I dug up an old extended gcd to build an adverb for modular divide NB. Find the gcd of two numbers
NB. and coef giving gcd as a linear combination of y gcd2x=: 3 : 0 'r0 r1'=.y 's0 s1'=.1 0x 't0 t1'=.0 1x while. r1 ~: 0 do. q=. r0 <.@% r1 'r0 r1'=. r1,r0-q*r1 's0 s1'=. s1,s0-q*s1 't0 t1'=. t1,t0-q*t1 end. r0,s0,t0 ) gcd2x 51 119 17 _2 1 _2 1 +/ . * 51 119 17 NB. adverb giving divide (inverse) mod m mi=:1 : 0"0 'r0 s0 t0'=:gcd2x m,y if. r0=1 do. m|t0 else. 1r0 end. : m|x*m mi y ) 17 mi 6 3 NB. Mike Day's Table 2 3 4 (17 mi)table >:i.8 +-+---------------------+ | |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| +-+---------------------+ I have some questions regarding system solving modulo m that I will offer in a new thread in a few days. Best, Cliff On Thu, Mar 30, 2023 at 12:11 PM Clifford Reiter <reit...@lafayette.edu> wrote: > 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
