Polynomial Factorization over Finite Fields

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Description

This lecture covers the Euclidean division in the field K[X], the Chinese Remainder Theorem, and the efficient computation of greatest common divisors of polynomials. It also introduces the Residue Number Systems and projections for polynomial factorization.

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Official source

Ontological neighbourhood

Mathematics

Algebra: Abstract algebra

Related lectures (29)

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In course

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Ontological neighbourhood

Mathematics

Algebra: Abstract algebra

Instructor

incididunt irure

Duis officia et dolore eu ex eu eu magna. Occaecat amet proident velit sit occaecat minim eiusmod dolor ullamco dolore aute enim excepteur. Ut in laborum voluptate consectetur amet.

Related lectures (29)

Polynomial Factorization: Field Approach

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

Polynomials: Roots and Factorization

Explores polynomial roots, factorization, and the Euclidean algorithm in depth.

Polynomial Methods: GCD Calculation Summary

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

Factoring Polynomials: Complexity and Algorithms

Delves into the complexity of factoring polynomials and the implications for security.

Euclidean Algorithm

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