schubertIntersect -- compute the intersection of ASM ideals

Usage:

schubertIntersect L
Inputs:
- L, a list, of ASMs or permutations in 1-line notation
Outputs:
- an ideal,

Description

Given a list of ASMs or permutations in 1-line notation, compute the intersection of the corresponding Schubert determinantal ideals.

i1 : schubertIntersect {{3,2,1,4}, {2,1,4,3}}

                                                             2        
o1 = ideal (z   , z   z   z   z    - z   z   z   z    - z   z   z    +
             1,1   1,3 2,1 2,2 3,1    1,2 2,1 2,3 3,1    1,3 2,1 3,2  
     ------------------------------------------------------------------------
          2                            2                               
     z   z   z   , z   z   z   z    - z   z   z    - z   z   z   z    +
      1,2 2,1 3,3   1,2 1,3 2,2 3,1    1,2 2,3 3,1    1,2 1,3 2,1 3,2  
     ------------------------------------------------------------------------
      2
     z   z   z   )
      1,2 2,1 3,3

o1 : Ideal of QQ[z   ..z   ]
                  1,1   4,4

i2 : schubertIntersect {matrix {{0,1,0},{1,-1,1},{0,1,0}}, {3,2,1}}

o2 = ideal (z   , z   z   )
             1,1   1,2 2,1

o2 : Ideal of QQ[z   ..z   ]
                  1,1   3,3

Ways to use schubertIntersect:

schubertIntersect(List)

For the programmer

The object schubertIntersect is a method function.

The source of this document is in MatrixSchubert/MatrixSchubertConstructionsDOC.m2:1252:0.