Polynomials | Field (mathematics)
In mathematics, a polynomial P(X) over a given field K is separable if its roots are distinct in an algebraic closure of K, that is, the number of distinct roots is equal to the degree of the polynomial. This concept is closely related to square-free polynomial. If K is a perfect field then the two concepts coincide. In general, P(X) is separable if and only if it is square-free over any field that contains K,which holds if and only if P(X) is coprime to its formal derivative DโP(X). (Wikipedia).
Is it a monomial, binomial, trinomial, or polynomial
๐ Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials
Is it a polynomial with two variables
๐ 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?
Summary for classifying polynomials
๐ Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials
๐ Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials
Galois theory: Separable extensions
This lecture is part of an online graduate course on Galois theory. We define separable algebraic extensions, and give some examples of separable and non-separable extensions. At the end we briefly discuss purely inseparable extensions.
From playlist Galois theory
FIT3.1.1. Roots of Polynomials
Field Theory: We recall basic factoring results for polynomials from Ring Theory and give a definition of a splitting field. This allows one to consider any irreducible polynomial as a set of roots, and in turn we consider when an irreducible polynomial can have multiple roots. We finish
From playlist Abstract Algebra
Calculus 1 Lecture 1.2 Part 2: Properties of Limits. Techniques of Limit Computation
From playlist Calculus 1 Playlist 1
Daniel Bertrand: Generalized Jacobians and Pellian polynomials
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Number Theory
How to determine if a term is a monomial or not
๐ Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials
Learn how to write a polynomial in standard form and classify
๐ Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
Haotian Jiang: Minimizing Convex Functions with Integral Minimizers
Given a separation oracle SO for a convex function f that has an integral minimizer inside a box with radius R, we show how to find an exact minimizer of f using at most โข O(n(n + log(R))) calls to SO and poly(n,log(R)) arithmetic operations, or โข O(nlog(nR)) calls to SO and exp(O(n)) ยท po
From playlist Workshop: Continuous approaches to discrete optimization
Thieu Vo, Ton Duc Thang University
April 2, Thieu Vo, Ton Duc Thang University Rational solutions of first-order algebraic difference equations
From playlist Spring 2021 Online Kolchin Seminar in Differential Algebra
Monotone Arithmetic Circuit Lower Bounds Via Communication Complexity - Arkadev Chattopadhyay
Computer Science/Discrete Mathematics Seminar I Topic: Monotone Arithmetic Circuit Lower Bounds Via Communication Complexity Speaker: Arkadev Chattopadhyay Affiliation: Tata Institute of Fundamental Research Date: February 15, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Sarah Post: Rational extensions of superintegrable systems, exceptional polynomials & Painleve eq.s
Abstract: In this talk, I will discuss recent work with Ian Marquette and Lisa Ritter on superintegable extensions of a Smorodinsky Winternitz potential associated with exception orthogonal polynomials (EOPs). EOPs are families of orthogonal polynomials that generalize the classical ones b
From playlist Integrable Systems 9th Workshop
Introduction to Spherical Harmonics
Using separation of variables in spherical coordinates, we arrive at spherical harmonics.
From playlist Quantum Mechanics Uploads
Classify a polynomial and determine degree and leading coefficient
๐ Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
Classify a polynomial and determine degree and leading coefficient
๐ Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
Classify a polynomial and determine degree and leading coefficient
๐ Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
Nijenhuis geometry for ECRs: Pre-recorded Lecture 2 Part A
Pre-recorded Lecture 2 Part A: Nijenhuis geometry for ECRs Date: 9 February 2022 Lecture slides: https://mathematical-research-institute.sydney.edu.au/wp-content/uploads/2022/02/Prerecorded_Lecture2.pdf ---------------------------------------------------------------------------------------
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems
Classify a polynomial and determine degree and leading coefficient
๐ Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations