Euler Mathematical Toolbox

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Euler Mathematical Toolbox (EuMathT) is a free, open-source tool for numerical computing. It combines a matrix language, a notebook-style interface, and a plotting window. It’s built for higher-level math like calculus, optimization, and statistics, and can work with real, complex, and interval numbers, as well as vectors and matrices. It can create 2D and 3D plots and uses Maxima for symbolic math.

The core is written in C/C++ and runs on Windows and Unix-like systems. The Windows version includes Maxima as a separate process for symbolic computations; the Linux/Unix versions do not include a built-in computer algebra subsystem. Euler started in 1988 on the Atari ST as Euler and was developed by René Grothmann of the Catholic University of Eichstätt-Ingolstadt, Germany. In 2007, Euler integrated with Maxima to add symbolic capabilities.

Data types include real, complex, and interval numbers, as well as sparse and compressed matrices, a long accumulator for exact products, and strings. The Euler matrix language is an interpreted language similar to MATLAB, designed to test numerical algorithms, visualize results, and teach mathematics.

The toolbox provides libraries for statistics, exact interval arithmetic, differential equations (including stiff equations), geometry, astronomy, and more. The interface features a text notebook and a graphics window, with graphics that can be embedded in the notebook or exported as PNG, SVG, WMF, or copied to the clipboard. It supports 2D/3D plots and special 3D visuals such as anaglyphs. There is also an option to export graphics to SVG.

Euler can interface with the open raytracer POV-Ray, and symbolic computations are done via Maxima, which can be called from within Euler to help with derivatives, Taylor expansions, and integrals. LaTeX can be used to display formulas, and formulas can be exported to HTML with LaTeX images or MathJax. There is a built-in Tiny C Compiler to compile C subroutines into Windows DLLs. Euler is similar in spirit to MATLAB and GNU Octave but is not compatible with them.

The software is released under the GNU General Public License. The latest stable release was in January 2024, and the project is hosted on SourceForge.