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

- 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.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/MatrixSchubert/MatrixSchubertConstructionsDOC.m2:1231:0.