Features

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

Euler Language

• interactive program with a syntax similar to Matlab,
• 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

• programming language in the style of Basic,
• 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 equatiosn,
• 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.

Maxima

• direct or compatible mode for access to Maxima in the user interface,
• option to start in Maxima mode with Euler as a Maxima interface,
• 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,
• 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.

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,
• 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.