combinat/01

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Design discussion for permutations and discrete functions

This is about permutations, and more generally about functions between finite sets.

Desirable features:

• - Python mantra: an object which looks like a list should behave like a list.

  I.e. if the users sees

  •        sage: p = ...
           sage: p
           [4,1,3,2]

  Then he will expect

  •        sage: p[0]
           4

  - The user should be able to manipulate permutations (functions) of

  any finite set, and manipulate them as is, without translations

  •        sage: F = Functions([3,4,8])
           sage: F.list()
           [3,3,3]
           [3,3,4]
           [3,3,8]
           ...
           [8,8,8]
           sage: p = F([8,3,4])
           [8,3,4]

  In particular, whatever the syntax is, one want to be able to do

  •        sage: p of 3
           8
           sage: p of 3 = 4
           sage: p
           [4,3,4]

  - Permutations(n) should be Permutations([1,...,n]) - Internally, permutations should be implemented as permutations of
  • [0...n-1] for speed (future cythonization)

Potential solutions:

- current one

•       sage: p = Permutation([3,1,2])
        sage: p[0]
        3
        sage: p[0] = 1; p[1] = 3    # actually not implemented