Polynomial Methods: GCD Calculation Summary

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Euclidean Division: Uniqueness and Remainder

Explores Euclidean division for polynomials, emphasizing uniqueness of quotient and remainder.

System Equivalence

Explores system equivalence, state-space representation, transfer functions, and Euclidean rings, emphasizing unimodular matrices and their properties.

Properties of Euclidean Domains

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

Division Euclidienne: Exemples

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

Number Theory: GCD and LCM

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

Polynomials and Endomorphisms

Covers the fundamentals of polynomials, endomorphisms, division, roots, matrices, and algebraic homomorphisms.

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.

Linear Algebra: Abstract Concepts

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

Algebraic Geometry: Rings and Bodies

Explores algebraic geometry, focusing on rings, bodies, quotient rings, and irreducible polynomials.