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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

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 (DOI: 10.2140/jsag.2021.11.61). That version can be obtained from the journal.

Version

This documentation describes version 1.2 of SparseResultants.

Citation

If you have used this package in your research, please cite it as follows:

@misc{SparseResultantsSource,
  title = {{SparseResultants: computations with sparse resultants. Version~1.2}},
  author = {Giovanni Staglian{\`o}},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

@article{SparseResultantsArticle,
  title = {{A package for computations with sparse resultants}},
  author = {Giovanni Staglian{\`o}},
  journal = {The Journal of Software for Algebra and Geometry},
  volume = {11},
  year = {2021},
}

Exports

For the programmer

The object SparseResultants is a package, defined in SparseResultants.m2.


The source of this document is in SparseResultants.m2:1037:0.