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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^4-3x+1) creates the rational function

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

•	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

$\frac{y^{3}}{x (I y + \frac{y}{2})}$

•	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
	see convert/confrac
horner	convert all polynomial subexpressions to horner form
	see convert/horner
factor	factor the numerator and denominator
parfrac	partial fraction expansion of a rational function
	see convert/parfrac
ratpoly	convert a series to a rational function (Pade approximation)
	see convert/ratpoly
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.

See Also

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