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

Synopsis

• Usage:

  vandermondeDeterminant(l,R)

• Inputs:
  • R, a polynomial ring,
  • l, a list, a subset of the indices of the generators of R
• Optional inputs:
  • AsExpression => a Boolean value, default value false, a Boolean value, default value is false. If true it returns the determinant as a product expression This is a particularly useful way to reduce the size of the object since a Vandermonde determinant has n! terms but only n*(n-1)/2 factors.
• Outputs:
  • a ring element, the determinant of the Vandermonde matrix formed by the generators indexed by l.

Description

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