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ILOG CPLEX
ILOG CPLEX is an environment for optimization problems. ILOG CPLEX algorithms can be accessed from the CPLEX Component Libraries as well as the CPLEX Interactive Optimizer, an easy-to-use interactive program. CPLEX provides all the basic features and utilities for using these solvers: sophisticated problem preprocessing; file reading and writing utilities; reporting; messaging control; interactive revision capability; efficient restart from an advanced basis; sensitivity analysis; and an infeasibility finder.
More informationLiE
LiE is the name of a software package that enables mathematicians and physicists to perform computations of a Lie group theoretic nature. It focuses on the representation theory of complex semisimple (reductive) Lie groups and algebras, and on the structure of their Weyl groups and root systems. LiE does not compute directly with elements of the Lie groups and algebras themselves; it rather computes with weights, roots, characters and similar objects.
More informationLinBox
LinBox is a C++ template library for exact, high-performance linear algebra computation with dense, sparse, and structured matrices over the integers and over finite fields. LinBox has the following top-level functions: solve linear system, matrix rank, determinant, minimal polynomial, characteristic polynomial, Smith normal form and trace. A good collection of finite field and ring implementations is provided, for use with numerous black box matrix storage schemes.
More informationMuPad
MuPAD is a mathematical expert system for doing symbolic and exact algebraic computations as well as numerical calculations with almost arbitrary accuracy. For example, the number of significant digits can be chosen freely. Apart from a vast variety of mathematical libraries the system provides tools for high quality visualization of 2- and 3-dimensional objects. On Microsoft Windows, Apple Macintosh and Linux systems, MuPAD offers a flexible notebook concept for creating mathematical documents combining texts, graphics, formulas, computations and mathematical visualizations and animations. On Microsoft Windows MuPAD further supports the technologies OLE, ActiveX Automation, DCOM, RTF and HTML. Thus it offers a natural integration in Office applications like Word or PowerPoint as well as others.
More informationScilab
Scilab is a numerical computation system similiar to Matlab or Simulink. Scilab includes hundreds of mathematical functions, and programs from various languages (such as C or Fortran) can be added interactively. It has sophisticated data structures (including lists, polynomials, rational functions, and linear systems), an interpreter, and a high-level programming language. Scilab has been designed to be an open system where the user can define new data types and operations on these data types by using overloading. A number of toolboxes are available with the system.
More informationSYNAPS
SYNAPS (Symbolic and Numeric APplicationS) is a library developed in C++. The aim of this open source project is to provide a coherent and efficient library for symbolic and numeric computation. It implements data-structures and classes for the manipulation of basic objects, such as (dense, sparse, structured) vectors, matrices, univariate and multivariate polynomials. It also provides fundamental methods such as algebraic number manipulation tools, different types of univariate and multivariate polynomial root solvers, resultant computations, ...
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