permutationMatrix -- convert a one-line notation or cyclic notation of a permutation to a matrix representation

Synopsis

• Usage:

  permutationMatrix s, permutationMatrix(n , c)

• Inputs:
  • s, a string, an array or a list of arrays giving a one-line notation or cyclic notation of a permutation
  • n, an integer, giving the number of integers getting permuted
  • c, a list, of arrays giving a cyclic notation of a permutation
• Outputs:
  • a matrix, the matrix representation of the permutation

Description

The following example converts the one-line notation of a transposition into a matrix representation.

i1 : M = permutationMatrix toString 213

o1 = | 0 1 0 |
     | 1 0 0 |
     | 0 0 1 |

              3       3
o1 : Matrix ZZ  <-- ZZ

The following example converts the cyclic notation of the same transposition into a matrix representation. Without n the function assumes n is the largest integer that appears in your array or list of arrays.

i2 : M = permutationMatrix(3,[1,2])

o2 = | 0 1 0 |
     | 1 0 0 |
     | 0 0 1 |

              3       3
o2 : Matrix ZZ  <-- ZZ

i3 : M = permutationMatrix [1,2]

o3 = | 0 1 |
     | 1 0 |

              2       2
o3 : Matrix ZZ  <-- ZZ

The following example converts the cyclic notation of a permutation of 4 into a matrix representation.

i4 : M = permutationMatrix(4,{[1,2],[3,4]})

o4 = | 0 1 0 0 |
     | 1 0 0 0 |
     | 0 0 0 1 |
     | 0 0 1 0 |

              4       4
o4 : Matrix ZZ  <-- ZZ

i5 : M = permutationMatrix {[1,2],[3,4]}

o5 = | 0 1 0 0 |
     | 1 0 0 0 |
     | 0 0 0 1 |
     | 0 0 1 0 |

              4       4
o5 : Matrix ZZ  <-- ZZ