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  2. Factorization of polynomials over finite fields - Wikipedia

    en.wikipedia.org/wiki/Factorization_of...

    Polynomial factoring algorithms use basic polynomial operations such as products, divisions, gcd, powers of one polynomial modulo another, etc. A multiplication of two polynomials of degree at most n can be done in O(n 2) operations in F q using "classical" arithmetic, or in O(nlog(n) log(log(n)) ) operations in F q using "fast" arithmetic.

  3. Greatest common divisor - Wikipedia

    en.wikipedia.org/wiki/Greatest_common_divisor

    This means that the computation of greatest common divisor has, up to a constant factor, the same complexity as the multiplication. However, if a fast multiplication algorithm is used, one may modify the Euclidean algorithm for improving the complexity, but the computation of a greatest common divisor becomes slower than the multiplication.

  4. Factorization of polynomials - Wikipedia

    en.wikipedia.org/wiki/Factorization_of_polynomials

    Modern algorithms and computers can quickly factor univariate polynomials of degree more than 1000 having coefficients with thousands of digits. [3] For this purpose, even for factoring over the rational numbers and number fields, a fundamental step is a factorization of a polynomial over a finite field.

  5. Polynomial greatest common divisor - Wikipedia

    en.wikipedia.org/wiki/Polynomial_greatest_common...

    Factoring polynomials can be difficult, especially if the polynomials have a large degree. The Euclidean algorithm is a method that works for any pair of polynomials. It makes repeated use of Euclidean division. When using this algorithm on two numbers, the size of the numbers decreases at each stage.

  6. Pro Football Hall of Fame 2025 semifinalists include Eli ...

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    The Pro Football Hall of Fame has narrowed down its list of candidates for the class of 2025 modern era to 25 semifinalists.. Tight end Antonio Gates, who was the most notable snub from the Class ...

  7. Catholic nun among 25 arrested in mob bust in northern Italy

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    A Catholic nun with the Sisters of Charity Institute in Milan was among 25 people arrested early Thursday morning for a litany of mafia-related crimes, including aiding and abetting extortion ...

  8. Unidentified male DNA found on JonBenét’s clothes - AOL

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    The key to solving JonBenét Ramsey's murder could lie in evidence found at the scene nearly 30 years ago.. When police searched the 6-year-old’s home in Boulder, Colo., on Dec. 26, 1996, they ...

  9. Factorization - Wikipedia

    en.wikipedia.org/wiki/Factorization

    The polynomial x 2 + cx + d, where a + b = c and ab = d, can be factorized into (x + a)(x + b).. In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

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