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# rankTableToASM -- to find the a partial ASM associated to a given rank table

- Usage:
    `rankTableToASM T`
- Inputs:
  - T, a matrix,
- Outputs:
  - a matrix,

## Description

Given a matrix that is a valid minimal rank table, returns the unique partial ASM of the same size associated to it. This algorithm follows

- [Wei, Equation (21)]: Weigandt, Prism tableaux for alternating sign matrix varieties (see arXiv:1708.07236).

    i1 : T = matrix {{0,0,1,1},{0,1,1,2},{1,2,2,3},{1,2,3,4}}

    o1 = | 0 0 1 1 |
         | 0 1 1 2 |
         | 1 2 2 3 |
         | 1 2 3 4 |

                  4       4
    o1 : Matrix ZZ  <-- ZZ

    i2 : rankTableToASM T

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

                  4       4
    o2 : Matrix ZZ  <-- ZZ

    i3 : U = matrix {{0,0,1,1,1},{1,1,1,2,2},{1,2,2,3,3},{1,2,3,4,4},{1,2,3,4,5}}

    o3 = | 0 0 1 1 1 |
         | 1 1 1 2 2 |
         | 1 2 2 3 3 |
         | 1 2 3 4 4 |
         | 1 2 3 4 5 |

                  5       5
    o3 : Matrix ZZ  <-- ZZ

    i4 : rankTableToASM U

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

                  5       5
    o4 : Matrix ZZ  <-- ZZ

## Ways to use rankTableToASM:

- `rankTableToASM(Matrix)`

## For the programmer

The object rankTableToASM is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/MatrixSchubert/MatrixSchubertConstructionsDOC.m2:1206:0.