Euler Mathematical Toolbox (or EuMathT; formerly Euler) is a free and

open-source Open source is source code that is made freely available for possible modification and redistribution. Products include permission to use and view the source code, design documents, or content of the product. The open source model is a decentrali ...

numerical software Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

package. It contains a

matrix Matrix (: matrices or matrixes) or MATRIX may refer to: Science and mathematics * Matrix (mathematics), a rectangular array of numbers, symbols or expressions * Matrix (logic), part of a formula in prenex normal form * Matrix (biology), the m ...

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

calculus Calculus is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the ...

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

, and

statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

. The software can handle real,

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 * Disease vector, an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematics a ...

s and

matrices Matrix (: matrices or matrixes) or MATRIX may refer to: Science and mathematics * Matrix (mathematics), a rectangular array of numbers, symbols or expressions * Matrix (logic), part of a formula in prenex normal form * Matrix (biology), the ...

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

Windows Windows is a Product lining, product line of Proprietary software, proprietary graphical user interface, graphical operating systems developed and marketed by Microsoft. It is grouped into families and subfamilies that cater to particular sec ...

. The

Unix Unix (, ; trademarked as UNIX) is a family of multitasking, multi-user 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, a ...

and

Linux Linux ( ) is a family of open source Unix-like operating systems based on the Linux kernel, an kernel (operating system), operating system kernel first released on September 17, 1991, by Linus Torvalds. Linux is typically package manager, pac ...

versions do not contain a computer algebra subsystem.

History

Euler Math Toolbox originated in 1988 as a program for

Atari ST Atari ST is a line of personal computers from Atari Corporation and the successor to the company's Atari 8-bit computers, 8-bit computers. The initial model, the Atari 520ST, had limited release in April–June 1985, and was widely available i ...

. 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, implementat ...

, 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, 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++. It handles real, complex, and interval values, as well as 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 for other symmetric bilinear forms, for example in a pseudo-Euclidean space. Not to be confused wit ...

, and strings. 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 Basic or BASIC may refer to: Science and technology * BASIC, a computer programming language * Basic (chemistry), having the properties of a base * Basic access authentication, in HTTP Entertainment * Basic (film), ''Basic'' (film), a 2003 film ...

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, while the graphics window displays the graphics output. Graphics can be added to the notebook window 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 provides an API for 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 In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a ...

) 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. Latices are found in nature, but synthetic latices are common as well. In nature, latex is found as a wikt:milky, milky fluid, which is present in 10% of all floweri ...

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

HTML Hypertext Markup Language (HTML) is the standard markup language for documents designed to be displayed in a web browser. It defines the content and structure of web content. It is often assisted by technologies such as Cascading Style Sheets ( ...

, 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 in ...

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

Tiny C Compiler The Tiny C Compiler, TCC, tCc, or TinyCC is a x86 (32-bits), X86-64 and ARM processor C compiler initially written by Fabrice Bellard. It is designed to work for slower computers with little disk space (e.g. on rescue disks). Windows operati ...

, 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 scientific programming language for scientific computing and numerical computation. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly ...

), but it is not compatible.

References

External links

*
Official forumOld GTK+ version of Euler for Unix/Linux
{{Numerical analysis software Free software programmed in C 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