I think I recall a conversation, some decades ago, with Roger about whether specifying a modulus for system solving makes sense for J. I thought maybe that was a use for the fit conjunction but now think that would be a poor choice for such a numeric function. I have vague memories of J essays on guass-jordan row reduction and extended gcds but didn't find them poking around J help. They could be useful for what I had in mind and modular inverses would be part of that. Perhaps someone has those handy and could offer an addon? New adverbs giving b m %.: a and m %.: a anyone? Best, Cliff
On Wed, Mar 29, 2023 at 5:02 PM 'Michael Day' via Programming < programm...@jsoftware.com> wrote: > While this primitve works nicely in an example: > > (2 3 4) (17&|@*)/ table >:i.8 > +-------+---------------------+ > |17&|@*/|1 2 3 4 5 6 7 8| > +-------+---------------------+ > |2 |2 4 6 8 10 12 14 16| > |3 |3 6 9 12 15 1 4 7| > |4 |4 8 12 16 3 7 11 15| > +-------+---------------------+ > > I find this less satisfying: > (2 3 4) (17&|@%)/ table >:i.8 > +-------+-----------------------------------------------+ > |17&|@%/|1 2 3 4 5 6 7 8| > +-------+-----------------------------------------------+ > |2 |2 1 0.666667 0.5 0.4 0.333333 0.285714 0.25| > |3 |3 1.5 1 0.75 0.6 0.5 0.428571 0.375| > |4 |4 2 1.33333 1 0.8 0.666667 0.571429 0.5| > +-------+-----------------------------------------------+ > > I have a function which does what one would expect. I'll rename it as > m17div here, details unimportant for this discussion: > (2 3 4) m17div/ table >:i.8 > +-------+---------------------+ > |m17div/|1 2 3 4 5 6 7 8| > +-------+---------------------+ > |2 |2 1 12 9 14 6 10 13| > |3 |3 10 1 5 4 9 15 11| > |4 |4 2 7 1 11 12 3 9| > +-------+---------------------+ > ( eg 3 % 2 == 10 mod 17 because 3 = 17 | 2 * 10 ) > > Would anyone else find this return of integer results useful or is it > better > to force a floating output? > > (Henry tells me that m&|@^ returns integer results, working ok when m^2 > can be represented as a non-extended integer.) > > Thanks, > > Mike > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
