NAGtypes : Table of Contents

• NAGtypes -- Common types used in Numerical Algebraic Geometry
• AbstractPoint -- a type used to store a point in complex space
• addition -- Union of polynomial spaces
• areEqual -- determine if solutions are equal
• areEqual(DualSpace,DualSpace) -- approximate equality of dual spaces
• areEqual(PolySpace,PolySpace) -- approximate equality of subspaces spanned by polynomials
• components(NumericalVariety) -- list components of a numerical variety
• declareIrreducible -- declares a component represented by the witness set irreducible
• DualSpace -- a dual functional vector subspace
• dualSpace -- construct a DualSpace
• evaluate -- evaluate a polynomial system or matrix at a point
• generalEquations -- random linear combinations of equations/generators
• homogenize(PolySystem,Ring,RingElement) -- homogenize a polynomial system
• intersection(PolySpace,PolySpace) -- Intersection of polynomial spaces
• isContained -- Is one space contained in the other
• isGEQ -- compare two points
• isRealPoint -- determine whether a point is real
• Norm -- p in the p-norm
• norm(Thing,AbstractPoint) -- p-norm of the point
• numericalAffineSpace -- affine space as a numerical variety
• NumericalVariety -- a numerical variety
• numericalVariety(List) -- construct a numerical variety
• point -- construct a Point
• PolySpace -- a polynomial vector subspace
• polySpace -- construct a PolySpace
• PolySystem -- a polynomial system
• polySystem -- construct a polynomial system
• project(AbstractPoint,ZZ) -- project a point
• ProjectiveNumericalVariety -- a projective numerical variety
• ProjectiveWitnessSet -- a projective witness set
• projectiveWitnessSet -- construct a ProjectiveWitnessSet
• random(PolySpace) -- random element of a subspace
• realPoints -- select real points
• reduceSpace -- reduce the generators of a space
• residual -- residual of a polynomial function at a point
• sliceEquations(Matrix,Ring) -- slicing linear functions
• solutionsWithMultiplicity -- replaces clusters of approximately equal points by single points with multiplicity
• sortSolutions(...,Tolerance=>...) -- the tolerance of a numerical computation
• sortSolutions(List) -- sort the list of solutions
• substitute(PolySystem,Ring) -- substitute a ring in a polynomial system
• System -- a system of functions
• toAffineChart(ZZ,List) -- coordinates of a point in the projective space in an affine chart
• WitnessSet -- a witness set
• witnessSet -- construct a WitnessSet
• WSet -- (under construction!) new types and methods needed to generalize WitnessSet