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

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.

Documentation

data ERChebPoly box b

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

Fields

chplCoeffs :: Map (TermKey box) b

Instances

Typeable2 ERChebPoly

(ERRealBase rb, RealFrac rb, DomainBox box varid Int, Ord box, Show varid, DomainBoxMappable boxb boxras varid rb [ERInterval rb], DomainBoxMappable boxra boxras varid (ERInterval rb) [ERInterval rb], DomainIntBox boxra varid (ERInterval rb)) => ERUnitFnBaseIElementary boxb boxra varid rb (ERInterval rb) (ERChebPoly box rb)

(ERRealBase rb, RealFrac rb, DomainBox box varid Int, Ord box, Show varid, DomainBoxMappable boxb boxras varid rb [ERInterval rb], DomainBoxMappable boxra boxras varid (ERInterval rb) [ERInterval rb], DomainIntBox boxra varid (ERInterval rb)) => ERUnitFnBaseIEncl boxb boxra varid rb (ERInterval rb) (ERChebPoly box rb)

(ERRealBase rb, RealFrac rb, DomainBox box varid Int, Ord box, Show varid, DomainBoxMappable boxb boxras varid rb [ERInterval rb], DomainBoxMappable boxra boxras varid (ERInterval rb) [ERInterval rb], DomainIntBox boxra varid (ERInterval rb)) => ERUnitFnBaseElementary boxb boxra varid rb (ERInterval rb) (ERChebPoly box rb)

(ERRealBase rb, RealFrac rb, DomainBox box varid Int, Ord box, Show varid, DomainBoxMappable boxb boxras varid rb [ERInterval rb], DomainBoxMappable boxra boxras varid (ERInterval rb) [ERInterval rb], DomainIntBox boxra varid (ERInterval rb)) => ERUnitFnBaseEncl boxb boxra varid rb (ERInterval rb) (ERChebPoly box rb)

(ERRealBase rb, RealFrac rb, DomainBox box varid Int, Ord box, Show varid, DomainBoxMappable boxb boxras varid rb [ERInterval 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)

(Data box, Data b, Ord box) => Data (ERChebPoly box b)

(Ord box, Ord b) => 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 = box