In mathematics, a monomial order (sometimes called a term order or an admissible order) is a total order on the set of all (monic) monomials in a given polynomial ring, satisfying the property of respecting multiplication, i.e., * If and is any other monomial, then . Monomial orderings are most commonly used with Gröbner bases and multivariate division. In particular, the property of being a Gröbner basis is always relative to a specific monomial order. (Wikipedia).
What is the definition of a monomial and polynomials with examples
👉 Learn how to classify polynomials based on the number of terms as well as the leading coefficient and the degree. When we are classifying polynomials by the number of terms we will focus on monomials, binomials, and trinomials, whereas classifying polynomials by the degree will focus on
From playlist Classify Polynomials
This video explains how to multiply monomials. http://mathispower4u.com
From playlist Multiplying Polynomials
Categories 6 Monoidal categories
This lecture is part of an online course on categories. We define strict monoidal categories, and then show how to relax the definition by introducing coherence conditions to define (non-strict) monoidal categories. We finish by defining symmetric monoidal categories and showing how super
From playlist Categories for the idle mathematician
Determine the leading coefficient and degree of a monomial
👉 Learn how to classify polynomials based on the number of terms as well as the leading coefficient and the degree. When we are classifying polynomials by the number of terms we will focus on monomials, binomials, and trinomials, whereas classifying polynomials by the degree will focus on
From playlist Find the leading coefficient and degree of a polynomial | expression
Geometry of Frobenioids - part 2 - (Set) Monoids
This is an introduction to the basic properties of Monoids. This video intended to be a starting place for log-schemes, Mochizuki's IUT or other absolute geometric constructions using monoids.
From playlist Geometry of Frobenioids
Nonlinear algebra, Lecture 1: "Polynomials, Ideals, and Groebner Bases", by Bernd Sturmfels
This is the first lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences. Topics covered: polynomilas, ideals and Groebner bases.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Is it a monomial, binomial, trinomial, or polynomial
👉 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
Resolution of singularities of complex algebraic varieties – D. Abramovich – ICM2018
Algebraic and Complex Geometry Invited Lecture 4.13 Resolution of singularities of complex algebraic varieties and their families Dan Abramovich Abstract: We discuss Hironaka’s theorem on resolution of singularities in charactetistic 0 as well as more recent progress, both on simplifying
From playlist Algebraic & Complex Geometry
MAG - Lecture 3 - Monomial orderings
metauni Algebraic Geometry (MAG) is a first course in algebraic geometry, in Roblox. In Lecture 3 we introduce monomial orderings, and some examples that suggest how monomial orderings control the division process. The webpage for MAG is https://metauni.org/mag/. This video was recorded
From playlist MAG
How to Multiply Two Monomials by a Trinomial and Binomial
👉 Learn how to multiply polynomials. We apply the distributive property to polynomials by multiplying a monomial to every term in a polynomial. When multiplying monomials it is important that we multiply the coefficients and apply the rules of exponents to add the powers of each variable.
From playlist How to Multiply Polynomials
MAG - Lecture 5 - Dickson's Lemma
metauni Algebraic Geometry (MAG) is a first course in algebraic geometry, in Roblox. In Lecture 5 we study monomial ideals and Dickson's Lemma, which says that any monomial ideal is finitely generated. The webpage for MAG is https://metauni.org/mag/. This video was recorded in The Rising
From playlist MAG
Polynomial Division: Dividing by a Monomial
This is 1 of 3 videos on Polynomial Division http://mathispower4u.wordpress.com/
From playlist Polynomial Operations
Romanos Malikiosis: Full spark Gabor frames in finite dimensions
Romanos Malikiosis: Full spark Gabor frames in finite dimensions Abstract: The lecture was held within the framework of the Hausdorff Trimester Program Mathematics of Signal Processing. Gabor frame is the set of all time-frequency translates of a complex function and is a fundamental too
From playlist HIM Lectures: Trimester Program "Mathematics of Signal Processing"
P. Salberger - Quantitative aspects of rational points on algebraic varieties (part3)
Let X be a subvariety of Pn defined over a number field and N(B) be the number of rational points of height at most B on X. There are then general conjectures of Manin on the asymptotic behaviour of N(B) when B goes to infinity. These conjectures can be studied using the Hardy-Littlewood m
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
SLT Supplemental - Seminar 5 - Polynomial division
This series provides supplemental mathematical background material for the seminar on Singular Learning Theory. In this seminar Spencer Wong introduces polynomial division as preparation for talking about Gröbner bases. The webpage for this seminar is http://metauni.org/posts/events/semin
From playlist Singular Learning Theory
Elisa Gorla: Complexity of Groebner bases computations and applications to cryptography - lecture 1
CIRM VIRTUAL EVENT Recorded during the meeting "French Computer Algebra Days" the March 02, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audio
From playlist Virtual Conference
Title: Sparse Resultant Formulas for Differential Polynomials
From playlist Spring 2014
MAG - Lecture 7 - The Buchberger Criterion
metauni Algebraic Geometry (MAG) is a first course in algebraic geometry, in Roblox. In Lecture 7 we prove the Buchberger criterion, which allows us to recognise Grobner bases for ideals by looking at S-polynomials. The webpage for MAG is https://metauni.org/mag/. This video was recorded
From playlist MAG