DecomposableSparseSystems -- Solving decomposable sparse polynomial systems

Description

There are two natural ways a sparse polynomial system can be decomposed in the sense of (T. Brysiewicz, J. I. Rodriguez, F. Sottile, and T. Yahl, Solving Decomposable Sparse Systems, arXiv:2001.04228, 2019). These methods detect and compute these decompositions and use them to compute solutions.

Authors

Certification

Version 1.0.1 of this package was accepted for publication in volume 11 of The Journal of Software for Algebra and Geometry on 25 March 2021, in the article Decomposable sparse polynomial systems (DOI: 10.2140/jsag.2021.11.53). That version can be obtained from the journal.

Version

This documentation describes version 1.0.1 of DecomposableSparseSystems.

Citation

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

@misc{DecomposableSparseSystemsSource,
  title = {{DecomposableSparseSystems: Solving decomposable sparse systems. Version~1.0.1}},
  author = {Taylor Brysiewicz and Jose Israel Rodriguez and Frank Sottile and Thomas Yahl},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

@article{DecomposableSparseSystemsArticle,
  title = {{Decomposable sparse polynomial systems}},
  author = {Taylor Brysiewicz and Jose Israel Rodriguez and Frank Sottile and Thomas Yahl},
  journal = {The Journal of Software for Algebra and Geometry},
  volume = {11},
  year = {2021},
}

Exports

Functions and commands
- isDecomposable -- Decides whether a polynomial system is decomposable
- isLacunary -- Decides whether a polynomial system is lacunary
- isTriangular -- Decides whether a polynomial system is triangular
- solveDecomposableSystem -- recursively solves a sparse (Laurent) polynomial system through a decomposition
Methods
- isDecomposable(List) -- see isDecomposable -- Decides whether a polynomial system is decomposable
- isLacunary(List) -- see isLacunary -- Decides whether a polynomial system is lacunary
- isTriangular(List) -- see isTriangular -- Decides whether a polynomial system is triangular
- solveDecomposableSystem(List) -- see solveDecomposableSystem -- recursively solves a sparse (Laurent) polynomial system through a decomposition
- solveDecomposableSystem(List,List) -- see solveDecomposableSystem -- recursively solves a sparse (Laurent) polynomial system through a decomposition
- solveDecomposableSystem(List,Nothing) -- see solveDecomposableSystem -- recursively solves a sparse (Laurent) polynomial system through a decomposition
Symbols
- FromGeneric -- see solveDecomposableSystem -- recursively solves a sparse (Laurent) polynomial system through a decomposition
- FromVertexGeneric -- see solveDecomposableSystem -- recursively solves a sparse (Laurent) polynomial system through a decomposition
- LacunarySystem -- see solveDecomposableSystem -- recursively solves a sparse (Laurent) polynomial system through a decomposition
- TriangularSystem -- see solveDecomposableSystem -- recursively solves a sparse (Laurent) polynomial system through a decomposition

For the programmer

The object DecomposableSparseSystems is a package, defined in DecomposableSparseSystems.m2, with auxiliary files in DecomposableSparseSystems/.

The source of this document is in DecomposableSparseSystems.m2:567:0.