augmentedEssentialSet -- find the essential set and rank conditions for a partial ASM or a permutation

• Usage:

  augmentedEssentialSet w

  augmentedEssentialSet A

• Inputs:
  • w, a list, or A is a Matrix
• Outputs:
  • a list,

i1 : w = {2,5,4,1,3}

o1 = {2, 5, 4, 1, 3}

o1 : List

i2 : augmentedEssentialSet w

o2 = {((2, 4), 1), ((3, 1), 0), ((3, 3), 1)}

o2 : List

i3 : A = matrix{{0,1,0},{1,-1,0},{0,0,0}}

o3 = | 0 1  0 |
     | 1 -1 0 |
     | 0 0  0 |

              3       3
o3 : Matrix ZZ  <-- ZZ

i4 : augmentedEssentialSet A

o4 = {((1, 1), 0), ((3, 3), 1)}

o4 : List