Rational Function Toolbox

A collection of functions for applying polynomial and rational functions to common problems

laurent(N,D) computes principle Laurent series about its poles

polyComp(p1,p2,...) composes polynomials in the order provided

polyDiffInt(p,d) performs polynomial differentiation and integration

polyInterp(x,f) generates the simplest polynomial function defined by its derivatives at various points

polyMod(p,m) finds a reduction of the given polynomial with respect to a polynomial modulus

polyMult(p1,p2,...) performs vector convolutions for polynomial multiplication

polyReduc(p,r) divides out roots from polynomials

polyRoots(p,tol) computes polynomial roots to arbitrary precision

polyShorten(p) eliminates leading zeros from polynomials

ratApprox(x,f) generates rational approximations using Chebeshev nodes

ratComp(n1,d1,n2,d2,...) composes rational function in the order provided

ratDiff(n,d,m) performs differentiation on rational functions

ratInterp(x,f,asym) generates the simplest interpolating rational function with given asymptotic degree

ratShorten(N,D) eliminates leading zeros from rational functions

ratSimplify(n,d) eliminates common factors in the numerator and denominator of a rational function

ratval(N,D,x) evaluates rational functions