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  2. Xcas - Wikipedia

    en.wikipedia.org/wiki/Xcas

    Xcas is a user interface to Giac, which is an open source [2] computer algebra system (CAS) for Windows, macOS and Linux among many other platforms. Xcas is written in C++ . [ 3 ] Giac can be used directly inside software written in C++.

  3. Microsoft Math Solver - Wikipedia

    en.wikipedia.org/wiki/Microsoft_Math_Solver

    Microsoft Math Solver (formerly Microsoft Mathematics and Microsoft Math) is an entry-level educational app that solves math and science problems. Developed and maintained by Microsoft, it is primarily targeted at students as a learning tool. Until 2015, it ran on Microsoft Windows.

  4. Quadratic sieve - Wikipedia

    en.wikipedia.org/wiki/Quadratic_sieve

    A variant of the quadratic sieve is available in the MAGMA computer algebra package. It is based on an implementation of Arjen Lenstra from 1995, used in his "factoring by email" program. msieve, an implementation of the multiple polynomial quadratic sieve with support for single and double large primes, written by Jason Papadopoulos. Source ...

  5. General number field sieve - Wikipedia

    en.wikipedia.org/wiki/General_number_field_sieve

    An optimal strategy for choosing these polynomials is not known; one simple method is to pick a degree d for a polynomial, consider the expansion of n in base m (allowing digits between −m and m) for a number of different m of order n 1/d, and pick f(x) as the polynomial with the smallest coefficients and g(x) as x − m.

  6. 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.

  7. 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.

  8. Lenstra elliptic-curve factorization - Wikipedia

    en.wikipedia.org/wiki/Lenstra_elliptic-curve...

    The second-fastest is the multiple polynomial quadratic sieve, and the fastest is the general number field sieve. The Lenstra elliptic-curve factorization is named after Hendrik Lenstra. Practically speaking, ECM is considered a special-purpose factoring algorithm, as it is most suitable for finding small factors.

  9. Completing the square - Wikipedia

    en.wikipedia.org/wiki/Completing_the_square

    Given a quadratic polynomial of the form + the numbers h and k may be interpreted as the Cartesian coordinates of the vertex (or stationary point) of the parabola. That is, h is the x -coordinate of the axis of symmetry (i.e. the axis of symmetry has equation x = h ), and k is the minimum value (or maximum value, if a < 0) of the quadratic ...