A possible version of the signature verb:
sig=: |.~ >:@(# -~ {: i. 1:)@min
min=: (_1 |. ] #^:_1 (= <./)@#~)^:(1 < +/@])^:a: 1"0
Perhaps not the fastest version, but it’s light on memory.
Cheers,
Louis
> On 13 Feb 2019, at 18:52, 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
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>>
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