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# grothendieckPolynomial -- computes the Grothendieck polynomial of a permutation

## Synopsis

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

## Description

Given a permutation in 1-line notation, finds its Grothenieck polynomial. Two algorithms are impliemented: DividedDifference (which is the default) and PipeDream.

 i1 : w = {2,1,4,3} o1 = {2, 1, 4, 3} o1 : List i2 : time grothendieckPolynomial w -- used 0.00394869s (cpu); 0.00645271s (thread); 0s (gc) 2 2 2 2 o2 = x x x - x x - x x - x x x + x + x x + x x 1 2 3 1 2 1 3 1 2 3 1 1 2 1 3 o2 : QQ[x ..x ] 1 4 i3 : time grothendieckPolynomial (w,Algorithm=>"PipeDream") -- used 0.000289771s (cpu); 0.00333063s (thread); 0s (gc) 2 2 2 2 o3 = x x x - x x - x x - x x x + x + x x + x x 1 2 3 1 2 1 3 1 2 3 1 1 2 1 3 o3 : QQ[x ..x ] 1 4

## Ways to use grothendieckPolynomial :

• grothendieckPolynomial(List)

## For the programmer

The object grothendieckPolynomial is .