 Rational Polynomials (Rational Functions) - Maple Programming Help

Rational Polynomials (Rational Functions)

Description

 • In Maple rational functions are created from names, integers, and other Maple values for the coefficients using the arithmetic operators +, -, *, /, and ^. For example:  7+x/(x^4-3*x+1)  creates the rational function

$7+\frac{x}{{x}^{4}-3x+1}$

 • It is a rational function in the variable x over the field of rational numbers.  Multivariate rational functions, and rational functions over other number rings and fields are constructed similarly. For example:  y^3/x/(sqrt(-1)*y+y/2)  creates

$\frac{{y}^{3}}{x\left(Iy+\frac{y}{2}\right)}$

 • a rational function in the variables x and y whose coefficients involve the imaginary number i which is denoted by capital I in Maple.
 • This remainder of this file contains a list of operations which are available for rational functions. Note: many of the functions and operations described in the help page for polynom apply to the rational function case.
 • Utility Functions for Manipulating Rational Functions.

 denom extract the denominator of a rational function normal normal form for rational functions numer extract the numerator of a rational function subs evaluate a rational function

 • Mathematical Operations on Rational Functions.

 asympt asymptotic series expansion diff differentiate a rational function int integrate a rational function (indefinite/definite integration) limit compute a limit of a rational function sum sum a rational function (indefinite or definite summation) series general power series expansion taylor Taylor series expansion

 • Operations for Regrouping Terms of Rational Functions.

 collect group coefficients of like terms together confrac convert a series or rational function to a continued fraction horner convert all polynomial subexpressions to horner form factor factor the numerator and denominator parfrac partial fraction expansion of a rational function ratpoly convert a series to a rational function (Pade approximation) sort sort all polynomial subexpressions

 • The type function can be used to test for rational polynomials. For example the test  type(a, ratpoly(integer, x)) tests whether the expression $a$ is a rational polynomial in the variable x with integer coefficients.  See type/ratpoly for further details.