isPartialASM -- whether a matrix is a partial alternating sign matrix

Synopsis

Usage:

isPartialASM M
Inputs:
- M, a matrix,
Outputs:
- a Boolean value,

Description

Given an integer matrix, checks that the matrix is a partial alternating sign matrix. A partial alternating sign matrix is a matrix with entries in $\{-1,0,1\}$ such that:

- The nonzero entries in each row and column alternate in sign,

- The first nonzero entry of any row or column (if there is one) is $1$.

i1 : M = matrix{{0,0,1,0,0,0,0,0},{1,0,1,0,1,0,0,0},{0,0,0,1,-1,0,0,1},{0,0,1,-1,1,0,0,0},{0,0,0,0,0,0,1,0},{0,0,0,0,0,1,0,0},{0,1,-1,1,0,0,0,0},{0,0,1,0,0,0,0,0}}

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

              8       8
o1 : Matrix ZZ  <-- ZZ

i2 : isPartialASM M

o2 = false

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

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

              5       5
o3 : Matrix ZZ  <-- ZZ

i4 : isPartialASM N

o4 = false

Ways to use isPartialASM :

isPartialASM(Matrix)

For the programmer

The object isPartialASM is a method function.