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One other program you might look into is Matlab (MATrix LABoratory) - or
its open source counterpart Octave.
Scilab is a scientific software package for numerical computations in a
user-friendly environment. It features:
Elaborate data structures (polynomial, rational and string matrices,
lists, multivariable linear systems,...).
Sophisticated interpreter and programming language with Matlab-like
syntax.
Hundreds of built-in math functions (new primitives can easily be
added).
Stunning graphics (2d, 3d, animation).
Open structure (easy interfacing with Fortran and C via online
dynamic link).
Many built-in libraries:
Linear Algebra (including sparse matrices, Kronecker form, ordered
Schur,...).
Control (Classical, LQG, H-infinity,...).
Package for LMI (Linear Matrix Inequalities) optimization.
Signal processing.
Simulation (various ode's, dassl,...).
Optimization (differentiable and non-differentiable, LQ solver).
Scicos, an interactive environment for modeling and simulation of
hybrid systems.
Metanet (network analysis and optimization).
Symbolic capabilities through Maple interface.