Commutative algebra | Algebraic geometry

Quasi-homogeneous polynomial

In algebra, a multivariate polynomial is quasi-homogeneous or weighted homogeneous, if there exist r integers , called weights of the variables, such that the sum is the same for all nonzero terms of f. This sum w is the weight or the degree of the polynomial. The term quasi-homogeneous comes from the fact that a polynomial f is quasi-homogeneous if and only if for every in any field containing the coefficients. A polynomial is quasi-homogeneous with weights if and only if is a homogeneous polynomial in the . In particular, a homogeneous polynomial is always quasi-homogeneous, with all weights equal to 1. A polynomial is quasi-homogeneous if and only if all the belong to the same affine hyperplane. As the Newton polytope of the polynomial is the convex hull of the set the quasi-homogeneous polynomials may also be defined as the polynomials that have a degenerate Newton polytope (here "degenerate" means "contained in some affine hyperplane"). (Wikipedia).

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Differential Equations | Homogeneous linear equations with constant coefficients

We introduce the strategy used for solving homogeneous linear differential equations with constant coefficients.

From playlist Linear Differential Equations

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From playlist Dualities in Topology and Algebra (Online)

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Felix Otto: The structure group revisited

CIRM VIRTUAL EVENT Recorded during the meeting "Pathwise Stochastic Analysis and Applications" the March 09, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematician

From playlist Virtual Conference

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From playlist Étale cohomology and the Weil conjectures

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Summary for classifying polynomials

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From playlist Research Spotlight

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From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"

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Loïc FOISSY - Cointeracting Bialgebras

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From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday

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Field (mathematics) | Convex hull | Newton polygon | Algebra | Homogeneous polynomial | Commutative ring