My contributions to Giac/Xcas computer algebra system, including the support for:
- graph theory (a comprehensive package containing over 200 commands, see doc/graphtheory-user_manual.pdf for details)
- signal processing and audio (creating wave files, convolution and (auto)correlation, filtering, windowing, resampling, noise removal)
- images
- continuous and short-time Fourier transform
- continuous and discrete Hilbert transform
- analytic signal representation
- empirical mode decomposition
- Hilbert-Huang transform
- constrained optimization in multivariate calculus (local and global extrema)
- calculus of variations
- numerical differentiation (Fornberg's algorithm)
- (mixed integer) (non)linear programming
- transportation problems
- curve interpolation and fitting (Thiele's algorithm, Floater and Hormann's algorithm, trigonometric polynomial fitting, Remez algorithm, L^2 polynomial approximation)
- B-splines with efficient fitting to data
- simplification of trigonometric expressions
- statistics (discrete random variables with sampling, kernel density estimation, maximum-likelihood fitting)
- ordinary differential equations (an implementation of Kovacic's algorithm and a second-degree boundary value problems solver)
- Diophantine equations
- K-means and hierarchical agglomerative clustering
- feed-forward neural networks
- LaTeX/MathML/TeXmacs conversion of Giac output
- colors and colormaps
- using Giac in TeXmacs