wiki/Essays/Symmetries_of_the_Square . Proofs of lots of identities re /: \: |. ] on permutations and |: \: |. ] on matrices.
http://code.jsoftware.com/wiki/Essays/Symmetric_Array A proof characterizing symmetric arrays. Permutations involved. http://code.jsoftware.com/wiki/Essays/Ackermann%27s_Function A proof on the Ackermann function. http://www.dyalog.com/blog/2015/01/cholesky-decomposition/ (APL) a proof re the Cholesky decomposition. http://code.jsoftware.com/wiki/Essays/Cholesky_Decomposition No proof provided, but can be easily translated from APL. See also the pages in the "See also" section. http://code.jsoftware.com/wiki/Essays/88_Hats An amusing mathematical puzzle. Generalized using group theory. http://code.jsoftware.com/wiki/Essays/Pascal%27s_Ladder An identity related to Pascal's triangle. http://code.jsoftware.com/wiki/Essays/N_Queens_Problem Classical puzzle. http://code.jsoftware.com/wiki/Essays/Queens_and_Knights Harder version of the n-queens problem. See also the pages in the "See also" section. etc. On Thu, Dec 12, 2019 at 6:37 PM ethiejiesa via Programming < [email protected]> wrote: > Hello J, > > Using J primitives, what are some nice algebraic identities you know of? > > I recently acquired a copy of "At Play with J" and in the process of > mulling > over chapter 7's permutation representations, I stumbled upon this nice > one, > which I assume is already well known: > > /: -: /:@/:@/: > > which essentially embodies the fact that /: maps a permutation to its > inverse, > so if y is a permutation of integers, then > > y -: /: /: y > > The extra layer of /: comes from the fact that /: is capable of mapping > arbitrary lists to permutations. > > Anyway, this got me excited about the idea of manipulating J expressions > algebraically. I would love to hear about any pearls you may know about. > > Cheers! > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
