On 2013-04-03, garymako...@googlemail.com <garymako...@googlemail.com> wrote:
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>
> Thanks Dima
>
> I have put the patch in using instructions
> at: http://ask.sagemath.org/question/1276/how-to-install-patches-or-should-we
> via the notebook() interface;
> only I am using SAGE 5.7 on a VM on an HP (usually I use Macs but I am not
> at home for a while) and so I do not know how to rebuild sage (ie sage -b
> or whatever) in this context, since the VM wraps everything ... sorry for
> such a dumb question!
Do you have "full" access to the VM, besides using its Sage server?
I.e. is it your private VM you installed yourself?
Then you can ssh to it (not sure what account/password to use though ---
but it's mentioned somewhere, in posts to this forum, IIRC)
and run sage -b at the shell prompt.
>
> Once I have that installed I will attempt to do what I'm doing using that
> patch and report back ....
>
> Thanks and regards
>
> Gary
>
>
> On Wednesday, April 3, 2013 4:20:17 AM UTC+1, Dima Pasechnik wrote:
>>
>> On 2013-04-02, garym...@googlemail.com <javascript:> <
>> garym...@googlemail.com <javascript:>> wrote:
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>> >
>> > Hi
>> >
>> > Let F be a (finite) field. I have a bunch B of sets S,T,... each
>> consisting
>> > of d N-tuples of elements of F.
>> >
>> > I would like to reduce the number of sets I have according to the
>> following
>> > rule. If there exists a permutation sigma in Sym_N (:= symmetric group
>> on N
>> > letters), such that if I permute the entries of every constituent
>> N-tuple v
>> > of set S by this *same *permutation sigma, I obtain the set T, then S~T
>> > (and so I may discard one of S or T). Note that S,T etc are sets and not
>> > d-tuples themselves - ie I am not interested in the ordering of the
>> > N-tuples inside S or T etc.
>> >
>> > That is, if S={v_1,v_2,...,v_d} and if for some sigma in Sym_N:
>> > T={v_1^(sigma),v_2^(sigma),...,v_d^(sigma)},
>> > where v^(sigma) denotes permuting the entries v[i] of v according to
>> > v^(sigma)[i] = v[sigma^(-1)(i)], then T is redundant and I may discard
>> it
>> > from B.
>> >
>> > Moreover I do NOT care which permutations sigma are needed - ie I would
>> > just like to output a minimal set of representatives of the equivalence
>> > classes under ~.
>> >
>> > I have seen the docs on the implementation of something similar for
>> tuples
>> > of integers, and obviously I could probably hack together a very
>> laborious
>> > identification of finite field elements with integers etc etc, ... but I
>> > was hoping someone might have a cleverer way please!!
>>
>> I suppose this should work in your setting
>>
>> http://trac.sagemath.org/sage_trac/attachment/ticket/14291/trac_14291-v2.patch
>>
>> (the patch from http://trac.sagemath.org/sage_trac/ticket/14291)
>> At least if the orbits are not too long, you can compute the orbits for
>> each element of your set, and then take a tranversal of these orbits.
>> With that patch installed:
>>
>> sage: S4 = PermutationGroup([ [('c','d')], [('a','c')], [('a','b')] ])
>> sage: S4.orbit((('a','c'),('b','d')),"OnSetsSets") # this is how to get an
>> orbit
>> [[['a', 'c'], ['b', 'd']], [['a', 'd'], ['b', 'c']], [['a', 'b'], ['c',
>> 'd']]]
>>
>>
>
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