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Portable Euler Math Toolbox is a useful application designed to help users to calculate numerical computations by using the computer algebra.
Portable Euler Math Toolbox (Euler for short) is a numerical and algebraic software, a mixture between a computer algebra system (CAS) and a numerical matrix language in the style of MATLAB.
The numerical kernel of Euler is based on a matrix language. This language can not only handle simple numbers, but also vectors and matrices of numbers. Moreover, Euler can compute expressions with complex numbers, intervals and strings. All these computations can be programmed in Euler functions, which might be loaded from external files into Euler. Indeed, a large part of the Euler syntax is based on functions written in the Euler programming language.
Euler can also produce graphics and save the graphics in various formats, among them PNG and SVG. Graphics can also be imported into th e text window, exported to files or to the clipboard. More on this in the reference for the user interface.
The Maxima subsystem communicates with Euler through pipes. It remains a separated system. However, there are various interactions between Euler and Maxima. Using symbolic expressions, Maxima works completely transparent inside Euler. This is a mighty environment to investigate mathematics.
Here are some key features of "Portable Euler Math Toolbox":
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,
· 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 se veral 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,
& #183; anaglyph output,
· point clouds, 3D paths,
· user can turn or zoom in,
· direction plots for differential equations,
· resizable graphics window,
· exports to PNG, EPS or the clipboard.
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.
What's New in This Release: [ read full changelog ]
· The execute command has been extended. The new features are hidden windows, non-wait execution, catching output. The result is the exit code of the program, or a vector of strings with one string for each line of output.
· There was a problem with very huge line plots in recent versions leading to a large delay or even a halt of the Windows graphics system. The reason was that Euler is using a path to connect the lines. For paths with many segments, Windows can not handle the plot. I fixed that by splitting large path s into chunks. Nevertheless, these plots take a short moment to appear.
Via: Portable Euler Math Toolbox 19.3
