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  2. Greatest common divisor - Wikipedia

    en.wikipedia.org/wiki/Greatest_common_divisor

    If one uses the Euclidean algorithm and the elementary algorithms for multiplication and division, the computation of the greatest common divisor of two integers of at most n bits is O(n 2). This means that the computation of greatest common divisor has, up to a constant factor, the same complexity as the multiplication.

  3. Euclidean algorithm - Wikipedia

    en.wikipedia.org/wiki/Euclidean_algorithm

    The greatest common divisor g is the largest natural number that divides both a and b without leaving a remainder. Synonyms for GCD include greatest common factor (GCF), highest common factor (HCF), highest common divisor (HCD), and greatest common measure (GCM).

  4. Polynomial greatest common divisor - Wikipedia

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

    In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor of both the two original polynomials. This concept is analogous to the greatest common divisor of two integers.

  5. Extended Euclidean algorithm - Wikipedia

    en.wikipedia.org/wiki/Extended_Euclidean_algorithm

    In computer algebra, the polynomials commonly have integer coefficients, and this way of normalizing the greatest common divisor introduces too many fractions to be convenient. The second way to normalize the greatest common divisor in the case of polynomials with integer coefficients is to divide every output by the content of r k ...

  6. Binary GCD algorithm - Wikipedia

    en.wikipedia.org/wiki/Binary_GCD_algorithm

    Visualisation of using the binary GCD algorithm to find the greatest common divisor (GCD) of 36 and 24. Thus, the GCD is 2 2 × 3 = 12.. The binary GCD algorithm, also known as Stein's algorithm or the binary Euclidean algorithm, [1] [2] is an algorithm that computes the greatest common divisor (GCD) of two nonnegative integers.

  7. Bézout's identity - Wikipedia

    en.wikipedia.org/wiki/Bézout's_identity

    Here the greatest common divisor of 0 and 0 is taken to be 0.The integers x and y are called Bézout coefficients for (a, b); they are not unique.A pair of Bézout coefficients can be computed by the extended Euclidean algorithm, and this pair is, in the case of integers one of the two pairs such that | x | ≤ | b/d | and | y | ≤ | a/d |; equality occurs only if one of a and b is a multiple ...

  8. Gröbner basis - Wikipedia

    en.wikipedia.org/wiki/Gröbner_basis

    where gcd denotes the greatest common divisor of the leading monomials of f and g. As the monomials that are reducible by both f and g are exactly the multiples of lcm, one can deal with all cases of non-uniqueness of the reduction by considering only the S-polynomials. This is a fundamental fact for Gröbner basis theory and all algorithms for ...

  9. List of mathematical abbreviations - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical...

    gcd – greatest common divisor of two numbers. (Also written as hcf.) gd – Gudermannian function. GF – Galois field. GF – generating function. GL – general linear group. G.M. – geometric mean. glb – greatest lower bound. (Also written as inf.) G.P. – geometric progression. grad – gradient of a function. graph – graph of a ...

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