Permutation

We represent a permutation as two lists of equal length representing preimages and images of moved points. I.e., fixed points do not occur in either of these lists. This enables us to compute the set of fixed points and the set of moved points easily.

p := coercePreimagesImages([[1,2,3],[1,2,3]])
  1
                    Type: Permutation PositiveInteger

movedPoints p
  {}
                    Type: Set PositiveInteger

even? p
  true
                     Type: Boolean

p := coercePreimagesImages([[0,1,2,3],[3,0,2,1]])$PERM ZMOD 4
  (1 0 3)
                     Type: Permutation IntegerMod 4

fixedPoints p
  {2}
                     Type: Set IntegerMod 4

q := coercePreimagesImages([[0,1,2,3],[1,0]])$PERM ZMOD 4
  (1 0)
                     Type: Permutation IntegerMod 4

fixedPoints(p*q)
  {2,0}
                     Type: Set IntegerMod 4
even?(p*q)
  false
                     Type: Boolean

See Also:

• )show Permutation