Domain error.
Henry Rich
On Tue, Apr 4, 2023, 6:56 PM 'Mike Day' via Programming <
programm...@jsoftware.com> wrote:
> Lovely. Hopefully including negative powers! How will you deal with
> ill-defined results,
> though?
>
> Thanks,
>
> Mike
>
> Sent from my iPad
>
> > On 4 Apr 2023, at 19:07, Henry Rich <henryhr...@gmail.com> wrote:
> >
> > Expect primitive support for modular inverse in an upcoming beta.
> >
> > Henry Rich
> >
> >
> >> On Tue, Apr 4, 2023, 1:49 PM 'Michael Day' via Programming <
> >> programm...@jsoftware.com> wrote:
> >>
> >> Thanks, Chris, and Cliff too.
> >>
> >> Yes, a mod inverse helps a lot. Once you've got an inverse, it's easy
> >> to derive a modular divide, or vice
> >> versa.
> >>
> >> inversep in primutil.ijs is well defined for a prime modulus - the name
> >> "primutil" does of course imply
> >> a prime modulus.
> >> inversep also appears to work ok for those numbers in the ring of
> >> integers modulo non-prime modulus.
> >>
> >> eg members of the ring modulo 10 are {1 3 7 9}
> >> {{ y,:y (10 mtimes) (10&inversep)"0 y}} 1 3 7 9
> >> 1 3 7 9
> >> 1 1 1 1
> >> {{ y,:y (10 mtimes) (10&mrecip)"0 y}} 1 3 7 9
> >> 1 3 7 9
> >> 1 1 1 1
> >>
> >> I find rather better performance with my mrecip:
> >> ts =: 6!:2 , 7!:2@]
> >>
> >> 1 p: 1000000009
> >> 1
> >>
> >> ts'100000009 mrecip 999999000 + >:i.1007'
> >> 0.0061255 22592
> >> ts'100000009 inversep"0] 999999000 + >:i.1007'
> >> 0.0798054 97160
> >> ts'100000009 mi"0] 999999000 + >:i.1007'
> >> 0.0908823 174192
> >>
> >> A bit surprising as the Extended Euler Algorithm is supposed to be best
> >> for getting a modular inverse.
> >>
> >> 1000000009 (mrecip-:inversep"0) 999999000 + >:i.1007
> >> 1
> >> 1000000009 ((1000000009 mi)"0 @] -:inversep"0) 999999000 + >:i.1007
> >> 1
> >>
> >> Here's mrecip:
> >>
> >> mrecip =: {{
> >> y (x&|@^) <: 5 p: x
> >> }}"0
> >>
> >> As for inversep, and Cliff's mi, mrecip is well-defined for prime x,
> >> and also for composite
> >> x for y in x's ring, ie where 1 = x +. y
> >>
> >> Results are NOT reliable for arguments not coprime with the modulus.
> >>
> >> Thanks,
> >>
> >> Mike
> >>
> >>> On 03/04/2023 16:22, chris burke wrote:
> >>> Cliff
> >>>
> >>> There are some mod functions in the math/misc addon, e.g. this gives
> >>> Mike Day's table
> >>>
> >>> load 'math/misc/primutil'
> >>> f=: (17 timesmod) (17&inversep)
> >>> 2 3 4 f"0 table >:i.8
> >>> +---+---------------------+
> >>> |f"0|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|
> >>> +---+---------------------+
> >>>
> >>> Any improvements welcome, thanks.
> >>>
> >>> Chris
> >>>
> >>> On Mon, Apr 3, 2023 at 5:49 AM Clifford Reiter<reit...@lafayette.edu>
> >> wrote:
> >>>> 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
> >>>>>>
> >>>>>>
> ----------------------------------------------------------------------
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> www.jsoftware.com/forums.htm
> >>>>>>
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> >>
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> >>
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