Maple (Software)

Maple ( mathematical manipulation language) is an English computer algebra system (CAS ) for algebra, calculus, discrete mathematics, numerical analysis, and many other branches of mathematics. It also provides an environment for the development of mathematical programs available and allows the visualization of mathematical structures.

History

The first version of Maple has been programmed in 1980 by Keith O. Geddes, Gaston H. Gonnet and their employees of the Symbolic Computation Group at the University of Waterloo in the Canadian city of Waterloo ( Ontario). The end of 1987 there were Maple in version 4.2.

Since 1988, Maple from Maplesoft, a division of Waterloo Maple company further developed and marketed. Waterloo Maple heard since September 2009 on the Japan-based company Cybernet Systems Co., Ltd..

In the scientific support of the Maple project was and still is a matter of developing fast and efficient algorithms for symbolic computations, and to integrate into the program. Are in this work and were next to the Ontario Research Centre for Computer Algebra ( ORCCA ), consisting of the Maple Symbolic Computation Group (University of Waterloo ) and the Symbolic Computation Laboratory ( University of Western Ontario), scientists at ETH Zurich, involved the Institut national de recherche en informatique et en automatique ( INRIA ) and many other laboratories around the world

Since 1998 there has been a collaboration between Maplesoft and the Numerical Algorithms Group (NAG ). NAG components were found for the first time in Maple Release 6 from the year 2000. These components in particular, led to a significant improvement in the computation speed and the accuracy of calculations in the field of linear algebra.

2003, there were Maple for Windows CE 2.0 for mobile use on the handheld Cassiopeia A- 23g. This was often used in a variety of upper stages.

2005 was introduced in Maple 10, a new document mode ( "document mode" ) within the standard version of Maple. Since it is possible to edit Maple inputs in normal mathematical notation. This can be texts and mathematical symbols in the same command line combined.

Maple 13 offered, among others, significant improvements in the output of 3D graphics, new procedures and new interactive tutors.

As of version 14 of Maple it is possible to access and share with other users on Maple Worksheets ( MapleCloud ). Here, you can but make only the members of certain groups which are available own resources to all Maple users worldwide or.

Maple 15 differed from the previous versions in particular by a significant increase in computing speed for computers that are equipped with multiple processors.

In addition to new packages (such as Group Theory), new arithmetic commands and numerous enhancements in Maple in the current version 17 an editor that supports the development of source code with syntax highlighting and other features. Moreover, function calls are now processed much faster by using hardware-assisted algorithms than before.

User interface

Main component of the graphical user interface of Maple is the respective worksheet in which you are working interactively. It appears as a window, be entered in the calculation instructions ( Maple inputs ). The Maple engine interprets these instructions and supplies expenditure ( Maple outputs ) back.

Typical Maple outputs are numerical values ​​, terms, functions, tables, 2 - and 3- dimensional graphics, animation objects and diagrams. It is possible to edit the objects or expressions through context - sensitive menus generated by Maple.

Inserting mathematical symbols, terms vectors and matrices in computer instructions is facilitated by the use of pallets. These consist of various tasks prefabricated code snippets that can be added to the worksheet using the mouse.

Since version 9, there are next to the Classic Worksheet Maple, a Java - based version of Maple Standard. The standard version of Maple offers a more comfortable surface, but on the other hand, significantly slower than the classical variant. Due to these two types, there are two different ways to store the worksheet. A distinction is standard Worksheets ( file extension: mw) and Classic Worksheets ( file extension: mws; compatible with older versions of Maple ).

Packages

Maple includes a core of commonly used standard algebraic statements ( main library ) and additional run-time using the with command loadable modules ( packages). The following are some of the most important of these a total of over a hundred packages are listed below:

  • Code generation ( tools for translating Maple code in other programming languages)
  • Combinat ( for solving combinatorial problems )
  • DEtools ( for calculating with differential equations)
  • DifferentialGeometry ( in differential geometry, in particular for calculating with Lie algebras and tensors )
  • Dynamic Systems ( for working with linear systems )
  • Geometry (for the two-dimensional Euclidean geometry)
  • Geom3d ( for three-dimensional Euclidean geometry)
  • Linear Algebra ( for calculations with vectors and matrices)
  • Logic (for the two-valued logic )
  • Maplets ( for the production of graphical user interfaces for Maple )
  • Numtheory ( for number theory )
  • PDEtools ( for solving partial differential equations)
  • Physics ( for calculations in theoretical physics )
  • Plots ( graphics package )
  • Plottools ( for creating and manipulating graphical objects )
  • Random tools ( for working with random objects)
  • Real domain ( provides a real-valued local context )
  • ScientificConstants (physical constants and properties of chemical elements )
  • ScientificErrorAnalysis (for the error calculation)
  • Statistics ( for statistics and the analysis of the data )
  • VectorCalculus (for the vector analysis )

Interfaces

Maple has interfaces to MATLAB, Fortran, C, C #, Java, and Visual Basic, which allow Maple Code Fortran, C, C # in -, Java, or Visual Basic program code to translate. Conversely, let Fortran, C, C # - or Java routines in Maple embed.

Application Examples

The following are simple examples of arithmetic instructions in typical Maple notation.

  • Calculate the square root of 2 with an accuracy of 21 significant digits:
  • Solving a quadratic equation:
  • Calculate the derivative of a function:
  • Calculating an indefinite and a definite integral:
  • Solving a linear differential equation of second order:
  • Calculate the Cartesian equation of a sphere:
  • Representation of a parameterized surface:
  • Representation of a standing wave:
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