I seem to have answered a similar But different question. a-:"2 (i.20)|."0 2 a 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 Linda
-----Original Message----- From: Programming <[email protected]> On Behalf Of Roger Hui Sent: Wednesday, February 13, 2019 7:29 PM To: [email protected] Subject: Re: [Jprogramming] nubsieve modulo rotation Idea k: a minimum vector necessarily begins with a minimum sub-sequence in x,(k-1){.x of length k , itself necessarily begins with the minimal item. On Wed, Feb 13, 2019 at 9:52 AM Roger Hui <[email protected]> wrote: > Yes, well, left as an exercise for the reader. :-) > > Idea: the minimum rotation of a vector necessarily begins with its > minimal item. > > On Wed, Feb 13, 2019 at 9:34 AM Henry Rich <[email protected]> wrote: > >> Yes; but now suppose the lines are very long. Is there a way to find >> the signature (I would call it a canonical form) that doesn't require >> enumerating rotations? (I haven't found a good way yet). >> >> Henry Rich >> >> On 2/13/2019 12:16 PM, Roger Hui wrote: >> > For each row, find a "signature", then find the nub sieve of the >> > signatures. The signature I use here is the minimum of all >> > possible rotations. >> > >> > signature=: {. @ (/:~) @ (i.@# |."0 1 ]) >> > >> > ~: signature"1 a >> > 1 1 1 1 1 0 1 1 1 1 1 0 >> > >> > >> > >> > >> > On Wed, Feb 13, 2019 at 8:55 AM R.E. Boss <[email protected]> wrote: >> > >> >> Let the 12 x 20 matrix be defined by >> >> a=: 0 : 0 >> >> 1 4 4 1 _4 _4 1 1 _4 _1 _1 _4 _4 _1 4 4 _1 _1 4 1 >> >> 1 4 4 1 _4 _4 1 1 _4 _1 _1 _4 _4 _1 4 1 4 _1 _1 4 >> >> 1 4 4 1 _4 _1 _4 1 1 _4 _1 _4 _4 _1 4 1 4 _1 _1 4 >> >> 4 1 1 4 _1 4 1 _4 _4 1 _4 _1 _1 _4 1 _4 _1 4 4 _1 >> >> 4 1 1 4 _1 4 1 _4 _4 1 1 _4 _1 _1 _4 _4 _1 4 4 _1 >> >> _1 4 1 1 4 4 1 _4 _4 1 1 _4 _1 _1 _4 _4 _1 4 4 _1 >> >> _1 4 4 _1 _4 _4 _1 _1 _4 1 1 _4 _4 1 4 4 1 1 4 _1 >> >> _1 4 4 _1 _4 _4 _1 _1 _4 1 1 _4 _4 1 4 _1 4 1 1 4 >> >> _1 4 4 _1 _4 1 _4 _1 _1 _4 1 _4 _4 1 4 _1 4 1 1 4 >> >> 4 _1 _1 4 1 4 _1 _4 _4 _1 _4 1 1 _4 _1 _4 1 4 4 1 >> >> 4 _1 _1 4 1 4 _1 _4 _4 _1 _1 _4 1 1 _4 _4 1 4 4 1 >> >> 1 4 _1 _1 4 4 _1 _4 _4 _1 _1 _4 1 1 _4 _4 1 4 4 1 >> >> ) >> >> >> >> Required is the nubsieve for the items modulo rotation. >> >> So two arrays are considered to be equal if one is a rotation of >> >> the >> other. >> >> >> >> The answer I found is >> >> 1 1 1 1 1 0 1 1 1 1 1 0 >> >> >> >> >> >> R.E. Boss >> >> ------------------------------------------------------------------ >> >> ---- For information about J forums see >> >> https://nam04.safelinks.protection.outlook.com/?url=http%3A%2F%2Fw >> >> ww.jsoftware.com%2Fforums.htm&data=02%7C01%7C%7C1224098d21c44d >> >> 75bc6408d6921380fc%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C63 >> >> 6857009797826451&sdata=apkgmVfZxBk1w8eRKWyXOUeZKSZ%2BmDJvsJb5W >> >> 4mQBrA%3D&reserved=0 >> > ------------------------------------------------------------------- >> > --- For information about J forums see >> > https://nam04.safelinks.protection.outlook.com/?url=http%3A%2F%2Fww >> > w.jsoftware.com%2Fforums.htm&data=02%7C01%7C%7C1224098d21c44d75 >> > bc6408d6921380fc%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C63685 >> > 7009797826451&sdata=apkgmVfZxBk1w8eRKWyXOUeZKSZ%2BmDJvsJb5W4mQB >> > rA%3D&reserved=0 >> >> >> --- >> This email has been checked for viruses by AVG. >> https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww >> .avg.com&data=02%7C01%7C%7C1224098d21c44d75bc6408d6921380fc%7C84d >> f9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C636857009797826451&sdata= >> 7n%2BdphLF5YuUD6GZpmsdXZZJrqppMxw%2FEhBurUCpnIw%3D&reserved=0 >> >> --------------------------------------------------------------------- >> - For information about J forums see >> https://nam04.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww. >> jsoftware.com%2Fforums.htm&data=02%7C01%7C%7C1224098d21c44d75bc64 >> 08d6921380fc%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C63685700979 >> 7826451&sdata=apkgmVfZxBk1w8eRKWyXOUeZKSZ%2BmDJvsJb5W4mQBrA%3D&am >> p;reserved=0 > > ---------------------------------------------------------------------- For information about J forums see https://nam04.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.jsoftware.com%2Fforums.htm&data=02%7C01%7C%7C1224098d21c44d75bc6408d6921380fc%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C636857009797826451&sdata=apkgmVfZxBk1w8eRKWyXOUeZKSZ%2BmDJvsJb5W4mQBrA%3D&reserved=0 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
