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2. Magma (computer algebra system) - Wikipedia

   en.wikipedia.org/wiki/Magma_(computer_algebra...

   Magma contains asymptotically fast algorithms for all fundamental integer and polynomial operations, such as the Schönhage–Strassen algorithm for fast multiplication of integers and polynomials. Integer factorization algorithms include the Elliptic Curve Method , the Quadratic sieve and the Number field sieve .

3. 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++.

4. 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.

5. 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.

6. 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 ...

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. 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.

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 ...