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// (c) Microsoft Corporation 2005-2009.
namespace Microsoft.FSharp.Math
/// A permutation of a finite range of integers 0 .. N-1, represented by a mapping of index positions
type Permutation = int -> int
[<System.Obsolete("This type abbreviation is now capitalized, please use 'Permutation'")>]
type permutation = int -> int
[<RequireQualifiedAccess>]
[<CompilationRepresentation(CompilationRepresentationFlags.ModuleSuffix)>]
module Permutation =
/// Create a permutation by specifying the result of permuting [| 0 .. n-1 |]. For example,
/// Permutation.ofArray [| 1;2;0 |] specifies a permutation that rotates all elements right one place.
val ofArray : destinations:int array -> Permutation
[<System.Obsolete("This function has been renamed. Use 'Permutation.ofArray' instead")>]
val of_array : destinations:int array -> Permutation
/// Create a permutation by specifying (source,destination) index pairs. For example,
/// Permutation(3,[ (0,2);(1,0); (2,1) ]) specifies a permutation that rotates
/// all elements left one place. Not all elements need be given, e.g.
/// Permutation(5,[ (1,2);(2,1) |]) specifies a permutation that swaps elements at indexes
/// 1 and 2.
val ofPairs : mappings: seq<int * int> -> Permutation
[<System.Obsolete("This function has been renamed. Use 'Permutation.ofPairs' instead")>]
val of_pairs : mappings: seq<int * int> -> Permutation
/// Return a swaps the given two elements over any size
val swap: n:int -> m:int -> Permutation
/// Return a permutation that, when applied, maps index 0 to size-1, size-1 to 0 etc.
val reversal: size:int -> Permutation
/// Return a permutation that rotates right by the given distance. If the distance
/// is negative then a left rotation results.
val rotation: size:int -> distance:int -> Permutation
/// The identity permutation over any size
val identity : Permutation
val inverse : size: int -> p:Permutation -> Permutation
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