next | previous | forward | backward | up | top | index | toc | Macaulay2 website
DecomposableSparseSystems :: DecomposableSparseSystems

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

Version

This documentation describes version 1.0.0 of DecomposableSparseSystems.

Source code

The source code from which this documentation is derived is in the file DecomposableSparseSystems.m2. The auxiliary files accompanying it are in the directory DecomposableSparseSystems/.

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
    • "LacunarySys" -- see solveDecomposableSystem -- recursively solves a sparse (Laurent) polynomial system through a decomposition
    • "TriangularSys" -- see solveDecomposableSystem -- recursively solves a sparse (Laurent) polynomial system through a decomposition

For the programmer

The object DecomposableSparseSystems is a package.