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Rational Polynomials (Rational Functions)
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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^4-3*x+1) creates the rational function
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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
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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.
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denom
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extract the denominator of a rational function
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normal
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normal form for rational functions
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numer
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extract the numerator of a rational function
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subs
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evaluate a rational function
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Mathematical Operations on Rational Functions.
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asympt
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asymptotic series expansion
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diff
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differentiate a rational function
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int
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integrate a rational function (indefinite/definite integration)
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limit
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compute a limit of a rational function
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sum
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sum a rational function (indefinite or definite summation)
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series
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general power series expansion
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taylor
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Taylor series expansion
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Operations for Regrouping Terms of Rational Functions.
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collect
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group coefficients of like terms together
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confrac
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convert a series or rational function to a continued fraction
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see convert[confrac]
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horner
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convert all polynomial sub-expressions to horner form
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see convert[horner]
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factor
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factor the numerator and denominator
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parfrac
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partial fraction expansion of a rational function
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see convert[parfrac]
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ratpoly
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convert a series to a rational function (Pade approximation)
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see convert[ratpoly]
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sort
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sort all polynomial sub-expressions
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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  is a rational polynomial in the variable x with integer coefficients. See type[ratpoly] for further details.
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Download Help Document
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