Changes
http://wiki.axiom-developer.org/296PERMGRPShouldComputeCycleindicatorPolynomial/diff
--
It would be nice if 'PERMGRP' could generate the cycle indicator polynomial for
a given permutation group.
Furthermore, it should be able to list all the elements of a given permutation
group as a stream.
Finally, it should be able to reduce the set of given generators to a minimal
set.
For the first two items I have a brute force solution, there might be better
ones, of course.
I guess that all of this will be merged into the combinat package.
Martin
PS: here is the code, for those who want to play with it::
-- generate all permutations given the generators
-- multiply each of the elements in result by each of the generators
listaux(gens: List PERM INT, result: List PERM INT): List PERM INT ==
removeDuplicates(append(result, reduce(append, [[p*q for q in result] for p
in gens])))
list(gens: List PERM INT): List PERM INT ==
result := [1$PERM INT]
lold := 0
lnew := 1
while lnew > lold repeat
result := listaux(gens, result)
lold := lnew
lnew := #(result)$List PERM INT
result
-- collect cyclePartitions into the cycle indicator polynomial
cyclePoly(lp: List Partition, vars: List POLY INT): POLY INT ==
n := #vars
p := lp.1
c := 1
result := 0
for q in rest lp repeat
if q = p then
c := c+1
else
fix := n-reduce(+, p::List INT, 0)
result := result + c * reduce((a,b) +-> a*b, _
[vars.i for i in p::List INT], _
(vars.1)**fix)
p := q
c := 1
fix := n-reduce(+, p::List INT)
result := result + c * reduce((a,b) +-> a*b, _
[vars.i for i in p::List INT], _
(vars.1)**fix)
--
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