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SparseResultants -- computations with sparse resultants


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.


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]).


Certification a gold star

Version 1.1 of this package was accepted for publication in volume 11 of The Journal of Software for Algebra and Geometry on 5 May 2021, in the article A package for computations with sparse resultants. That version can be obtained from the journal or from the Macaulay2 source code repository.


This documentation describes version 1.2 of SparseResultants.

Source code

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


For the programmer

The object SparseResultants is a package.