Permutations: Difference between revisions

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=={{header|GAP}}==

GAP can handle permutations and groups. Here is a straightforward implementation : for each permutation p in S(n) (symmetric group),

compute the images of 1...n by p. As an alternative, List(SymmetricGroup(n)) would yield the permutations as GAP ''Permutation'' objects,

compute the images of 1 .. n by p. As an alternative, List(SymmetricGroup(n)) would yield the permutations as GAP ''Permutation'' objects,

which would probably be more manageable in later computations.

<lang gap>gap>~~perms := n ->~~ List(SymmetricGroup(n), p -> ~~List~~([1..n], ~~x -> x^~~p));

<lang gap>gap>List(SymmetricGroup(4), p -> Permuted([1 .. 4], p));

perms(4);

[ [ 1, 2, 3, 4 ], [ 4, 2, 3, 1 ], [ 2, 4, 3, 1 ], [ 3, 2, 4, 1 ], [ 1, 4, 3, 2 ], [ 4, 1, 3, 2 ], [ 2, 1, 3, 4 ],

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[ 4, 3, 2, 1 ], [ 2, 3, 4, 1 ], [ 3, 4, 2, 1 ] ]</lang>

GAP has also built-in functions to get permutations

<lang gap># All arrangements of 4 elements in 1..4

<lang gap># All arrangements of 4 elements in 1 .. 4

Arrangements([1..4], 4);

Arrangements([1 .. 4], 4);

# All permutations of 1..4

# All permutations of 1 .. 4

PermutationsList([1..4]);</lang>

PermutationsList([1 .. 4]);</lang>

Here is an implementation using a function to compute next permutation in lexicographic order:

<lang gap>NextPermutation := function(a)