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# schubertDeterminantalIdeal -- compute an alternating sign matrix ideal (for example, a Schubert determinantal ideal)

## Synopsis

• Usage:
schubertDeterminantalIdeal w
schubertDeterminantalIdeal A
• Inputs:
• Optional inputs:
• CoefficientRing => ..., default value QQ
• Variable => ..., default value z
• Outputs:

## Description

Given a permutation in 1-line notation or, more generally, a partial alternating sign matrix, outputs the associated alternating sign matrix ideal (which is called a Schubert determinantal ideal in the case of a permutation). (The convention throughout this package is that the permutation matrix of a pemutation $w$ has 1's in positions $(i,w(i))$.)

This function computes over the coefficient field of rational numbers unless an alternative is specified.

 i1 : schubertDeterminantalIdeal({1,3,2},CoefficientRing=>ZZ/3001) o1 = ideal(- z z + z z ) 1,2 2,1 1,1 2,2 ZZ o1 : Ideal of ----[z ..z ] 3001 1,1 3,3 i2 : schubertDeterminantalIdeal(matrix{{0,0,0,1},{0,1,0,0},{1,-1,1,0},{0,1,0,0}}, Variable => y) o2 = ideal (y , y , y , y , - y y + y y , - y y + 1,1 1,2 1,3 2,1 1,2 2,1 1,1 2,2 1,2 3,1 ------------------------------------------------------------------------ y y , - y y + y y ) 1,1 3,2 2,2 3,1 2,1 3,2 o2 : Ideal of QQ[y ..y ] 1,1 4,4

## Ways to use schubertDeterminantalIdeal :

• schubertDeterminantalIdeal(List)
• schubertDeterminantalIdeal(Matrix)

## For the programmer

The object schubertDeterminantalIdeal is .