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ExampleSystems -- examples of polynomial systems

Description

This package is a database for examples of polynomial systems in Macaulay2, including standard systems of interest in various applications, such as engineering, chemistry, robotics, and economics.

References:

Authors

Version

This documentation describes version 0.5 of ExampleSystems.

Citation

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

@misc{ExampleSystemsSource,
  title = {{ExampleSystems: database of polynomial systems. Version~0.5}},
  author = {Anton Leykin and Justin Chen and Kelly Maluccio and Leah Gold},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

Exports

  • Functions and commands
    • bellido -- Bellido system
    • boon -- a neurophysiology problem posted by Sjirk Boon
    • butcher -- Butcher's problem
    • camera1s -- a system for camera displacement between two positions, with scaled first frame.
    • caprasse -- the system caprasse of the PoSSo test suite
    • cassou -- the system of Pierrette Cassou-Nogu`es
    • chemequ -- chemical equilibrium of hydrocarbon combustion
    • cohn3 -- modular equations for special algebraic number fields
    • comb3000s -- a combustion chemistry example for a temperature of 3000 degrees
    • cyclic -- an example of a square polynomial system
    • dipole2 -- Dipole2 system
    • eco8 -- an 8-dimensional economics problem
    • geneig -- generalized eigenvalue problem
    • heart -- an 8-dimensional economics problem
    • ipp -- six-revolute-joint problem of mechanics
    • katsura -- an example of a 0-dimensional square polynomial system
    • ku10 -- a 10-dimensional system of Ku
    • lorentz -- equilibrium points of a 4-dimensional Lorentz attractor
    • lumped -- lumped parameter chemically reacting system
    • noon5 -- A neural network modeled by an adaptive Lotka-Volterra system with 5 variables
    • proddeco -- system with a product-decomposition structure
    • puma -- hand position and orientation of PUMA robot
    • quadgrid -- interpolating quadrature formula for function defined on a grid
    • rabmo -- optimal multi-dimensional quadrature formulas
    • randomGeneralizedEigenvalueProblem -- an example of a 0-dimensional square polynomial system
    • randomSystem -- an example of a 0-dimensional square polynomial system
    • rbpl24s -- parallel robot with 24 real solutions, after variable scaling
    • reimer5 -- 5-dimensional Reimer system
    • rose -- the system Rose, a general economic equilibrium model
    • sendra -- the system sendra
    • trinks -- system of Trinks from the PoSSo test suite
    • virasoro -- the construction of Virasoro algebras
    • wood -- system derived from optimizing the Wood function
    • wright -- system of A.H. Wright
  • Methods
    • bellido(Ring) -- see bellido -- Bellido system
    • boon(Ring) -- see boon -- a neurophysiology problem posted by Sjirk Boon
    • butcher(Ring) -- see butcher -- Butcher's problem
    • camera1s(Ring) -- see camera1s -- a system for camera displacement between two positions, with scaled first frame.
    • caprasse(Ring) -- see caprasse -- the system caprasse of the PoSSo test suite
    • cassou(Ring) -- see cassou -- the system of Pierrette Cassou-Nogu`es
    • chemequ(Ring) -- see chemequ -- chemical equilibrium of hydrocarbon combustion
    • cohn3(Ring) -- see cohn3 -- modular equations for special algebraic number fields
    • comb3000s(Ring) -- see comb3000s -- a combustion chemistry example for a temperature of 3000 degrees
    • cyclic(ZZ,Ring) -- see cyclic -- an example of a square polynomial system
    • dipole2(Ring) -- see dipole2 -- Dipole2 system
    • eco8(Ring) -- see eco8 -- an 8-dimensional economics problem
    • geneig(Ring) -- see geneig -- generalized eigenvalue problem
    • heart(Ring) -- see heart -- an 8-dimensional economics problem
    • ipp(Ring) -- see ipp -- six-revolute-joint problem of mechanics
    • katsura(ZZ,Ring) -- see katsura -- an example of a 0-dimensional square polynomial system
    • ku10(Ring) -- see ku10 -- a 10-dimensional system of Ku
    • lorentz(Ring) -- see lorentz -- equilibrium points of a 4-dimensional Lorentz attractor
    • lumped(Ring) -- see lumped -- lumped parameter chemically reacting system
    • noon5(Ring) -- see noon5 -- A neural network modeled by an adaptive Lotka-Volterra system with 5 variables
    • proddeco(Ring) -- see proddeco -- system with a product-decomposition structure
    • puma(Ring) -- see puma -- hand position and orientation of PUMA robot
    • quadgrid(Ring) -- see quadgrid -- interpolating quadrature formula for function defined on a grid
    • rabmo(Ring) -- see rabmo -- optimal multi-dimensional quadrature formulas
    • randomGeneralizedEigenvalueProblem(ZZ) -- see randomGeneralizedEigenvalueProblem -- an example of a 0-dimensional square polynomial system
    • randomSystem(ZZ,ZZ,Ring) -- see randomSystem -- an example of a 0-dimensional square polynomial system
    • rbpl24s(Ring) -- see rbpl24s -- parallel robot with 24 real solutions, after variable scaling
    • reimer5(Ring) -- see reimer5 -- 5-dimensional Reimer system
    • rose(Ring) -- see rose -- the system Rose, a general economic equilibrium model
    • sendra(Ring) -- see sendra -- the system sendra
    • trinks(Ring) -- see trinks -- system of Trinks from the PoSSo test suite
    • virasoro(Ring) -- see virasoro -- the construction of Virasoro algebras
    • wood(Ring) -- see wood -- system derived from optimizing the Wood function
    • wright(Ring) -- see wright -- system of A.H. Wright

For the programmer

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

The source of this document is in ExampleSystems.m2:86:0.