Lecture

Polynomials: Roots and Factorization

Related lectures (30)

Covers the theory and operations related to polynomials, including ideals, minimal polynomials, irreducibility, and factorization.

Ideals: Polynomials and Definitions

Explores ideals in K[X], including PGCD, uniqueness, coprimality, and theorems of Bézout and Gauss.

Polynomial Factorization: Field Approach

Covers the factorization of polynomials over a field, including division with remainder and common divisors.

Euclidean Algorithm

Explains the Euclidean algorithm for polynomials over a field K, illustrating its application with examples.

Polynomial Methods: GCD Calculation Summary

Covers the calculation of the greatest common divisor using polynomial methods and the Euclidean algorithm.

Complex Roots and Polynomials

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.

Polynomial Factorization over Finite Fields

Introduces polynomial factorization over finite fields and efficient computation of greatest common divisors of polynomials.

Division Euclidienne: Exemples

Explains the Euclidean division of polynomials and demonstrates its application through examples and root-based divisibility.

Factorisation: Real Coefficients Examples

Covers the factorization of polynomials with real coefficients in the complex domain, demonstrating how to find complex roots and obtain irreducible factors.

Complex Polynomials and Factorization

Explores complex polynomials, factorization, roots of equations, equilateral triangles, and infinite sums in sequences.

Complex Numbers: Operations and Applications

Explores complex number properties, roots, and polynomial equations in the complex plane.

Number Theory: GCD and LCM

Covers GCD, LCM, and the Euclidean algorithm for efficient computation of GCD.

Polynomials: Definition and Operations

Covers polynomials, their operations, division theorem, and provides illustrative examples.

Finite Fields: Properties and Applications

Explores the properties and applications of finite fields, including isomorphism and cyclic properties.

Polynomial Factorization and Decomposition

Covers polynomial factorization, irreducible polynomials, ideal decomposition, and the theorem of Bézout.

Chinese Remainder Theorem: Rings and Fields

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

Properties of Euclidean Domains

Covers the properties of Euclidean domains and irreducible elements in polynomial rings.

Properties of Euclidean Domains

Explores the properties of Euclidean domains, including gcd, lcm, and the Chinese remainder theorem for polynomial rings.

Number Theory: GCD and LCM

Covers GCD, LCM, and the Euclidean algorithm for efficient computation.

Polynomial Equations: Solving Methods

Covers various methods for solving polynomial equations through examples.