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In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers ; they may be taken in any field K .
Go: the standard library package math/big implements arbitrary-precision integers (Int type), rational numbers (Rat type), and floating-point numbers (Float type) Guile: the built-in exact numbers are of arbitrary precision. Example: (expt 10 100) produces the expected (large) result. Exact numbers also include rationals, so (/ 3 4) produces 3/4.
Laplace solved this problem for the case of rational functions, as he showed that the indefinite integral of a rational function is a rational function and a finite number of constant multiples of logarithms of rational functions [citation needed]. The algorithm suggested by Laplace is usually described in calculus textbooks; as a computer ...
Dirichlet function: is an indicator function that matches 1 to rational numbers and 0 to irrationals. It is nowhere continuous. Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function.
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.
Rational functions can be either finite or infinite for finite values, or finite or infinite for infinite x values. Thus, rational functions can easily be incorporated into a rational function model. Rational function models can often be used to model complicated structure with a fairly low degree in both the numerator and denominator.
Henri Padé. In mathematics, a Padé approximant is the "best" approximation of a function near a specific point by a rational function of given order. Under this technique, the approximant's power series agrees with the power series of the function it is approximating.
Rational functions are quotients of two polynomial functions, and their domain is the real numbers with a finite number of them removed to avoid division by zero. The simplest rational function is the function , whose graph is a hyperbola, and whose domain is the whole real line except for 0.