Rational Polynomials (Rational Functions)
<Text-field style="Heading 2" layout="Heading 2" bookmark="info">Description</Text-field> 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 NiMsJiIiKCIiIiomSSJ4RzYiRiUsKCokRiciIiVGJUYnISIkRiVGJSEiIkYl 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 NiMqKEkieUc2IiIiJEkieEdGJSEiIiwmKiZeIyIiIkYsRiRGLEYsRiQjRiwiIiNGKA== 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.
denomextract the denominator of a rational functionnormalnormal form for rational functionsnumerextract the numerator of a rational functionsubsevaluate a rational function
Mathematical Operations on Rational Functions. asymptasymptotic series expansiondiffdifferentiate a rational functionintintegrate a rational function (indefinite/definite integration)limitcompute a limit of a rational functionsumsum a rational function (indefinite or definite summation)seriesgeneral power series expansiontaylorTaylor series expansion
Operations for Regrouping Terms of Rational Functions. collectgroup coefficients of like terms togetherconfracconvert a series or rational function to a continued fractionsee convert/confrachornerconvert all polynomial subexpressions to horner formsee convert/hornerfactorfactor the numerator and denominatorparfracpartial fraction expansion of a rational functionsee convert/parfracratpolyconvert a series to a rational function (Pade approximation)see convert/ratpolysortsort 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 NiNJImFHNiI= is a rational polynomial in the variable x with integer coefficients. See type/ratpoly for further details. See Alsoconvertpolynomseriestypetype/ratpoly