grothendieckPolynomial -- computes the Grothendieck polynomial of a permutation

Usage:

grothendieckPolynomial w
Inputs:
- w, a list,
Optional inputs:
- Algorithm => a string, 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 0.00600603s (cpu); 0.00595252s (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 0.00253608s (cpu); 0.0029753s (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 a method function with options.

The source of this document is in MatrixSchubert/permutationMethodsDOC.m2:455:0.