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Everything about Rational function
Ratio of polynomial functions
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. In this case, one speaks of a rational function and a rational fraction over K. The values of the variables may be taken in any field L containing K. Then the domain of the function is the set of the values of the variables for which the denominator is not zero, and the codomain is L. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Rational functionA 5-minute orientation
- Skim a recent paper: Exploration of the Muribaculaceae Family in the Gut Microbiota: Diversity, Metabolism, and FunctionInfluential work since 2022
- Pick up a classic book: Theorie des kommunikativen HandelnsThe most-reprinted book on the subject
- Read the landmark paper: Homeostasis model assessment: insulin resistance and ?-cell function from fasting plasma glucose and insulin concentrations in manCited 26,960 times
- Go sideways: Partial fraction decompositionA closely related topic
- Go sideways: Irreducible polynomialA closely related topic
📖 Definitions
Noun Any function expressible as the quotient of two (coprime) polynomials (and which thus has poles at a finite, discrete set of points which are the roots of the denominator).
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Homeostasis model assessment: insulin resistance and ?-cell function from fasting plasma glucose and insulin concentrations in man
A rational model of function learning
Onb-function, spectrum and rational singularity
Rational Transfer Function Approximation
Rational Function Neural Network
Optimal Designs for Rational Function Regression
A Rational Basis for Function Approximation
Rational function optimization using genetic algorithms
🆕 Influential since 2022
Exploration of the Muribaculaceae Family in the Gut Microbiota: Diversity, Metabolism, and Function
Liquid–liquid phase separation drives cellular function and dysfunction in cancer
Understanding Fc function for rational vaccine design against pathogens
Rational design of disordered proteins for sequence–function investigation
Approximation types describing extensions of valuations to rational function fields
📚 Books worth reading
Theorie des kommunikativen HandelnsJürgen Habermas · 1981
Habermas and the Dialectic of ReasonDavid Ingram · 1987- 📕Software test engineering with IBM Rational functional testerDaniel Gouveia, Christopher J. Davis · 2009
- 📕Towards a rational model for the triple velocity correlations of turbulenceB. A. Younis · 1999
Théorie de l'agir communicationnelJürgen Habermas · 1987- 📕Mimarlıkta rasyonellikEbru Özeke Tökmeci · 2013
- 📕The greatest integer function in the domain of the rational numbersFolke August Ryde · 1973
- 📕Architektura racjonalnej EuropyŁukasz Wojciechowski · 2019
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Partial fraction decomposition In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the…
- Irreducible polynomial In mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials.…
- Polynomial In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the…
- Algebraically closed field In mathematics, a field F is algebraically closed if every non-constant polynomial with coefficients in F has a root in F. In other words, a field is algebraica…
- Monic polynomial In algebra, a monic polynomial is a non-zero univariate polynomial (that is, a polynomial in a single variable) in which the leading coefficient (the coefficien…
- Algebraic integer In algebraic number theory, an algebraic integer is a complex number that is integral over the integers. That is, an algebraic integer is a complex root…
- Algebraic number In mathematics, an algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients…
- Algebraic function In mathematics, an algebraic function is a function that satisfies a polynomial equation. Thus an equation of the following form holds: an(x)f(x)n+an−…