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CASA
CASA is a special-purpose system for computational algebra and constructive algebraic geometry. The system has been developed since 1990. CASA is the ongoing product of the Computer Algebra Group at the Research Institute for Symbolic Computation (RISC-Linz), the University of Linz, Austria, under the direction of Prof. Winkler. The system is built on the kernel of the widely used computer algebra system Maple.
More informationCGAL
CGAL is a collaborative effort of several sites in Europe and Israel. The goal is to make the most important of the solutions and methods developed in computational geometry available to users in industry and academia in a C++ library. The goal is to provide easy access to useful, reliable geometric algorithms The CGAL library contains: the Kernel with geometric primitives such as points, vectors, lines, predicates for testing things such as relative positions of points, and operations such as intersections and distance calculation, the Basic Library which is a collection of standard data structures and geometric algorithms, such as convex hull in 2D/3D, (Delaunay) triangulation in 2D/3D, planar map, polyhedron, smallest enclosing circle, and multidimensional query structures, the Support Library which offers interfaces to other packages, e.g., for visualisation, and I/O, and other support facilities.
More informationCoCoA
CoCoA is a system for Computations in Commutative Algebra. It is able to perform simple and sophisticated operations on multivaraiate polynomials and on various data related to them (ideals, modules, matrices, rational functions). For example, it can readily compute Grobner bases, syzygies and minimal free resolution, intersection, division, the radical of an ideal, the ideal of zero-dimensional schemes, Poincare' series and Hilbert functions, factorization of polynomials, toric ideals. The capabilities of CoCoA and the flexibility of its use are further enhanced by the dedicated high-level programming language. For convenience, the system offers a textual interface, an Emacs mode, and a graphical user interface common to most platforms.
More informationConvex
Convex is a Maple package for convex geometry. It can deal with rational polytopes, cones and other polyhedra of arbitrary dimension. Polyhedral complexes and fans are also supported, as well as computations in face lattices. The integration into Maple makes Convex particularly suited for "applied" problems where polyhedra arise together with other mathematical structures.
More informationGAP
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. GAP is developed by international cooperation. The system, including source, is distributed freely under the terms of the GNU General Public License. You can study and easily modify or extend GAP for your special use. The current version is GAP 4, the older version GAP 3 is still available.
More informationpolymake
polymake is an object-oriented system for experimental discrete mathematics. The typical working cycle of a polymake user starts with the construction of an object of interest, auch as a convex polytope, a finite simplicial complex, a graph, etc. It is then possible to ask the system for some of the object's properties or for some form of visualization. Further steps might include more elaborate constructions based on previously defined objects. Each class of polymake objects comes with a set of rules which describe how a new property of an object can be derived from previously known ones. It is a key feature that the user can extend or modify the set of rules, add further properties or even new classes of objects (with entirely new rule bases). The functions provided include: several convex hull algorithms, face lattices of convex polytopes, Voronoi diagrams and Delaunay decompositions (in arbitrary dimensions), simplicial homology (with integer coefficients), simplicial cup and cap products, intersection forms of triangulated 4-manifolds. Several forms of (interactive) visualization via interfaces to Geomview, JavaView and other programs.
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 informationSINGULAR
SINGULAR is a Computer Algebra system for polynomial computations in commutative algebra, algebraic geometry, and singularity theory. SINGULAR's main computational objects are ideals and modules over a large variety of baserings. The baserings are polynomial rings over a field (e.g., finite fields, the rationals, floats, algebraic extensions, transcendental extensions), or localizations thereof, or quotient rings with respect to an ideal. SINGULAR features fast and general implementations for computing Groebner and standard bases, including e.g. Buchberger's algorithm and Mora's Tangent Cone algorithm. Furthermore, it provides polynomial factorizations, resultant, characteristic set and gcd computations, syzygy and free-resolution computations, and many more related functionalities. Based on an easy-to-use interactive shell and a C-like programming language, SINGULAR's internal functionality is augmented and user-extendible by libraries written in the SINGULAR programming language. A general and efficient implementation of communication links allows SINGULAR to make its functionality available to other programs.
More informationSums over integral points of a polygon
Maple program for computing the sum of values of a polynomial function over the set of integral points of a polygon and the corresponding weighted Ehrhart quasi-polynomial.
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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