SparseResultants -- computations with sparse resultants

Description

This package provides the methods sparseResultant and sparseDiscriminant to calculate sparse resultants and sparse discriminants. See also the package Resultants, which includes methods to calculate dense resultants and dense discriminants.

For the definitions, see one of the following books:

(1) Using Algebraic Geometry, by David A. Cox, John Little, Donal O'shea;

(2) Discriminants, Resultants, and Multidimensional Determinants, by Israel M. Gelfand, Mikhail M. Kapranov and Andrei V. Zelevinsky.

Caveat

Currently, the algorithms implemented are based on elimination via Gröbner basis methods. This should be significantly improved by implementing more specialized algorithms.

Author

Giovanni Staglianò <giovannistagliano@gmail.com>

Version

This documentation describes version 0.9 of SparseResultants.

Source code

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

Exports

Functions and commands
- denseDiscriminant -- dense discriminant (classical discriminant)
- denseResultant -- dense resultant (classical resultant)
- exponentsMatrix -- exponents in one or more polynomials
- genericLaurentPolynomials -- generic Laurent polynomials
- genericMultihomogeneousPolynomial -- generic multi-homogeneous polynomial
- sparseDiscriminant -- sparse discriminant (A-discriminant)
- sparseResultant -- sparse resultant (A-resultant)