Mark Dickinson <dicki...@gmail.com> added the comment: Results from Magma, Sage and Gap:
Magma provides functions "Subsets(S, k)" and "Permutations(S, k)". From the documentation: Subsets(S, k) : The set of subsets of the set S of size k. If k is larger than the cardinality of S then the result will be empty. Permutations(S, k) : The set of permutations (stored as sequences) of each of the subsets of the set S of cardinality k. GAP has the same behaviour: even if you've never encountered GAP before, it's fairly Pythonesque, so the following extract from a GAP 4 REPL means exactly what you think it does: gap> Combinations([1,2,3,4], 3); [ [ 1, 2, 3 ], [ 1, 2, 4 ], [ 1, 3, 4 ], [ 2, 3, 4 ] ] gap> Combinations([1,2,3,4], 5); [ ] Permutations work the same way (but the function is called Arrangements): gap> Arrangements([1,2,3,4], 3); [ [ 1, 2, 3 ], [ 1, 2, 4 ], [ 1, 3, 2 ], [ 1, 3, 4 ], [ 1, 4, 2 ], [ 1, 4, 3 ], [ 2, 1, 3 ], [ 2, 1, 4 ], [ 2, 3, 1 ], [ 2, 3, 4 ], [ 2, 4, 1 ], [ 2, 4, 3 ], [ 3, 1, 2 ], [ 3, 1, 4 ], [ 3, 2, 1 ], [ 3, 2, 4 ], [ 3, 4, 1 ], [ 3, 4, 2 ], [ 4, 1, 2 ], [ 4, 1, 3 ], [ 4, 2, 1 ], [ 4, 2, 3 ], [ 4, 3, 1 ], [ 4, 3, 2 ] ] gap> Arrangements([1,2,3,4], 5); [ ] Combinations([1,2,3,4], -1) gives an error. Interestingly, Arrangements([1,2,3,4], -1) returns the empty list. GAP also has a NrCombinations function returning the number of combinations: gap> NrCombinations([1,2,3,4], 5); 0 gap> NrCombinations([1,2,3,4], -1); 0 My Sage installation currently seems to be broken, but from the documentation it looks as though it just steals the functions from GAP. _______________________________________ Python tracker <rep...@bugs.python.org> <http://bugs.python.org/issue4816> _______________________________________ _______________________________________________ Python-bugs-list mailing list Unsubscribe: http://mail.python.org/mailman/options/python-bugs-list/archive%40mail-archive.com
