And what would you use if you need a noun? Normal form? Again, more of a mouthful.
Other terms I would use for identity problems, when explaining to laymen, is "ID number". They usually get it immediately. On Wed, Feb 13, 2019 at 6:55 PM Raul Miller <[email protected]> wrote: > I like “normalize” personally. > > The ideas I associate with “signature” are not robust enough for a reliable > nub (and so would require additional care elsewhere). > > If that matters... > > Thanks, > > — > Raul > > On Wednesday, February 13, 2019, Roger Hui <[email protected]> > wrote: > > > In this context, I prefer words like signature or representative rather > > than canonical form. Shorter and less scary and puts one's mind on the > > right track in multiple problems. > > > > e.g. What's a good representative for identity problems? ~. i. ] (index > > in nub). What's a good representative for ordering problems? (Seen a > > couple of weeks ago.) /:~@, i.!.0 ] (ordinals). > > > > > > > > > > > > On Wed, Feb 13, 2019 at 5:19 PM Henry Rich <[email protected]> wrote: > > > > > This is what I was looking for. It works on REB's testcase but has > less > > > than quadratic run time I think. > > > > > > NB. Get # left-shifts to canonicalize y > > > > > > canonshift =: 3 : 0 > > > > > > NB. Try each atom of y until we find one that works > > > > > > for_t. /:~ ~. y do. > > > > > > NB. get spacing between positions of t, including the wraparound > > > > > > cyclt =. 2 -~/\ tpos =. (, (#y) + {.) t I.@:= y > > > > > > NB. if there is only 1 value, use its position > > > > > > if. 1 = # cyclt do. {. tpos end. > > > > > > NB. If all spacings are the same, try the next value > > > > > > if. (}. -: }:) cyclt do. continue. end. > > > > > > NB. Canonicalize cyclt. Use its result to canonicalize y > > > > > > (canonshift cyclt) { tpos return. > > > > > > end. > > > > > > NB. No atom worked; must be abcabc...; canonize by moving smallest to > > front > > > > > > (i. <./) y > > > > > > ) > > > > > > ~: (|.~ canonshift)"1 a > > > 1 1 1 1 1 0 1 1 1 1 1 0 > > > > > > The canonical form used here does not always put the smallest atom at > the > > > front, but I think it causes vector that differ only by a rotation to > > > canonicalize identically. > > > > > > Henry Rich > > > > > > > > > > > > On 2/13/2019 7:29 PM, Roger Hui wrote: > > > > 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 > > > http://www.jsoftware.com/forums.htm > > > >>>> ------------------------------------------------------------ > > ---------- > > > >>>> For information about J forums see > > > http://www.jsoftware.com/forums.htm > > > >>> > > > >>> --- > > > >>> This email has been checked for viruses by AVG. > > > >>> https://www.avg.com > > > >>> > > > >>> ------------------------------------------------------------ > > ---------- > > > >>> 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
