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SparseResultants :: SparseResultants

SparseResultants -- computations with sparse resultants

Description

This package provides the methods sparseResultant and sparseDiscriminant to calculate sparse resultants and sparse discriminants. As an application, the method determinant(MultidimensionalMatrix) is also provided. 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) Discriminants, Resultants, and Multidimensional Determinants, by Israel M. Gelfand, Mikhail M. Kapranov and Andrei V. Zelevinsky;

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

Caveat

Currently, most of the algorithms implemented are based on elimination via Gröbner basis methods. This should be significantly improved by implementing more specialized algorithms (see e.g. [2, Chapter 7,Section 6]).

Author

Version

This documentation describes version 1.1 of SparseResultants.

Source code

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

Exports

For the programmer

The object SparseResultants is a package.