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

Internal module for Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.

Implementation of addition and multiplication over polynomials with pointwise rounding uniform over the whole unit domain.

Documentation

chplBall2DownUp :: (ERRealBase b, DomainBox box varid Int, Ord box) => (ERChebPoly box b, b) -> (ERChebPoly box b, ERChebPoly box b)

Negate a polynomial exactly.

chplBall2DownUpWd :: (ERRealBase b, DomainBox box varid Int, Ord box) => (ERChebPoly box b, b) -> (ERChebPoly box b, ERChebPoly box b, b)

chplBall2Down :: (ERRealBase b, DomainBox box varid Int, Ord box) => (ERChebPoly box b, b) -> ERChebPoly box b

chplBall2Up :: (ERRealBase b, DomainBox box varid Int, Ord box) => (ERChebPoly box b, b) -> ERChebPoly box b

ballAddConst :: (ERRealBase b, DomainBox box varid Int, Ord box) => b -> ERChebPoly box b -> (ERChebPoly box b, b)

Add a constant to a polynomial, rounding downwards and upwards.

ballAdd :: (ERRealBase b, DomainBox box varid Int, Ord box) => ERChebPoly box b -> ERChebPoly box b -> (ERChebPoly box b, b)

Add two polynomials, rounding downwards and upwards.

ballMultiply

Arguments

:: (ERRealBase b, DomainBox box varid Int, Ord box)

=> ERChebPoly box b

-> ERChebPoly box b

-> (ERChebPoly box b, b)

lower and upper bounds on the product and an upper bound on their difference

Multiply two polynomials, rounding downwards and upwards.

ballScale

Arguments

:: (ERRealBase b, DomainBox box varid Int, Ord box)

=> b

-> ERChebPoly box b

-> (ERChebPoly box b, b)

lower and upper bounds on the product and an upper bound on their difference

Multiply a polynomial by a scalar rounding downwards and upwards.

ballSquare :: (ERRealBase b, DomainBox box varid Int, Ord box) => ERChebPoly box b -> (ERChebPoly box b, b)

Multiply a polynomial by itself, rounding downwards and upwards.