fultonGens -- compute the Fulton generators of an ASM ideal (for example, a Schubert determinantal ideal)

Synopsis

Usage:

fultonGens w

fultongens A
Inputs:
- w, a list, or A is a Matrix
Optional inputs:
- CoefficientRing => a ring, default value QQ
- Variable => a symbol, default value z
Outputs:
- a list,

Description

Given a partial alternating sign matrix or permutation in 1-line notation, returns the list of Fulton generators for the corresponding Schubert determinantal ideal or, more generally, ASM ideal.

i1 : netList fultonGens({2,5,4,1,3}, CoefficientRing => ZZ/101)

     +---------------------+
o1 = |- z   z    + z   z   |
     |   1,2 2,1    1,1 2,2|
     +---------------------+
     |- z   z    + z   z   |
     |   1,3 2,1    1,1 2,3|
     +---------------------+
     |- z   z    + z   z   |
     |   1,3 2,2    1,2 2,3|
     +---------------------+
     |- z   z    + z   z   |
     |   1,4 2,1    1,1 2,4|
     +---------------------+
     |- z   z    + z   z   |
     |   1,4 2,2    1,2 2,4|
     +---------------------+
     |- z   z    + z   z   |
     |   1,4 2,3    1,3 2,4|
     +---------------------+
     |z                    |
     | 1,1                 |
     +---------------------+
     |z                    |
     | 2,1                 |
     +---------------------+
     |z                    |
     | 3,1                 |
     +---------------------+
     |- z   z    + z   z   |
     |   1,2 3,1    1,1 3,2|
     +---------------------+
     |- z   z    + z   z   |
     |   2,2 3,1    2,1 3,2|
     +---------------------+
     |- z   z    + z   z   |
     |   1,3 3,1    1,1 3,3|
     +---------------------+
     |- z   z    + z   z   |
     |   2,3 3,1    2,1 3,3|
     +---------------------+
     |- z   z    + z   z   |
     |   1,3 3,2    1,2 3,3|
     +---------------------+
     |- z   z    + z   z   |
     |   2,3 3,2    2,2 3,3|
     +---------------------+

i2 : netList fultonGens(matrix{{0,1,0},{1,-1,1},{0,1,0}}, Variable => a)

     +---------------------+
o2 = |a                    |
     | 1,1                 |
     +---------------------+
     |- a   a    + a   a   |
     |   1,2 2,1    1,1 2,2|
     +---------------------+

Ways to use fultonGens :

fultonGens(List)
fultonGens(Matrix)

For the programmer

The object fultonGens is a method function with options.