Polynomials: Rings and Operations

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Related lectures (32)

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Polynomials on a Field: Basics and Operations

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Polynomials, Division, and Ideals

Explores polynomials, their operations, and the concept of ideals in polynomial rings.

Polynomials: Definitions and Operations

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

Analyse 2: Division euclidienne

Explores the process of division euclidienne in polynomials, emphasizing the importance of polynomial degrees during operations.

Linear Algebra: Abstract Concepts

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Stein Algorithm: Polynomial Identity Testing

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

Chinese Remainder Theorem: Rings and Fields

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Ring Structure: Polynomials and Coefficients

Covers the ring structure, focusing on polynomials and coefficients, including associativity, distributivity, and the product of rings.

Linear Combinations and Vector Spaces

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Polynomial Identity Testing

Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.