Maple (software)

Maple (software)
Name	Maple
Developer	Waterloo Maple / Maplesoft / Waterloo Maple Inc.
Released	1981
Programming language	C, C++, Java
Operating system	Microsoft Windows, macOS, Linux, FreeBSD
Genre	Computer algebra system
License	Proprietary

Maple (software) is a symbolic and numeric computing environment and technical computing platform originally developed at the University of Waterloo and commercialized by Waterloo Maple (later Maplesoft). It integrates symbolic algebra, numeric computation, visualization, and programming into a single environment aimed at engineers, scientists, mathematicians, and educators. Maple has been used in academia, industry, and government for research, teaching, and product development.

History

Maple traces origins to efforts at the University of Waterloo in the early 1980s, where faculty and students sought to build an interactive symbolic computation system leveraging advances in computer algebra research represented by projects such as Macsyma, Reduce (computer algebra system), and SAC-2. Founders from Waterloo formed Waterloo Maple Software to commercialize the system; early milestones include releases for VAX and Unix platforms and later ports to MS-DOS and Windows. Over successive decades Maple incorporated algorithms and ideas from institutions including Massachusetts Institute of Technology, Stanford University, ETH Zurich, and Cambridge University, and competed in markets alongside Mathematica, Matlab, SageMath, and Mathematical Toolbox (MATLAB). Corporate changes saw Maplesoft become a prominent Canadian software company with partnerships and deployments across entities like NASA, European Space Agency, Siemens, and higher education institutions such as MIT and Stanford University.

Features and Functionality

Maple offers symbolic manipulation, numeric computation, and interactive visualization within a document-centric interface similar to notebook systems used by Wolfram Research, Jupyter Project, and Mathematica. Core capabilities include algebraic simplification, symbolic integration and differentiation, solving of ordinary and partial differential equations, series expansions, and summation of symbolic series—drawing on algorithmic foundations from the Risch algorithm, Groebner basis, and numerical linear algebra libraries such as LAPACK and BLAS. The system includes specialized toolboxes for signal processing, optimization, control systems, and statistics that interoperate with plotting engines and rendering frameworks used in OpenGL-based visualization and export to formats employed by LaTeX and PDF. Maple's programming language supports procedural, functional, and rule-based paradigms, enabling extension by researchers from institutions like University of Cambridge, Princeton University, and University of California, Berkeley.

Architecture and Implementation

Maple's architecture separates a symbolic engine, numeric libraries, a document interface, and external connectivity layers. The core is implemented in a mixture of C and C++, with runtime components invoking libraries such as LAPACK for dense linear algebra and arbitrary-precision arithmetic backends influenced by projects like GNU Multiple Precision Arithmetic Library. Interoperability is achieved through connectors and APIs for languages and systems including Java, Python (programming language), MATLAB (software), and standards such as OpenMath and MathML. The worksheet environment employs a front end that manages evaluation, typesetting, and plotting, while a kernel executes computations and manages memory, process control, and concurrency with design influences from Unix process models and client–server architectures common in scientific computing stacks.

Licensing and Editions

Maple is distributed under proprietary licenses by Maplesoft, with multiple commercial, academic, and home editions tailored to different user communities. Academic licensing models have served universities and research labs such as University of Toronto and Imperial College London, while commercial licensing targets corporations including General Electric and Boeing. Editions range from full-featured developer and enterprise packages to limited deployment runtime environments and toolboxes similar in market segmentation to products from Wolfram Research and MathWorks. Licensing terms have evolved to include network licenses, site licenses, and cloud deployment options integrated with services like institutional Microsoft Azure and virtualization platforms used by research centers.

Applications and Use Cases

Maple is used across domains for symbolic derivation, model derivation, prototyping, and teaching. In engineering practice it supports control systems design, signal processing, and computational fluid dynamics modeling applied in companies like Siemens and Schlumberger; in physics and applied mathematics it aids derivations in areas connected to research at Princeton University and CERN. Educators at institutions such as Harvard University, University of Oxford, and McGill University use Maple for undergraduate and graduate instruction, problem set generation, and interactive demonstrations. Researchers integrate Maple with documentation workflows employing LaTeX, with data exchange to R (programming language), Python (programming language), and numerical solvers used at labs including Los Alamos National Laboratory and Lawrence Livermore National Laboratory.

Reception and Criticism

Maple has been praised for its symbolic capabilities, extensibility, and educational tools, earning adoption in curricula across universities like Stanford University and University of Cambridge; reviewers have compared its strengths and weaknesses relative to Mathematica, MATLAB, and open-source alternatives such as SageMath. Criticisms have focused on licensing cost, performance of specific algorithms compared with specialized libraries, and the learning curve for users migrating from other platforms; these concerns mirror debates seen in communities around Prolog adoption and proprietary software policy at institutions like University of California, Berkeley. Maplesoft has addressed some critiques via regular updates, community toolboxes, and partnerships with research groups at institutions including ETH Zurich and Imperial College London.

Category:Computer algebra systems Category:Proprietary software