# 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.

## 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 .