Rational Polynomials (Rational Functions)

Description


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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^43*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

$\frac{{y}^{3}}{x\left(\mathrm{I}y\+\frac{1}{2}y\right)}$
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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


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



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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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