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ExampleSystems :: ExampleSystems

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.

Source code

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

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.