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2. Quadratic sieve - Wikipedia

   en.wikipedia.org/wiki/Quadratic_sieve

   The quadratic sieve attempts to find pairs of integers x and y(x) (where y(x) is a function of x) satisfying a much weaker condition than x 2 ≡ y 2 (mod n). It selects a set of primes called the factor base , and attempts to find x such that the least absolute remainder of y ( x ) = x 2 mod n factorizes completely over the factor base.

3. UBASIC - Wikipedia

   en.wikipedia.org/wiki/UBASIC

   The ppmpx36e version of the multi-polynomial quadratic sieve needs 8.8F and Windows. Some versions of UBASIC came with a defective UBCONST7.DAT file. You should check yours against the one supplied in 8.8F. If it is not identical then you should switch. UBASIC is available for IBM PC/AT and compatibles; NEC PC-9801; NEC PC-H98; Fujitsu FM-R ...

4. Fast Library for Number Theory - Wikipedia

   en.wikipedia.org/wiki/Fast_Library_for_Number_Theory

   The two major areas of functionality currently implemented in FLINT are polynomial arithmetic over the integers and a quadratic sieve. The library is designed to be compiled with the GNU Multi-Precision Library (GMP) and is released under the GNU General Public License.

5. Magma (computer algebra system) - Wikipedia

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

   Integer factorization algorithms include the Elliptic Curve Method, the Quadratic sieve and the Number field sieve. Algebraic number theory; Magma includes the KANT computer algebra system for comprehensive computations in algebraic number fields. A special type also allows one to compute in the algebraic closure of a field. Module theory and ...

6. HiGHS optimization solver - Wikipedia

   en.wikipedia.org/wiki/HiGHS_optimization_solver

   HiGHS is open-source software to solve linear programming (LP), mixed-integer programming (MIP), and convex quadratic programming (QP) models. [1] Written in C++ and published under an MIT license, HiGHS provides programming interfaces to C, Python, Julia, Rust, JavaScript, Fortran, and C#. It has no external dependencies.

7. General number field sieve - Wikipedia

   en.wikipedia.org/wiki/General_number_field_sieve

   The principle of the number field sieve (both special and general) can be understood as an improvement to the simpler rational sieve or quadratic sieve. When using such algorithms to factor a large number n, it is necessary to search for smooth numbers (i.e. numbers with small prime factors) of order n 1/2.