Euler Math Toolbox 12.8

Major Features: 

1. 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,
   • Full maxima interface,
   • Extensive help and user support.
2. 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,
3. Programming language:
   • 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.

• Matlab:
• • Added a comparison between Matlab and Euler to assist users coming from Matlab.
• Euler Pages:
• • Changed the look of the Euler pages. Formatted output now stands out on gray background.
• Anonymous functions:
• • New anonymous functions. These functions are expressions in strings with other parameters than x, y, z.
  • It is preferred to use functions instead of these constructions. However, this syntax may sometimes be useful. The syntax does not work in symbolic expressions.
• Fixes:
• • Errors in the examples (thanks to Radovan).
  • Turned off Maxima printing in &expression (e.g. the tex command). Use printing Maxima functions from :.