Below are some programs that can be freely dowloaded and used.

Macaulay2 package for resultants :

With Nicolàs Botbol and Manuel Dubinsky, we have implemented a Macaulay2 package for elimination theory, in particular for resultant computations. An introductory file is available (pdf format).

The lastest version of this package can be downloaded, together with the latest version of Macaulay2, with a subversion client from the Macaulay2 download pages. The documentation is visible here.

Maple package for computing multvariate resultants :

The file MResultants.mpl provides functions for

  • the computation of Sylvester, Bezout and hybrid Sylvester-Bezout matrices associated to the Sylvester resultant of two polymonials. The degree of the input polynomials are arguments, so that the universal property of the resultant is emphasized.
  • the computation of the Macaulay formula associated to the resultant of several homogeneous polynomials. This formula expresses the resultant as the quotient of two determinants. It has the advantage of computing exactly the resultant (and not just up to the multiplication by a nonzero constant).

Maple packages for matrix implicit representations of parameterizations of curves and surfaces :

During its PhD thesis, Thang Luu Ba has implemented several tools to produce and handle matrix representation of curves and surfaces. You can get them from its webpage here.

Matrix implicit representations of parameterizations of curves and surfaces in AXEL :

Valentin Michelet has implemented an algorithm for solving the curve/surface intersection problem by means of matrix implicit representations. It is available in the software AXEL. It is part of shape plugin as the IntersectionRationalProcess process.