Genius is an arbitrary precision integer and multiple precision floating point calculator. It includes its own programming language similar in some aspects to C, bc, or Pascal. It can deal with rational numbers and complex numbers. It has matrix support as well. It uses the gmp library so it is very fast for calculations of large numbers. It has a command line and a GNOME interface. The GNOME interface supports plotting functions and 3D surfaces.
Groups, Algorithms, and Programming (GAP) is a system for computational discrete algebra with particular emphasis on computational group theory and related areas. It provides a Pascal-like interpreted language, data types for many algebraic objects, a function library, and large libraries of data.
Isabelle is a popular generic theorem prover developed at Cambridge University and TU Munich. Existing logics like Isabelle/HOL provide a theorem proving environment ready to use for sizable applications. Isabelle may also serve as framework for rapid prototyping of deductive systems. It comes with a large library including Isabelle/HOL (classical higher-order logic), Isabelle/HOLCF (Scott's Logic for Computable Functions with HOL), Isabelle/FOL (classical and intuitionistic first-order logic), and Isabelle/ZF (Zermelo-Fraenkel set theory on top of FOL).
KSEG is a program for exploring Euclidean geometry, similar to Geometer's Sketchpad. It features points, lines, transformations, measurements, calculations, simple editable recursive Constructions (similar to macros), adaptively sampled loci, and selection groups. Several languages are supported. KSEG is very fast, stable, and has an efficient and consistent UI. It uses Qt and does not require KDE.
Maxima is a Common Lisp implementation of MIT's Macsyma system for computer based algebra. It features plotting over the network via netmath, computations over the network, extensive testing on a large array of problems, a source level debugger for maxima code, ease of extension in fundamentally new ways, access to Common Lisp and portability to many systems.
OBJ3 is a program specification and proof system based on order sorted equational logic. It has been successfully used for research and teaching in software design and specification, rapid prototyping, theorem proving, user interface design, and hardware verification, among other things. It was the first language to implement parameterized programming and its module system influenced the designs of the Ada, C++, and ML module systems.
Statist is a statistics program with an interactive menu that makes it very easy to use. It can also be run in scripts, and large data sets are handled reasonably well even on small machines. In spite of its low overhead, it can do quite a few regression functions and tests. It can produce colorized output, and uses gnuplot to create graphics.
WIMS (WWW Interactive Mathematics Server) is a CGI Web application designed to host interactive mathematical educational activities such as exercises, computational math, and graphing tools. It features automatic score processing with strong anti-cheating mechanisms, virtual classes allowing teachers to guide/control student works, online exercise creation, animated graphics, a message board allowing inline mathematical formulas, and more. It can also be easily used for education within other disciplines.
Yacas is a general purpose, easy to use Computer Algebra System (a CAS is a program that can be used to do symbolic manipulation of mathematical expressions). It is built on top of its own programming language designed for this purpose, in which new algorithms can easily be implemented. In addition, it comes with extensive documentation on the functionality implemented and methods used to implement them.
This is an application to help user (mathematician) to make regression between series of data, draw grpahics, and export them into various formats by means of common graphics packages (i.e., gnuplot, plotutils). It is written in Python. The user interfeace is built upon the wxPython (wxWindows) widget set. The idea of usage is as follows: the user builds a project which is represented as a tree of modules; modules can generate data variables, as well as consume them. Essentialy, such a tree represents an algorithm of data analysis. The system is intended to educate students.