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NumericalAlgebraicGeometry : Table of Contents
NumericalAlgebraicGeometry
-- Numerical Algebraic Geometry
addition
-- Union of polynomial spaces
AffinePatches
-- reserved for developers
BERTINI
-- use Bertini for homotopy continuation
Certified
-- a value for the option Predictor that triggers certified tracking
colon
-- colon of a (truncated) dual space
decompose(WitnessSet)
-- decompose a witness set into irreducibles
deflate
-- first-order deflation
DoublePrecision
-- a constant equal to 53 (the number of bits of precision)
gateHomotopy(..., Parameters => ...)
-- specifies parameter names
gateHomotopy(..., Software => ...)
-- specifies where evaluation should be done (M2=top level, M2engine=core)
gateHomotopy(..., Strategy => ...)
-- strategy is either to "compress" or not (any other value)
gateHomotopy(GateMatrix,GateMatrix,InputGate)
-- homotopy system via SLPexpressions
goodInitialPair(List)
-- make an intial pair conjectured to be good by Shub and Smale
HOM4PS2
-- use HOM4PS for homotopy continuation
intersection
-- Intersection of polynomial spaces
isContained
-- Is one space contained in the other
isOn
-- determines if a point belongs to a variety
isPointEmbedded(Point,Ideal,List)
-- determine if the point is an embedded component of the scheme
isPointEmbeddedInCurve(Point,Ideal)
-- determine if the point is an embedded component of a 1-dimensional scheme
isSolution(Point,PolySystem)
-- check if a point satisfies a polynomial system approximately
isSubset(NumericalVariety,NumericalVariety)
-- check containment
NAGtrace(ZZ)
-- set the trace level in NumericalAlgebraicGeometry package
newton
-- Newton-Raphson method
numerical homotopy tracking options
-- options for core functions of Numerical Algebraic Geometry
numericalIntersection
-- intersection of numerical varieties
numericalIrreducibleDecomposition(Ideal)
-- constructs a numerical variety defined by the given ideal
numericalRank
-- numerical rank of a matrix
parameterHomotopy(List,List,List)
-- solve a parametric system of equations
PHCPACK
-- use PHCpack for homotopy continuation
randomInitialPair
-- a random initial pair
randomSd(List)
-- a random homogeneous system of polynomial equations
refine(List,List)
-- refine numerical solutions to a system of polynomial equations
regeneration(List)
-- solve a system of polynomial equations with regeneration method
Regularity
(missing documentation)
removeRedundantComponents(NumericalVariety)
-- remove redundant components
sample(WitnessSet)
-- sample a point on a component
setDefault
-- set/get the default parameters for continuation algorithms
setDefault(..., Tolerance => ...)
-- specifies the tolerance of a numerical computation
Software
-- specify internal or external software
solveGenericSystemInTorus(List)
-- solve a generic system of sparse polynomial equations in the torus
solveSystem(..., PostProcess => ...)
-- specifies whether to postprocess the solutions
solveSystem(List)
-- solve a system of polynomial equations
squareUp
-- square up a polynomial system
totalDegreeStartSystem(List)
-- construct a start system for the total degree homotopy
track(List,List,List)
-- track a user homotopy
union(NumericalVariety,NumericalVariety)
-- union of numerical varieties