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SpechtModule :: vandermondeDeterminant

vandermondeDeterminant -- the vandermonde determinant for a set of generators of a ring

Synopsis

Description

A Vandermonde matrix is a matrix of n elements is constructed by putting in each column all the powers from 0 to n-1 of each of the elements.

If xi are the elements used to construct the matrix then it can be proven that the determinant has the following form.

0 ≤i < j < n (xj-xi)

i1 : R = QQ[x_0..x_3]

o1 = R

o1 : PolynomialRing
i2 : vandermondeDeterminant({0,2,3},R)

        2        2    2      2        2      2
o2 = - x x  + x x  + x x  - x x  - x x  + x x
        0 2    0 2    0 3    2 3    0 3    2 3

o2 : R
i3 : factor oo

o3 = (x  - x )(x  - x )(x  - x )(-1)
       2    3   0    3   0    2

o3 : Expression of class Product

Ways to use vandermondeDeterminant :