rankTableFromMatrix -- returns the minimal rank table from an arbitrary integer matrix

Synopsis

Usage:

rankTableFromMatrix M
Inputs:
- M, a matrix,
Outputs:
- a matrix,

Description

Given an integer matrix (viewed as rank conditions to be imposed on a generic matrix), returns the unique integer matrix that both defines the same ideal of minors and also is the minimal rank table of some ASM. See Section 1 and Equation (21) of

[Wei]: Weigandt, Prism tableaux for alternating sign matrix varieties (see arXiv:1708.07236).

i1 : M = matrix {{1,0,0},{0,23,24},{23,24,25}};

              3       3
o1 : Matrix ZZ  <-- ZZ

i2 : rankTableFromMatrix M

o2 = | 0 0 0 |
     | 0 1 1 |
     | 1 2 2 |

              3       3
o2 : Matrix ZZ  <-- ZZ

i3 : N = matrix{{0,3,4},{1,1,1}};

              2       3
o3 : Matrix ZZ  <-- ZZ

i4 : rankTableFromMatrix N

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

              2       3
o4 : Matrix ZZ  <-- ZZ

Ways to use rankTableFromMatrix :

rankTableFromMatrix(Matrix)

For the programmer

The object rankTableFromMatrix is a method function.