Hi Community,
I excuse this simple questions, if here is not the place to ask them,
please tell me. I am trying some applications of groups for sound
organization, I studied some theory, for implementation i intend using
sage, on which i installed external python libraries with perfect
success! Thanks, guys, sage is surprisingly nice!
Anyway, I am not used to computational algebra, and here goes some
simple questions:
1) I have a set X on which i am trying to implement permutations. I
know that if G is Group : G.degree() gives me the number of elements
in which G acts. How can I call all groups with degree equal to the
number of elements on X? I mean to get a set of groups whose:
XG = {G is Group : G.degree() == len(X)} or even:
XG = {G is Group : G.degree() <= len(X)}
It would be nice to have classifications for all groups in XG or
choose to only select permutation groups. Including which ones are
subgroups of which.
2) Say X = numpy.array([3.5, 8.5, 9.0]) and S=SymmetricGroup(3)
And I want to apply permutations, elements of S in X.
For one element:
I have to give X's index permuted and write it somewhere:
sage: perm = numpy.zeros([len(X)])
sage: list(S)[3]
(1,2,3)
sage: for i in X:
....: perm[list(S)[3](X.index(i) +1) -1]=i
sage: perm
array([9.00000000000000, 3.50000000000000, 8.50000000000000], dtype=object)
for all elements in S:
sage: perms = zeros(( len(list(S)), len(X) ))
sage: perms
array([[ 0., 0., 0.],
[ 0., 0., 0.],
[ 0., 0., 0.],
[ 0., 0., 0.],
[ 0., 0., 0.],
[ 0., 0., 0.]])
sage: for j in list(S):
....: for i in X:
....: perms[ list(S).index(j) ][ j( X.index(i) +1) -1] = i
sage: perms
array([[ 3.5, 8.5, 9. ],
[ 3.5, 9. , 8.5],
[ 8.5, 3.5, 9. ],
[ 9. , 3.5, 8.5],
[ 8.5, 9. , 3.5],
[ 9. , 8.5, 3.5]])
Exactly what is the order in which elements are listed in list(G)?
To list(G) for G with big order takes a long time. Is there a way to
use elements in list(G) which is faster?
thanks in advance,
gk
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