Meromorphic functions | Functions and mappings | Polynomials | Types of functions | Special functions | Analytic functions
In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation. Quite often algebraic functions are algebraic expressions using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power. Examples of such functions are: * * * Some algebraic functions, however, cannot be expressed by such finite expressions (this is the Abel–Ruffini theorem). This is the case, for example, for the Bring radical, which is the function implicitly defined by . In more precise terms, an algebraic function of degree n in one variable x is a function that is continuous in its domain and satisfies a polynomial equation where the coefficients ai(x) are polynomial functions of x, with integer coefficients. It can be shown that the same class of functions is obtained if algebraic numbers are accepted for the coefficients of the ai(x)'s. If transcendental numbers occur in the coefficients the function is, in general, not algebraic, but it is algebraic over the field generated by these coefficients. The value of an algebraic function at a rational number, and more generally, at an algebraic number is always an algebraic number.Sometimes, coefficients that are polynomial over a ring R are considered, and one then talks about "functions algebraic over R". A function which is not algebraic is called a transcendental function, as it is for example the case of . A composition of transcendental functions can give an algebraic function: . As a polynomial equation of degree n has up to n roots (and exactly n roots over an algebraically closed field, such as the complex numbers), a polynomial equation does not implicitly define a single function, but up to nfunctions, sometimes also called branches. Consider for example the equation of the unit circle:This determines y, except only up to an overall sign; accordingly, it has two branches: An algebraic function in m variables is similarly defined as a function which solves a polynomial equation in m + 1 variables: It is normally assumed that p should be an irreducible polynomial. The existence of an algebraic function is then guaranteed by the implicit function theorem. Formally, an algebraic function in m variables over the field K is an element of the algebraic closure of the field of rational functions K(x1, ..., xm). (Wikipedia).
Determine if a Function is a Polynomial Function
This video explains how to determine if a function is a polynomial function. http://mathispower4u.com
From playlist Determining the Characteristics of Polynomial Functions
Functions of equations - IS IT A FUNCTION
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Determining if a function is a polynomial or not then determine degree and LC
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
Learn how to identify if a function is a polynomial and identify the degree and LC
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
Abstract Algebra | Injective Functions
We give the definition of an injective function, an outline of proving that a given function is injective, and a few examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Define linear functions. Use function notation to evaluate linear functions. Learn to identify linear function from data, graphs, and equations.
From playlist Algebra 1
Classify a polynomial then determining if it is a polynomial or not
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
Determining if a equation is a polynomial or not
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
Nigel Higson: The Oka principle and Novodvorskii’s theorem
Talk by Jonathan Rosenberg in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on November 11, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
From continuous rational to regulous functions – Krzysztof Kurdyka & Wojciech Kucharz – ICM2018
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Guy Casale, University of Rennes
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From playlist Spring 2021 Online Kolchin Seminar in Differential Algebra
Duality in Algebraic Geometry by Suresh Nayak
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
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The Drinfeld-Sokolov reduction of admissible representations of affine Lie algebras - Gurbir Dhillon
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From playlist Mathematics
Nigel Higson: Real reductive groups, K-theory and the Oka principle
The lecture was held within the framework of Follow-up Workshop TP Rigidity. 29.4.2015
From playlist HIM Lectures 2015
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This talk was the introduction to the Berkeley graduate number theory discussion seminar on 2020-10-28, and the aim was to explain why number theorists might be interested in sporadic simple groups. We give a brief summary of monstrous moonshine relating sporadic groups to modular functi
From playlist Math talks
Richard Gustavson, Manhattan College
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From playlist Spring 2022 Online Kolchin seminar in Differential Algebra
MAST30026 Lecture 16: Stone-Weierstrass theorem (Part 2)
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From playlist MAST30026 Metric and Hilbert spaces
SHM - 16/01/15 - Constructivismes en mathématiques - Frédéric Brechenmacher
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From playlist Les constructivismes mathématiques - Séminaire d'Histoire des Mathématiques
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👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?