Thanks Raul. Heavy stuff indeed.
I guess I was expecting ‘match’ -: to be an exact compare including data type! > On 20 Nov 2022, at 14:58, Raul Miller <rauldmil...@gmail.com> wrote: > > digitsE=:10&#.^:_1 NB. Elijah's convert to digits > digitsR=:"."0": NB. My convert to digits > datatype digitsE 357686312646216567629137x > extended > datatype digitsR 357686312646216567629137x > floating > truncs=. [:~. [:10x&#.\. digitsR > truncs 357686312646216567629137x > 3.57686e23 5.76863e22 7.68631e21 6.86313e20 8.63126e19 6.31265e18 > 3.12646e17 1.26462e16 2.64622e15 6.46217e14 4.62166e13 6.21657e12 > 2.16568e11 1.65676e10 6.56763e9 5.67629e8 6.76291e7 7.62914e6 629137 > 29137 9137 137 37 7 > digitsR=:<.@"."0": NB. My convert to digits > truncs 357686312646216567629137x > 357686312646216567629137 57686312646216567629137 > 7686312646216567629137 686312646216567629137 86312646216567629137 > 6312646216567629137 312646216567629137 12646216567629137 > 2646216567629137 646216567629137 46216567629137 6216567629137 > 216567629137 165676291... > datatype digitsR 357686312646216567629137x > integer > > Note especially the table at > https://www.jsoftware.com/help/dictionary/dictg.htm > > J's numeric type system was designed for efficiency and the sort of > accuracy typically needed in physics and education contexts rather > than the needs of high precision number theory contexts (which wasn't > really a part of Ken Iverson's background). > > I hope this helps, > > -- > Raul > >> On Sun, Nov 20, 2022 at 4:39 AM Richard Donovan <rsdono...@hotmail.com> >> wrote: >> >> Proving that I am still baffled by J! >> >> Elijah has a different way to convert a number to its >> digits than I normally use, so I set out to compare.. >> >> digitsE=:10&#.^:_1 NB. Elijah's convert to digits >> digitsR=:"."0": NB. My convert to digits >> >> (digitsE-:digitsR) 357686312646216567629137x >> 1 NB. Well that's alright! >> >> digitsE 357686312646216567629137x >> 3 5 7 6 8 6 3 1 2 6 4 6 2 1 6 5 6 7 6 2 9 1 3 7 >> digitsR 357686312646216567629137x >> 3 5 7 6 8 6 3 1 2 6 4 6 2 1 6 5 6 7 6 2 9 1 3 7 >> NB. Still looking good! >> >> >> NB. Set up truncs with Elijah's routine.. >> truncs=. [:~. [:10&#.\. digitsE >> >> NB. Works perfectly! :o) >> truncs 357686312646216567629137x >> 357686312646216567629137 ...etc >> >> 1 p: truncs 357686312646216567629137x >> 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 >> NB. Perfect! >> >> NB. Set up truncs with my routine.. >> truncs=. [:~. [:10&#.\. digitsR >> >> NB. Should be the same??? >> >> truncs 357686312646216567629137x >> 3.57686e23 5.76863e22... WRONG!!! :o( >> >>>> On 19 Nov 2022, at 22:04, Elijah Stone <elro...@elronnd.net> wrote: >>> >>> x: ". y where y is simply a string of digits will interpret those digits >>> as a (fixed-width) integer and _then_ convert the latter to >>> extended-precision. You could append an 'x', or perhaps consider the >>> following definition: >>> >>> truncs=. [:~. [:10&#.\. 10&#.^:_1 NB.equivalent to ltrunc^:a: >>> ,.truncs 357686312646216567629137x >>> 357686312646216567629137 >>> 57686312646216567629137 >>> 7686312646216567629137 >>> 686312646216567629137 >>> 86312646216567629137 >>> 6312646216567629137 >>> 312646216567629137 >>> 12646216567629137 >>> 2646216567629137 >>> 646216567629137 >>> 46216567629137 >>> 6216567629137 >>> 216567629137 >>> 16567629137 >>> 6567629137 >>> 567629137 >>> 67629137 >>> 7629137 >>> 629137 >>> 29137 >>> 9137 >>> 137 >>> 37 >>> 7 >>> >>>> On Sat, 19 Nov 2022, Richard Donovan wrote: >>>> >>>> Hi >>>> >>>> I am doing experiments with large primes, in particular looking at primes >>>> that remain primes when n digits are truncated from the left. For example >>>> 6391373 391373 91373 1373 373 73 3 remains prime at each >>>> step. >>>> >>>> The largest of these in base 10 is 357686312646216567629137. >>>> >>>> I wrote the following code in preparation for further investigation but I >>>> find that the 24 digit number above is not handled as I wish it to be, as >>>> you will see below. >>>> >>>> What have I missed? >>>> >>>> Thanks >>>> >>>> >>>> >>>> >>>> digits >>>> "."0@": >>>> >>>> ltrunc >>>> 3 : 0"0 0 0 >>>> n=: ": 0, }. digits y >>>> x: ". n-. ' ' >>>> ) >>>> >>>> >>>> >>>> NB. Works fine with 7 digit number... >>>> ltrunc^:a: 6391373 >>>> 6391373 391373 91373 1373 373 73 3 0 >>>> >>>> >>>> NB. But I can’t get it working for a 24 digit number! >>>> ltrunc 357686312646216567629137 >>>> 0 0 5 7 6 8 6 0 2 3 >>>> ltrunc 357686312646216567629137x >>>> 57686312646216568012800 >>>> ltrunc x:357686312646216567629137x >>>> 57686312646216568012800 >>>> >>>> Is there a way around the limit? >>>> >>>> ---------------------------------------------------------------------- >>>> 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
