Features
Here is a short list of the features of Euler Math Toolbox. Since Euler is a very huge system, by far not all algorithms and functions can be listed on this page.

Main Features
- Nice and simple interface with fully editable command window,
- export to HTML and various graphic formats,
- fast numerical kernel with exact and interval arithmetic,
- easy to use symbolic expressions and functions, seamlessly integrated into the Euler syntax,
- full Maxima interface,
- extensive help and user support.
Euler Language
- Interactive program with a simple, versatile syntax,
- numerical mathematics with real numbers and complex numbers,
- interval arithmetic,
- vectors and matrices of real, complex, or interval numbers,
- flexible and rich matrix language,
- intelligent operator expansion for matrices and vectors,
- matrix product, powers, inverse etc.,
- support for large, sparse matrices,
- strings and vectors of strings,
- functions for string manipulation,
- evaluation of expressions stored in strings,
- exact scalar product and residuum calculation,
- exact solutions of linear systems,
- data type for sparse matrices,
Programming Language
- Programs in the style of a modern Basic dialect,
- multiple function results,
- one-line functions for simple functions,
- access to global variables in functions on demand,
- parameters by value or reference,
- default values for parameters,
- type checking for parameters,
- extra parameters,
- external files with Euler commands and function definitions.
Numerical Functions
- Newton, bisection, secant methods using functions or expressions,
- Newton interval method in one or several variables,
- Broyden, Newton, Nelder-Mead method for functions in several variables,
- Runge, Heun and adaptive Runge method for differential equations,
- Bauhuber method for roots of polynomials,
- Romberg, Gauß, adaptive integration,
- polynomial interpolation and spline interpolation,
- polynomial and linear fit, singular value fit,
- Simplex algorithm,
- integer branch and bound algorithm,
- conjugate gradient and Gauß-Seidel for sparse matrices,
- residuum iteration for exact solutions,
- guaranteed interval solutions,
- FFT and two dimensional FFT,
- singular value decomposition,
- eigenvalue and eigenspace,
- Jacobi method,
- Remez algorithm,
- quicksort algorithm,
- many more algorithms implemented in the Euler language.
Symbolical Mathematics
- symbolic expressions and functions provide integrated access to Maxima,
- symbolic variables,
- direct or compatible mode for access to Maxima,
- option to start in Maxima mode with Euler as a Maxima interface,
- easy exchange of results between Maxima and Euler,
- gnuplot included,
- Euler functions can use Maxima,
- Maxima can be called at compile time of Euler functions,
- many algorithms in Euler using Maxima, e.g. the Newton method,
- Euler strings can be easily parsed by Maxima before they are used in Euler,
- numerical variables can be defined both in Euler and Maxima,
- expressions in Euler strings can easily be used in Maxima commands.
Graphics
- 2D graphics with several line styles, all colors, or points.
- axis labels and titles,
- annotations and labels,
- plots only valid function values,
- bar plots or distribution plots,
- 3D graphics with hidden lines, vanishing point projection,
- surface contour lines and shading,
- 3D anaglyph output for red/cyan,
- point clouds, 3D paths,
- implicit plots in two and three variables,
- user can turn or zoom in,
- direction plots for differential equations,
- resizable graphics window,
- exports to PNG, SVG, EPS or the clipboard,
- PNG export and notebook images optionally with anti-aliasing.
- Povray interface for perfect 3D graphics.
Statistics
- Random variables, with normal, uniform or integer distribution,
- normal, F- and T-distribution and inverse distributions,
- binomial distribution and inverse distribution,
- statistical tests,
- beta- and gamma-functions, complex gamma function,
- interval counting,
- distribution plots.
Interface
- Notebook style interface with editable commands,
- free copy and paste,
- free editable comments,
- saves in text format,
- current graphics can be included in the notebook,
- Latex formulas in comments or commands,
- export to HTML,
- status line help, help command, list command,
- documentation in PDF format for Euler and Maxima,
- configuration in file or registry,
- Euler home file in user directory,
- support for installation on sticks or networks.