Cactus is a general, modular, parallel environment for solving systems of partial differential equations. The code has been developed over many years by a large international collaboration of numerical relativity and computational science research groups and can be used to provide a portable platform for solving any system of partial differential equations.
GNU TeXmacs is a free wysiwyw (what you see is what you want) editing platform with special features for scientists. The software aims to provide a unified and user friendly framework for editing structured documents with different types of content: text, mathematics, graphics, interactive content. TeXmacs can also be used as an interface to many external systems for computer algebra, numerical analysis, and statistics. New presentation styles can be written by the user and new features can be added to the editor using Scheme.
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.
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.
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.