Calc is arbitrary precision arithmetic system that uses a C-like language. It's useful as a calculator, an algorithm prototype, and as a mathematical research tool. More importantly, calc provides a machine-independent means of computation. Calc comes with a rich set of builtin mathematical and programmatic functions.
CCMATH is a mathematics library, coded in C, that contains functions for linear algebra, numerical integration, geometry and trigonometry, curve fitting, roots and optimization, Fourier analysis, simulation generation, statistics, special functions, sorts and searches, time series models, complex arithmetic, and high precision computations.
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.
GtkMathView is a GTK widget for rendering MathML documents. It is meant to be a standalone, light-weight component and not a full browser. GTK applications can use the widget as a window for displaying mathematical formulas and doing simple interactions. Among other features, GtkMathView includes support for breaking long mathematical expressions, rendering of stretchy operators, and provides a customizable support for additional fonts.
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).