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

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

Implementation of safely rounded integration of polynomials and other related functions.

Documentation

chplIntegrate

Arguments

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

=> varid

variable to integrate by

-> ERChebPoly box b

-> (ERChebPoly box b, ERChebPoly box b)

Approximate from below and from above the integral of a polynomial.

Based on the following formulas for Chebyshev polynomials:

     \int T_n(x)dx = 
        T_{n+1}(x)/2(n+1) - T_{n-1}(x)/2(n-1)

     \int T_1(x)dx = 
        T_2(x)/4 + 1/4

     \int T_0(x)dx = 
        T_1(x)

chplVolumeAboveZero :: (ERRealBase b, DomainBox box varid Int, Ord box, DomainBoxMappable boxb boxbb varid b [(b, b)]) => [varid] -> ERChebPoly box b -> (b, b)

measure the volume between a polynomial and the zero axis on [-1,1]^n

chplDifferentiate

Arguments

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

=> ERChebPoly box b

-> varid

variable to differentiate over

-> ERChebPoly box b

Differentiate a polynomial using one of its variables.