There's quite a bit of material on permutations and permutation groups on J Wiki. I recommend you to search the site on the word "permutation"… https://code.jsoftware.com/mediawiki/index.php?search=permutation&title=Special%3ASearch&go=Go
On Wed, 16 Oct 2019 at 18:36, 'robert therriault' via Programming < [email protected]> wrote: > Hi Peter, > > I see that Raul has already answered, but here is my two cents, since I > had approached your question in a different way. > > A. 3 2 4 1 NB. Monadic A. (Anagram Index) returns the permutation for > 3 2 4 1 > 15 > 15 A. 0 1 2 3 NB. Dyadic A. (Anagram) returns the permutation applied > to 0 1 2 3 (0 origin makes things a little clearer) > 2 1 3 0 > 15 A.^:_1 [ 2 1 3 0 NB. inverse using power conjunction ^:_1 > 0 1 2 3 > 15 A.^:1 [ 0 1 2 3 NB. apply once using power conjunction ^:1 > 2 1 3 0 > 15 A.^:2 [ 0 1 2 3 NB. apply twice using power conjunction ^:2 > 3 1 0 2 > 15 A.^:3 [ 0 1 2 3 NB. apply three times using power conjunction (back > to original) ^:3 > 0 1 2 3 > C. 2 1 3 0 NB. Monadic C. (Cycle) reveals cycles of the permutation > ┌─┬─────┐ > │1│3 0 2│ > └─┴─────┘ > > Also, Roger covers some of this ground in the Idiosyncratic Introduction > to J lab as one of his lessons. > > Cheers, bob > > > On Oct 16, 2019, at 10:24 AM, Raul Miller <[email protected]> wrote: > > > > That example wouldn't be a permutation in J, because J indices start > > at 0. But let's assume you meant to subtract 1 from each of those > > values... > > > > Anyways, I think you are asking about this: > > > > https://www.jsoftware.com/help/dictionary/dccapdot.htm > > > > "If p is a permutation of the atoms of i.n, then p is said to be a > > permutation vector of order n, and if n=#b, then p{b is a permutation > > of the items of b ." > > > > So "a permutation" would a list of indices p such that (i.#p)-:/:~p > > > > And, an inverse permutation would be a list of indices ip such that > (i.#p)-:ip{p > > > > So a function which produces the inverse of a permutation is /: > > > > And, a function composing two permutations into one is { > > > > Does this help? > > > > Thanks, > > > > -- > > Raul > > > > On Wed, Oct 16, 2019 at 12:53 PM <[email protected]> wrote: > >> > >> Hello again, > >> > >> To my understanding an example of the usual representation of a > >> permutation is 3 2 4 1, meaning the permutation takes 3 to 1, 2 to 2, > >> 4 to 3 and 1 to 4. The inverse is 4 2 1 3. OK? > >> > >> In J, > >> what is a function producing the inverse of a permutation? > >> what is a function composing two permutations into one? > >> > >> Thanks, ... Peter E. > >> > >> > >> > >> > >> > >> -- > >> https://en.wikibooks.org/wiki/Medical_Machines > >> Tel: +1 604 670 0140 Bcc: peter at easthope. ca > >> > >> ---------------------------------------------------------------------- > >> 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 > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
