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SP::NewtonInterp -- Newton interpolation formula

Call(s)


SP::NewtonInterp(f,n)

Parameters

f- any expression in the basis of monomials
n- any positive integer denoting the degree of a symmetric group

Introduction

The SP::NewtonInterp function expresses the function f(x1, x2, ...) in terms of XX Schubert polynomials. It uses the Newton interpolation formula involving the permutations in the symmetric group of degree n.

Don't forget it is an interpolation...

On the contrary, the function x2XX uses Monk formula instead of divided differences to decompose (exactly) a polynomial into the XX basis.

When called with one argument, the second argument is set to the value of the variable Sn that fixes the degree of the symmetric group.

The result is not expanded.

Example 1

>> muEC::SP::NewtonInterp(2*x2 + 4*a^2*x1^2, 4);
                 2   2
      (2 y2 + 4 a  y1 ) XX[1, 2, 3, 4] +
      
             2         2
         (4 a  y1 + 4 a  y2 - 2) XX[2, 1, 3, 4] +
      
            2
         4 a  XX[3, 1, 2, 4] + 2 XX[1, 3, 2, 4]
>> expand( muEC::SP::Tox(%) );
                                        2   2
                              2 x2 + 4 a  x1

Related Functions

x2XX

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MuPAD Combinat, an open source algebraic combinatorics package