Skip, Here is a little simpler version of fps1. I looked at forks in LJ and what I am looking for is a dyadic fork. This doesn’t seem to have one either. fps2=: 13 :'y#~0=(+/"1) 2|_ q:y' (fps 2+i.1000)-:fps2 2+i.1000 1 fps2 ┌─ ] ├─ ~ ─── # │ ──┤ ┌─ 0 │ ├─ = │ │ ┌─ [: └─────┤ │ ┌─ / ─── + │ ├─ " ─┴─ 1 └───┤ │ ┌─ 2 │ ├─ | └─────┤ ┌─ _ └─────┼─ q: └─ ] Linda -----Original Message----- From: Programming <programming-bounces at forums.jsoftware.com> On Behalf Of Linda Alvord Sent: Saturday, November 3, 2018 10:03 PM To: programming at jsoftware.com Subject: Re: [Jprogramming] Square Roots and Extended Arithmetic Skip, I can't find the fork in fps1 (fps 2+i.1000)-:fps1 2+i.1000 1 fps1 ┌─ ] ├─ ~ ─── # │ ──┤ ┌─ 0 │ ├─ = │ │ ┌─ [: └─────┤ │ ┌─ / ─── + │ ├─ " ─┴─ 1 └───┤ │ ┌─ [: │ ├─ ] └─────┤ ┌─ 2 │ ├─ | └─────┤ ┌─ _ └───┼─ q: └─ ] fps ┌─ ] ├─ ~ ─── # │ ──┤ ┌─ [: │ │ ┌─ = └─────┼────┴─ >. └─ %: Linda -----Original Message----- From:S Programming <programming-bounces at forums.jsoftware.com> On Behalf Of Skip Cave Sent: Saturday, November 3, 2018 10:43 AM To: Programming at jsoftware.com Subject: Re: [Jprogramming] Square Roots and Extended Arithmetic Also, there's a completely different way to attack the problem of finding perfect squares using the dyadic form of q: (Prime Exponents). I discovered this while reading NuVoc about q: fps1 =: 13 :'y#~0=+/"1]2|_ q:y' fps1 2+i.100 4 9 16 25 36 49 64 81 100 fps1 8200+i.1000 8281 8464 8649 8836 9025 %: 8281 8464 8649 8836 9025 91 92 93 94 95 fps1 ] #~ 0 = [: +/"1 [: ] 2 | _ q: ] The secret is: if all exponents of the prime factors of an integer are even, the number is a perfect square. Skip Skip Cave Cave Consulting LLC ---------------------------------------------------------------------- For information about J forums see https://nam02.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.jsoftware.com%2Fforums.htm&data=02%7C01%7C%7C6e9f540deff6465f962f08d641f9af42%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C636768937966605630&sdata=0byKD4NRbwlIJ40aleddiF2ggzI2PsNZwGU9vmmIQ58%3D&reserved=0 ---------------------------------------------------------------------- For information about J forums see https://nam02.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.jsoftware.com%2Fforums.htm&data=02%7C01%7C%7C6e9f540deff6465f962f08d641f9af42%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C636768937966605630&sdata=0byKD4NRbwlIJ40aleddiF2ggzI2PsNZwGU9vmmIQ58%3D&reserved=0