Hi Gary,

On 2013-03-04, GaryMak <garymako...@googlemail.com> wrote:
>> sage: Permutations(50).random_element()
>> [11, 4, 30, 48, 49, 36, 22, 16, 27, 6, 44, 33, 13, 50, 9, 35, 15, 12, 
>> 26, 45, 1, 18, 2, 40, 19, 10, 28, 7, 37, 46, 25, 29, 34, 41, 38, 24, 8, 
>> 20, 32, 21, 14, 23, 31, 47, 43, 17, 3, 39, 5, 42]
>
> I have a set of size (say) 50 and I would like to generate a randomly-ordered 
> list of its elements. The trouble is, if I
> use Permutations(my_set).random_element() it seems to want to generate the 
> whole lot of them before picking out a random
> one!! Sorry but I cannot find how else to invoke this functionality, but I 
> know there must be a better way ....

Permutations(50).random_element() is quite fast, and I think it does
*not* try to enumerate Sym(50).

I'd do:
  sage: L = some list
  sage: p = Permutations(len(L)).random_element()
  sage: L_rand = [L[p[i]-1] for i in range(len(L))]

Note that it is p[i]-1, because addressing list elements in Python is
zero-based, but Permutations(50) permutes the numbers from 1 to 50, not
from 0 to 49.

Best regards,
Simon

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