MultipolynomialResultants is a package to compute resultants and discriminants.
Let
F0,...,Fn be
n+1 homogeneous polynomials in
n+1 variables
x0,...,xn over a commutative ring
K. The resultant
R(F0,...,Fn) is a certain polynomial in the coefficients of
F0,...,Fn; when
K is an algebraically closed field,
R(F0,...,Fn) vanishes if and only if
F0,...,Fn have a common nontrivial root. The discriminant of a homogeneous polynomial is defined, up to a scalar factor, as the resultant of its partial derivatives. For the general theory, see one of the following:
1) David A. Cox, John Little, Donal O'shea -
Using Algebraic Geometry, Graduate Texts in Mathematics, Volume 185 (2005).
2) Israel M. Gelfand, Mikhail M. Kapranov, Andrei V. Zelevinsky -
Discriminants, Resultants, and Multidimensional Determinants, Mathematics: Theory & Applications (1994).
In this package, there are currently two algorithms implemented:
Poisson (default) and
Macaulay.