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Maple vs Mathematica

Contents 1 Numerics 2 Symbolics 3 Graphics 4 Programming 5 Interface 6 Import Export 7 Price 8 Companies

[edit] Numerics

Both Mathematica and Maple support computations using floats, arbitrary precision and complex arithmetic. Mathematica provides precision tracking to identify and control the propogation of rounding errors and other loss of reliable precision. Maple does not.

Maple provides linear algebra and other matrix operations by a choice of two sets of libraries. The linalg package uses Maple's native numerica capabilities and is very flexible but very slow. It provides less flexible (eg pre-declaration of the data structure causing errors if the wrong kind of data is used) but faster via libraries licensed from the NAG FORTRAN libraries. Mathematica is marginally faster than the NAG libraries but without loss of flexibility.

Mathematica provides optimized computations for image processing including morphological image processing. Maple has a package for non-morphological image processing only, using only slower, more general linear algebra capabilities.

[edit] Symbolics

Both Maple and Mathematica provide symbolic computing capabilities.

In general Maple is more powerful on solving Integral equations and Groebner basis, Mathematica is more powerful for integration, recurrrence relations, equation solving and simplification. Differential equation solving is comparible between the systems.

Both systems provide domain control. Maple can declare symbols to be real, complex, or within intervals. Mathematica can declare real, complex, interval and integer attributes.

[edit] Graphics

Both systems provide a range of 2D and 3D graphics. The range is far greater in Mathematica.

Both Maple and Mathematica provide adaptive re-sampling for smoother 2D plots (though this is turned off by default in Maple) but only Mathematica extends this capability to 3D plots.

Both provide mouse driven rotatable 3D graphics. Maple provides 3D fly-by views, Mathematica does not. Mathematica graphics can contain active elements such as tooltips, mouse-over effects, tab and menu views and draggable elements. Maple cannot.

[edit] Programming

Maple provides a procedural language somewhat similar to Pascal.

Mathematica provides a mixed procudural/functional language, combining elements of C++ and APL.

An Integrated Development Environment (IDE), based on Eclipse, is provided for large project work for Mathematica. Maple has no IDE.

A runtime version of Mathematica, Mathematica Player, allows code written in Mathematica to be run without a Mathematica license. Maple code requires a full Maple license to run.

[edit] Interface

Both systems use a notebook style interface. Both systems support typeset math. Both systems support interface building.

Maple provides a set of around 50 special-case interfaces for helping explore specific topics. Mathematica provides none in the interface but hosts a web resource http://demonstrations.wolfram.com with around 5000 user created special-case interfaces.

[edit] Import Export

Mathematica provides around 130 import/export filters using a standard interface. Maple provides around 15 import export filters.

[edit] Price

Pricing is similar for both products.

[edit] Companies

Mathematica is produced by Wolfram Research in the USA (http://wolfram.com). It also makes webMathematica, gridMathematica and provides the websites http://mathworld.wolfram.com and http://wolframalpha.com. It has around 500 employees.

Maple is produced by MapleSoft in Canada (http://maplesoft.com). It also makes MapleTA and MapleSIM. It has around 100 employees.