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^4-3*x+1) creates the rational function
$7+\frac{x}{{x}^{4}-3x+1}$
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
$\frac{{y}^{3}}{x\left(\mathrm{I}y+\frac{y}{2}\right)}$
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
convert
polynom
type
type/ratpoly
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