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# schubertPolynomial -- computes the Schubert polynomial of a permutation

## Synopsis

• Usage:
schubertPolynomial w
• Inputs:
• Optional inputs:
• Algorithm => , default value "DividedDifference", algorithm "Transition" also available

## Description

Given a permutation in 1-line notation, finds its (single) Schubert polynomial. Two algorithms are impliemented: DividedDifference (which is the default) and Transition (which makes use of the transition equations for Schubert polynomials).

 i1 : w = {2,1,5,4,3} o1 = {2, 1, 5, 4, 3} o1 : List i2 : schubertPolynomial w 3 2 2 3 2 2 2 2 2 3 2 o2 = x x + x x + x x + 2x x x + x x x + x x + x x x + x x + x x x + 1 2 1 2 1 3 1 2 3 1 2 3 1 3 1 2 3 1 4 1 2 4 ------------------------------------------------------------------------ 2 2 2 x x x + x x x + x x x x + x x x 1 2 4 1 3 4 1 2 3 4 1 3 4 o2 : QQ[x ..x ] 1 5 i3 : schubertPolynomial (w,Algorithm=>"Transition") 3 2 2 3 2 2 2 2 2 3 2 o3 = x x + x x + x x + 2x x x + x x x + x x + x x x + x x + x x x + 1 2 1 2 1 3 1 2 3 1 2 3 1 3 1 2 3 1 4 1 2 4 ------------------------------------------------------------------------ 2 2 2 x x x + x x x + x x x x + x x x 1 2 4 1 3 4 1 2 3 4 1 3 4 o3 : QQ[x ..x ] 1 5

## Ways to use schubertPolynomial :

• schubertPolynomial(List)

## For the programmer

The object schubertPolynomial is .