SuRiZaMaNaP: Maple (software)

Maple™ is the essential technical computing software for today’s engineers, mathematicians, and scientists. Whether you need to do quick calculations, develop design sheets, teach fundamental concepts, or produce sophisticated high-fidelity simulation models, Maple’s world-leading computation engine offers the breadth, depth, and performance to handle every type of mathematics.

HISTORY

The first concept of Maple arose from a meeting in November 1980 at the University of Waterloo. Researchers at the university wished to purchase a computer powerful enough to run Macsyma. Instead, it was decided that they would develop their own computer algebra system that would be able to run on more reasonably priced computers.

The initial development of Maple proceeded very quickly, with the first limited version appearing in December 1980. Researchers tried and discarded many different ideas creating a continually evolving system. Maple was demonstrated first at conferences beginning in 1982. The name is a reference to Maple’s Canadian heritage.
By the end of 1983, over 50 universities had copies of Maple installed on their machines. In 1984, the research group arranged with Watcom Products Inc to license and distribute Maple.
In 1988 Waterloo Maple Inc. was founded. The company’s original goal was to manage the distribution of the software. Eventually, the company evolved to have an R&D department where much of Maple’s development is done today, but significant development of Maple continues at university research labs including: the Symbolic Computation Laboratory at the University of Waterloo; the Ontario Research Centre for Computer Algebra at the University of Western Ontario; and labs at other universities worldwide.
In 1989, the first graphical user interface for Maple was developed and included with version 4.3 for the Macintosh. Prior versions of Maple included only a command line interface with two dimensional output. X11 and Windows versions of the new interface followed in 1990 with Maple V.
In 1999, with the release of Maple 6, Maple included some of the NAG Numerical Libraries,^[3] and made improvements to arbitrary precision arithmetic.
In 2003, the current "standard" interface was introduced with Maple 9. This interface is primarily written in Java (although portions, such as the rules for typesetting mathematical formulae, are written in the Maple language). The Java interface was criticized for being slow;^[4] improvements have been made in later versions, although the Maple 11 documentation^[5] recommends the previous (“classic”) interface for users with less than 500 MB of physical memory. This classic interface is no longer being maintained.
Between the mid 1995 and 2005 Maple lost significant market share to competitors due to a weaker user interface.^[6] In 2005, Maple 10 introduced a new “document mode”, as part of the standard interface. The main feature of this mode is that math is entered using two dimensional input, so that it appears similar to formulae in a book. In 2008, Maple 12 added additional user interface features found in Mathematica, including special purpose style sheets, control of headers and footers, bracket matching, auto execution regions, command completion templates, syntax checking and auto-initialization regions. Additional features were added for making Maple easier to use as a MATLAB toolbox.^[7]
In September 2009 Maple and Maplesoft were acquired by the Japanese software retailer Cybernet Systems.

EXAMPLE OF MAPLE CODE

System of partial differential equations

Solve the system of partial differential equations

${\frac {\partial }{\partial x}}v \left( x,t \right) =-u \left( x,t \right) v \left( x,t \right)$

${\frac {\partial }{\partial t}}v \left( x,t \right) =-v \left( x,t \right) {\frac {\partial }{\partial x}}u \left( x,t \right) +v \left( x,t \right) \left( u \left( x,t \right) \right) ^{2}$

${\frac {\partial }{\partial t}}u \left( x,t \right) +2\,u \left( x,t \right) {\frac {\partial }{ \partial x}}u \left( x,t \right) -{\frac {\partial ^{2}}{\partial {x}^{2}}}u \left( x,t \right) =0$

with $v(x,t)\neq 0$ .

eqn1:= diff(v(x, t), x) = -u(x,t)*v(x,t):
eqn2:= diff(v(x, t), t) = -v(x,t)*(diff(u(x,t), x))+v(x,t)*u(x,t)^2:
eqn3:= diff(u(x,t), t)+2*u(x,t)*(diff(u(x,t), x))-(diff(diff(u(x,t), x), x))= 0:
pdsolve({eqn1,eqn2,eqn3,v(x,t)<>0},[u,v]): op(%);

Answer:

$v \left( x,t \right) ={e^{\sqrt {{\it \_c}_{{1}}}x}}{\it \_C3 }\,{e^{{\it \_c}_{{1}}t}}{\it \_C1}+{\frac {{\it \_C3}\,{e^{{\it \_c}_ {{1}}t}}{\it \_C2}}{{e^{\sqrt {{\it \_c}_{{1}}}x}}}}, \ \ u \left( x,t \right) =-{\frac {\sqrt {{\it \_c}_{{1}}} \left( {\it \_C1}\, \left( {e^{\sqrt {{\it \_c}_{{1}}}x}} \right) ^{2}-{\it \_C2} \right) }{{\it \_C1}\, \left( {e^{\sqrt {{\it \_c}_{{1}}}x}} \right) ^{2}+{\it \_C2}} }$

Plotting of function of two variables

Plot

x 2 + y 2

with

x

and

y

ranging from -1 to 1

plot3d(x^2+y^2,x=-1..1,y=-1..1);

USE OF MAPLE ENGINE

The Maple engine is used within several other products from Maplesoft:

Maple T.A., Maplesoft’s online testing suite, uses Maple to algorithmically generate questions and grade student responses.
MapleNet allows users to create JSP pages and Java Applets. MapleNet 12 and above also allow users to upload and work with Maple worksheets containing interactive components.
Maple Reader, Maplesoft’s platform for DRM-controlled electronic books uses the Standard Maple interface. There are currently no available books using this product.
MapleSim, an engineering simulation tool.

Listed below are third party commercial products that no longer use the Maple engine:

Versions of MathCad released between 1994 and 2006 included a Maple-derived algebra engine (MKM, aka Mathsoft Kernel Maple), though subsequent versions use MuPAD.
Symbolic Math Toolbox in MATLAB contained a portion of the Maple 10 engine but now uses MuPAD.
Older versions of the mathematical editor Scientific Workplace included Maple as a computational engine, though current versions include MuPAD.

PRODUCT	DESCRIPTION
MapleSim	High-performance multi-domain modeling and simulation.
Maple	The essential technical computing software for today’s engineers.
MapleSim Connector	Automatic generation of Simulink® S-functions from MapleSim models. The generated ANSI-C code is compatible with Real-Time Workshop for simulation on supported platforms such as dSPACE and xPC Target.
MapleSim Control Design Toolbox	A solid set of essential control design tools that extend MapleSim's exceptional plant modeling capabilities to support control design.
BlockImporter™	Import a Simulink® model into Maple and convert it to a set of mathematical equations to be analyzed, optimized, simplified, turned into a MapleSim custom component for inclusion in MapleSim, and exported back to Simulink® using the MapleSim Connector.
Maple Toolbox for MATLAB®	A technical computing solution that is tightly integrated with MATLAB®.

SuRiZaMaNaP

Tuesday, September 21, 2010

Maple (software)

System of partial differential equations

Plotting of function of two variables

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