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!!
Thanks
Gary.
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