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  2. Algebraic-group factorisation algorithm - Wikipedia

    en.wikipedia.org/wiki/Algebraic-group...

    If the algebraic group is the multiplicative group mod N, the one-sided identities are recognised by computing greatest common divisors with N, and the result is the p − 1 method. If the algebraic group is the multiplicative group of a quadratic extension of N, the result is the p + 1 method; the calculation involves pairs of numbers modulo N.

  3. 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.

  4. Factorization of polynomials - Wikipedia

    en.wikipedia.org/wiki/Factorization_of_polynomials

    In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain. Polynomial factorization is one of the fundamental components of computer algebra systems.

  5. Exercise (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Exercise_(mathematics)

    Later most exercises involve at least two digits. A common exercise in elementary algebra calls for factorization of polynomials. Another exercise is completing the square in a quadratic polynomial. An artificially produced word problem is a genre of exercise intended to keep mathematics relevant. Stephen Leacock described this type: [1]

  6. Difference of two squares - Wikipedia

    en.wikipedia.org/wiki/Difference_of_two_squares

    The formula for the difference of two squares can be used for factoring polynomials that contain the square of a first quantity minus the square of a second quantity. For example, the polynomial x 4 − 1 {\displaystyle x^{4}-1} can be factored as follows:

  7. Integer factorization - Wikipedia

    en.wikipedia.org/wiki/Integer_factorization

    Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem. To factorize a small integer n using mental or pen-and-paper arithmetic, the simplest method is trial division : checking if the number is divisible by prime numbers 2 ...

  8. Matrix decomposition - Wikipedia

    en.wikipedia.org/wiki/Matrix_decomposition

    In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems.

  9. Factorization of polynomials over finite fields - Wikipedia

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

    In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors.This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm.

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