AERN-RnToRm-0.3.0.1: polynomial function enclosures (PFEs) approximating exact real functions

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Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom

Description

Arithmetic of multivariate polynomials represented by their coefficients it the Chebyshev basis.

The polynomials are never to be used outside the domain `[-1,1]^n`.

All operations are rounded in such a way that the resulting polynomial is a point-wise upper or lower bound of the exact result.

Synopsis

# Documentation

data ERChebPoly box b Source

A polynomial represented by its coefficients it the Chebyshev basis.

The polynomials are never to be used outside the domain `[-1,1]^n`.

All operations are rounded in such a way that the resulting polynomial is a point-wise upper or lower bound of the exact result.

Constructors

 ERChebPoly FieldschplCoeffs :: Map (TermKey box) b

Instances

 Typeable2 ERChebPoly (ERRealBase rb, RealFrac rb, DomainBox box varid Int, Ord box, DomainBoxMappable boxb boxbb varid rb [(rb, rb)], DomainBoxMappable boxra boxras varid (ERInterval rb) [ERInterval rb], DomainIntBox boxra varid (ERInterval rb)) => ERUnitFnBase boxb boxra varid rb (ERInterval rb) (ERChebPoly box rb) (Eq box, Eq b) => Eq (ERChebPoly box b) (ERRealBase b, DomainBox box varid Int, Ord box) => Fractional (ERChebPoly box b) (Data box, Data b, Ord box) => Data (ERChebPoly box b) (ERRealBase b, DomainBox box varid Int, Ord box) => Num (ERChebPoly box b) (ERRealBase b, DomainBox box varid Int, Ord box) => Ord (ERChebPoly box b) (ERRealBase b, DomainBox box varid Int, Ord box) => Show (ERChebPoly box b) (Ord a, Binary a, Binary b) => Binary (ERChebPoly a b)

type TermKey box = boxSource