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# schubertDecompose -- finds the decomposition of an ASM ideal into Schubert determinantal ideals

## Synopsis

• Usage:
schubertDecompose I
• Inputs:
• Outputs:

## Description

Given an ASM ideal $I_A$, it can be decomposed into Schubert determinantal ideals as $I_A = I_{w_1} \cap ... \cap I_{w_k}$, where the $w_i$ are permutations. As output, each element in the list is the permutation associated to a prime component in the Schubert decomposition of the antidiagonal initial ideal of $I$.

 i1 : A = matrix{{0,0,1,0,0},{1,0,0,0,0},{0,1,-1,1,0},{0,0,0,0,1},{0,0,1,0,0}}; 5 5 o1 : Matrix ZZ <-- ZZ i2 : J = schubertDeterminantalIdeal A; o2 : Ideal of QQ[z ..z ] 1,1 5,5 i3 : netList schubertDecompose J +-+-+-+-+-+ o3 = |4|1|2|5|3| +-+-+-+-+-+ |3|1|4|5|2| +-+-+-+-+-+

If the ASM ideal for an ASM $A$ has not het been computed, one may also give the ASM $A$ as input.

 i4 : A = matrix{{0,0,0,1},{0,1,0,0},{1,-1,1,0},{0,1,0,0}}; 4 4 o4 : Matrix ZZ <-- ZZ i5 : netList schubertDecompose A +-+-+-+-+ o5 = |4|3|1|2| +-+-+-+-+ |4|2|3|1| +-+-+-+-+

## Ways to use schubertDecompose :

• schubertDecompose(Ideal)
• schubertDecompose(Matrix)

## For the programmer

The object schubertDecompose is .