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

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

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.

Mathematical Operations on Rational Functions.

Operations for Regrouping Terms of Rational Functions.

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