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NAGtypes :: NAGtypes

NAGtypes -- Common types used in Numerical Algebraic Geometry

Description

The package defines types used by the package NumericalAlgebraicGeometry as well as other numerical algebraic geometry packages: e.g., an interface package PHCpack.

Main datatypes:
  • Point -- numerical approximation of a point in a complex space (and related methods)
  • WitnessSet -- a witness set representing (possibly positive-dimensional) solution components
  • NumericalVariety -- a numerical description of a variety
Other service functions:

Author

Version

This documentation describes version 1.4.0.1 of NAGtypes.

Source code

The source code from which this documentation is derived is in the file NAGtypes.m2.

Exports

  • Types
  • Functions and commands
    • areEqual -- determine if solutions are equal
    • classifyPoint (missing documentation)
    • generalEquations -- random linear combinations of equations/generators
    • isGEQ -- compare two points
    • isRealPoint -- determine whether a point is real
    • numericalVariety, see numericalVariety(List) -- construct a numerical variety
    • plugIn (missing documentation)
    • coordinates, see Point -- a type used to store a point in complex space
    • point, see point(List) -- construct a Point
    • realPoints -- determine whether a point is real
    • relativeErrorEstimate (missing documentation)
    • residual (missing documentation)
    • setName -- give a name to a witness set
    • sliceEquations, see sliceEquations(Matrix,Ring) -- slicing linear functions
    • sortSolutions, see sortSolutions(List) -- sort the list of solutions
    • equations, see WitnessSet -- a witness set
    • points, see WitnessSet -- a witness set
    • slice, see WitnessSet -- a witness set
    • witnessSet -- construct a WitnessSet
  • Methods
    • areEqual(Point,Point), see areEqual -- determine if solutions are equal
    • check(NumericalVariety) (missing documentation)
    • classifyPoint(Point) (missing documentation)
    • degree(NumericalVariety) (missing documentation)
    • dim(NumericalVariety) (missing documentation)
    • isRealPoint(Point), see isRealPoint -- determine whether a point is real
    • net(NumericalVariety) (missing documentation)
    • norm(Thing,Point) -- p-norm of the point
    • plugIn(List,Point) (missing documentation)
    • coordinates(Point), see Point -- a type used to store a point in complex space
    • matrix(Point), see Point -- a type used to store a point in complex space
    • net(Point), see Point -- a type used to store a point in complex space
    • status(Point), see Point -- a type used to store a point in complex space
    • point(Point) (missing documentation)
    • relativeErrorEstimate(Point) (missing documentation)
    • residual(List,Point) (missing documentation)
    • setName(WitnessSet,Thing), see setName -- give a name to a witness set
    • codim(WitnessSet), see WitnessSet -- a witness set
    • degree(WitnessSet), see WitnessSet -- a witness set
    • dim(WitnessSet), see WitnessSet -- a witness set
    • equations(WitnessSet), see WitnessSet -- a witness set
    • ideal(WitnessSet), see WitnessSet -- a witness set
    • net(WitnessSet), see WitnessSet -- a witness set
    • points(WitnessSet), see WitnessSet -- a witness set
    • ring(WitnessSet), see WitnessSet -- a witness set
    • slice(WitnessSet), see WitnessSet -- a witness set
  • Symbols
    • IsIrreducible (missing documentation)
    • MaxConditionNumber (missing documentation)
    • Multiplicity (missing documentation)
    • Norm (missing documentation)
    • ConditionNumber, see Point -- a type used to store a point in complex space
    • Coordinates, see Point -- a type used to store a point in complex space
    • DeflationNumber, see Point -- a type used to store a point in complex space
    • ErrorBoundEstimate, see Point -- a type used to store a point in complex space
    • Infinity, see Point -- a type used to store a point in complex space
    • LastT, see Point -- a type used to store a point in complex space
    • MaxPrecision, see Point -- a type used to store a point in complex space
    • MinStepFailure, see Point -- a type used to store a point in complex space
    • NumberOfSteps, see Point -- a type used to store a point in complex space
    • NumericalRankFailure, see Point -- a type used to store a point in complex space
    • Regular, see Point -- a type used to store a point in complex space
    • Singular, see Point -- a type used to store a point in complex space
    • SolutionStatus, see Point -- a type used to store a point in complex space
    • WindingNumber, see Point -- a type used to store a point in complex space
    • Tolerance -- specifies the tolerance of a numerical computation
    • Equations, see WitnessSet -- a witness set
    • Points, see WitnessSet -- a witness set
    • Slice, see WitnessSet -- a witness set