SP::NewtonInterp
--
Newton interpolation formula
SP::NewtonInterp(f,n)
f | - | any expression in the basis of monomials |
n | - | any positive integer denoting the degree of a symmetric group |
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.
>> 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
MuPAD Combinat, an open source algebraic combinatorics package