schubertAdd -- compute the sum of ASM ideals

Given a list of ASMs or permutations in 1-line notation, compute the sum of the corresponding Schubert determinantal (or ASM) ideals

An arbitrary (finite) sum of partial ASM ideals is again a partial ASM ideal. See

• [Wei, Section 3.5]: Weigandt, Prism tableaux for alternating sign matrix varieties (see arXiv:1708.07236).

• [KW, Lemma 2.6]: Klein and Weigant, Bumpless pipe dreams encode Gröbner geometry of Schubert polynomials (see arXiv:2108.08370).

The canonical rank table of the sum will be entrywise minimum of the rank tables of the summands. This function computes the sum of ASM ideals by computing the individual rank tables, using entrywiseMinRankTable to find the entrywise minimum, and then constructing the partial ASM from that rank table.

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

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

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

i2 : schubertAdd {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