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PARI/GP is a computer algebra system that facilitates number-theory computation. Besides support of factoring, algebraic number theory, and analysis of elliptic curves, it works with mathematical objects like matrices, polynomials, power series, algebraic numbers, and transcendental functions. [3]
Euler Math Toolbox originated in 1988 as a program for Atari ST. At that time, the title of the program was simply Euler, but it turned out to be too unspecific for the Internet. The main aim of the program was to create a tool for testing numerical algorithms, to visualize results, and to demonstrate mathematical content in the classroom.
In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than 10 100. Heuristically, its complexity for factoring an integer n (consisting of ⌊log 2 n ⌋ + 1 bits) is of the form
Shogun, an open-source large-scale machine-learning toolbox that provides several SVM implementations (like libSVM, SVMlight) under a common framework and interfaces to Octave, MATLAB, Python, R; Waffles is a free-software collection of command-line tools designed for scripting machine-learning operations in automated experiments and processes.
Mastering symbolic math was a herculean task; but numerical capabilities were critical to get a piece of the much larger engineering and lower-end scientific markets. At MIT Macsyma had a link to the IMSL (now a product of Perforce Software ) numerical libraries, but this link was severed when Macsyma moved to Symbolics.
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Fermat's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares: =. That difference is algebraically factorable as (+) (); if neither factor equals one, it is a proper factorization of N.
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