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Software

MikTeX — is an up-to-date TeX implementation for the Windows operating system.
TeX is a typesetting system written by Donald E. Knuth, who says that it is "intended for the creation of beautiful books — and especially for books that contain a lot of mathematics".
http://www.miktex.org/
Magma — The Computational Algebra System for Algebra, Number Theory and Geometry
Magma is a large, well-supported software package designed to solve computationally hard problems in algebra, number theory, geometry and combinatorics. It provides a mathematically rigorous environment for computing with algebraic, number-theoretic, combinatoric and geometric objects.
http://magma.maths.usyd.edu.au/magma/
PARI/GP is a widely used computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves...), but also contains a large number of other useful functions to compute with mathematical entities such as matrices, polynomials, power series, algebraic numbers etc., and a lot of transcendental functions. PARI is also available as a C library to allow for faster computations.
http://pari.math.u-bordeaux.fr/
GAP — Groups, Algorithms, Programming — a System for Computational Discrete Algebra
GAP is a system for computational discrete algebra, with particular emphasis on Computational Group Theory. GAP provides a programming language, a library of thousands of functions implementing algebraic algorithms written in the GAP language as well as large data libraries of algebraic objects. GAP is used in research and teaching for studying groups and their representations, rings, vector spaces, algebras, combinatorial structures, and more. The system, including source, is distributed freely. You can study and easily modify or extend it for your special use.
http://www-gap.dcs.st-and.ac.uk/
GNU Octave is a high-level interpreted language, primarily intended for numerical computations. It provides capabilities for the numerical solution of linear and nonlinear problems, and for performing other numerical experiments. It also provides extensive graphics capabilities for data visualization and manipulation. Octave is normally used through its interactive command line interface, but it can also be used to write non-interactive programs. The Octave language is quite similar to Matlab so that most programs are easily portable.
http://www.gnu.org/software/octave


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