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!
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:
> > ------=_Part_3109_14045404.1364925152232
> > Content-Type: text/plain; charset=ISO-8859-1
> >
> > 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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