Rational Polynomials (Rational Functions)
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.
extract the denominator of a rational function
normal form for rational functions
extract the numerator of a rational function
evaluate a rational function
Mathematical Operations on Rational Functions.
asymptotic series expansion
differentiate a rational function
integrate a rational function (indefinite/definite integration)
compute a limit of a rational function
sum a rational function (indefinite or definite summation)
general power series expansion
Taylor series expansion
Operations for Regrouping Terms of Rational Functions.
group coefficients of like terms together
convert a series or rational function to a continued fraction
convert all polynomial subexpressions to horner form
factor the numerator and denominator
partial fraction expansion of a rational function
convert a series to a rational function (Pade approximation)
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.
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