Euler (now Euler Mathematical Toolbox or EuMathT) is a free and open-source numerical software package. It contains a

matrix Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** ''The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchis ...

language, a graphical notebook style interface, and a plot window. Euler is designed for higher level math such as

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...

optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...

, and statistics. The software can handle

real Real may refer to: Currencies * Brazilian real (R$) * Central American Republic real * Mexican real * Portuguese real * Spanish real * Spanish colonial real Music Albums * ''Real'' (L'Arc-en-Ciel album) (2000) * ''Real'' (Bright album) (2010) ...

complex Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex system, a system composed of many components which may interact with each ...

and interval numbers,

vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...

s and

matrices Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** ''The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchis ...

, it can produce 2D/ 3D plots, and uses Maxima for symbolic operations. The software is compilable with

Windows Windows is a group of several proprietary graphical operating system families developed and marketed by Microsoft. Each family caters to a certain sector of the computing industry. For example, Windows NT for consumers, Windows Server for ser ...

. The

Unix Unix (; trademarked as UNIX) is a family of multitasking, multiuser computer operating systems that derive from the original AT&T Unix, whose development started in 1969 at the Bell Labs research center by Ken Thompson, Dennis Ritchie, an ...

and

Linux Linux ( or ) is a family of open-source Unix-like operating systems based on the Linux kernel, an operating system kernel first released on September 17, 1991, by Linus Torvalds. Linux is typically packaged as a Linux distribution, w ...

versions do not contain a computer algebra subsystem.

History

Euler Math Toolbox originated in 1988 as a program for Atari ST. At that time, the title of the program was simply Euler, but it turned out to be too unspecific for the Internet. The main aim of the program was to create a tool for testing numerical algorithms, to visualize results, and to demonstrate mathematical content in the classroom. Euler Math Toolbox uses a matrix language similar to

MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementa ...

, a system that had been under development since the 1970s. Then and now the main developer of Euler is René Grothmann, a mathematician at the

Catholic University of Eichstätt-Ingolstadt The Katholische Universität Eichstätt-Ingolstadt (KU) is a Roman Catholic research university in Eichstätt and Ingolstadt, Bavaria, Germany. Compared to other German universities it is a rather small institution with 4,800 students in 2019; n ...

, Germany. In 2007, Euler was married with the Maxima computer algebra system. Symbolic expressions and other functions were added to communicate with Maxima, and to reach a good degree of integration into the numerical Euler core.

Overview

The Euler core is a numerical system written in C/

C++ C++ (pronounced "C plus plus") is a high-level general-purpose programming language created by Danish computer scientist Bjarne Stroustrup as an extension of the C programming language, or "C with Classes". The language has expanded significan ...

. It handles real, complex, and interval values, and matrices of these types. Other available data types are sparse, compressed matrices, a long accumulator for an exact

scalar product In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an alge ...

, and

strings String or strings may refer to: *String (structure), a long flexible structure made from threads twisted together, which is used to tie, bind, or hang other objects Arts, entertainment, and media Films * ''Strings'' (1991 film), a Canadian anim ...

. Strings are used for expressions, file names etc. Based on this core, additional functions are implemented in the Euler matrix language, which is an interpreted programming language in the style of an advanced BASIC dialect. Euler contains libraries for statistics, exact numerical computations with interval inclusions, differential equations and stiff equations, astronomical functions, geometry, and more. The clean interface consists of a text window, and a graphics window. The text window contains fully editable notebooks, and the graphics window the graphics output. Graphics can be added to the notebook window too, or can be exported in various formats ( PNG, SVG, WMF, Clipboard). Graphic types include line, bar or point plots in 2D and 3D, including anaglyph plots of 3D surfaces and other 3D plots. Euler has an API to use the open raytracer

POV-Ray The Persistence of Vision Ray Tracer, most commonly acronymed as POV-Ray, is a cross-platform ray-tracing program that generates images from a text-based scene description. It was originally based on DKBTrace, written by David Kirk Buck and Aaro ...

. Euler handles symbolic computations via Maxima, which is loaded as a separate process, communicating with Euler through pipes. The two programs can exchange variables and values. Indeed, Maxima is used in various Euler functions (e.g. Newton's method) to assist in the computation of derivatives, Taylor expansions and integrals. Moreover, Maxima can be called at definition time of an Euler function.

LaTeX Latex is an emulsion (stable dispersion) of polymer microparticles in water. Latexes are found in nature, but synthetic latexes are common as well. In nature, latex is found as a milky fluid found in 10% of all flowering plants (angiosperms ...

can be used from within Euler to display formulas. For export of formulas to

HTML The HyperText Markup Language or HTML is the standard markup language for documents designed to be displayed in a web browser. It can be assisted by technologies such as Cascading Style Sheets (CSS) and scripting languages such as JavaSc ...

, either the generated LaTeX images or

MathJax MathJax is a cross-browser JavaScript library that displays mathematical notation in web browsers, using MathML, LaTeX and ASCIIMathML markup. MathJax is released as open-source software under the Apache License. The MathJax project started i ...

can be used. A special export option exports all graphics to SVG. Euler also includes the

Tiny C Compiler The Tiny C Compiler (a.k.a. TCC, tCc, or TinyCC) is an x86, X86-64 and ARM processor C compiler initially written by Fabrice Bellard. It is designed to work for slow computers with little disk space (e.g. on rescue disks). Windows operating sys ...

, which allows subroutines in C to be compiled, and included via a Windows DLL. Euler has a lot of similarity to MATLAB and its free clones (

GNU Octave GNU Octave is a high-level programming language primarily intended for scientific computing and numerical computation. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a langu ...

), but it is not compatible.

References

External links

*
Official forumOld GTK+ version of Euler for Unix/Linux
{{Numerical analysis software C (programming language) software Data analysis software Free mathematics software Numerical analysis software for Linux Numerical programming languages Plotting software Science software for Windows Science software that uses GTK

History

Overview

See also

References

External links