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

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

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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.

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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.

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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

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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

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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

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.

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