Given a list (say, of numbers) L, the method L.sort() will put its elements in order. The function sorted(L) returns a new list with the elements of L in order. I would like a version of sorted that will not return the elements of L in sorted order, but rather, the permutation that puts them in sorted order. Does this exist in Sage? Thanks.
IIUC, the numpy library has a routine to do this already:
sage: L = [2,3,1,6,8,-3,9]
sage: numpy.argsort(L)+1
array([6, 3, 1, 2, 4, 5, 7])
Alternatively, you can use a Schwartzian transform (a.k.a. the "decorate-sort-undecorate" idiom). Starting from our list, we can enumerate it, counting from 1 (the "decorate" part)
sage: list(enumerate(L, 1))
[(1, 2), (2, 3), (3, 1), (4, 6), (5, 8), (6, -3), (7, 9)]
Sort these by the second term, the value:
sage: sorted(enumerate(L, 1), key=lambda x: x[1])
[(6, -3), (3, 1), (1, 2), (2, 3), (4, 6), (5, 8), (7, 9)]
Extract the sorted indices:
sage: ii = [pair[0] for pair in sorted(enumerate(L, 1), key=lambda x: x[1])]
sage: ii
[6, 3, 1, 2, 4, 5, 7]
Finally, we can make this into a proper Permutation:
sage: Permutation(ii)
[6, 3, 1, 2, 4, 5, 7]
sage: Permutation(ii).to_cycles()
[(1, 6, 5, 4, 2, 3), (7,)]
and confirm it by applying it to our list:
sage: P = Permutation(ii)
sage: P.action(L)
[-3, 1, 2, 3, 6, 8, 9]
Hello,
It is possible to do
sage: L = [2,3,1,6,8,-3,9]
sage: Word(L).standard_permutation()
[3, 4, 2, 5, 6, 1, 7]
which is the inverse as the one given is the other answers... but then
sage: Word(L).standard_permutation().inverse()
[6, 3, 1, 2, 4, 5, 7]
A slightly more compact version of DSM's answer:
sage: L = [2,3,1,6,8,-3,9]
sage: L2 = sorted(L)
sage: P = Permutation([list(L).index(x)+1 for x in L2])
Testing the answer:
sage: P
[6, 3, 1, 2, 4, 5, 7]
sage: P.action(L)
[-3, 1, 2, 3, 6, 8, 9]
I wouldn't be surprised if this were slower to execute.
Asked: 2013-03-27 19:44:08 +0200
Seen: 3,212 times
Last updated: Mar 28 '13
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