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MultipolynomialResultants :: MultipolynomialResultants

MultipolynomialResultants -- package for computation of resultants and discriminants

Description

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.

Author

Version

This documentation describes version 1.1 of MultipolynomialResultants.

Source code

The source code from which this documentation is derived is in the file MultipolynomialResultants.m2.

Exports

  • Functions and commands
  • Symbols
    • Algorithm -- name for an optional argument
    • Macaulay, see Algorithm -- name for an optional argument
    • Poisson, see Algorithm -- name for an optional argument