Completely on point, as usual. Thank you for the excellent resources. Roger Hui <[email protected]> wrote:
> 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
