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 $x_i$ are the elements used to construct the matrix then it can be proven that the determinant has the following form.
$\prod_{0 \leq i < j < n} (x_j-x_i) $
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 |
The object vandermondeDeterminant is a method function with options.