Berlekamp's Algorithm: Polynomial Factorization

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Properties of Euclidean Domains

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

Complex Factorization Examples

Explores complex polynomial factorization examples, demonstrating the process and implications of complex roots in real polynomials.

Gaussian Lemma III: Irreducibility and Primitive Polynomials

Explains irreducibility in polynomial equations and the properties of primitive polynomials.

Complex Numbers: Roots and Equations

Explores complex numbers, roots, equations, and polynomial factorization with real coefficients.

Irreducible Polynomials and Finite Fields

Explores irreducible polynomials, finite fields, and the construction of unique finite fields from irreducible polynomials.

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.

Chinese Remainder Theorem: Rings and Fields

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

Complex Roots and Polynomials

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

Finite Fields: Construction and Properties

Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.

Polynomial Equations: Solving Methods

Covers various methods for solving polynomial equations through examples.