Maple

Definition

Maple is a symbolic and numeric computation language and software system developed by Maplesoft for mathematics, engineering, and education. It allows users to perform exact algebraic manipulation, calculus, equation solving, and numerical computation within an interactive worksheet environment, combining a programming language with document-style output that mixes typeset mathematics, executable code, and graphics into a single readable, shareable document format.

Overview

Maple was first released in the early 1980s at the University of Waterloo as a computer algebra system aimed at making symbolic mathematics accessible without requiring users to hand-derive every algebraic step by hand, a process that was tedious and error-prone for anything beyond simple expressions. Its core strength is symbolic computation: manipulating expressions such as polynomials, integrals, or differential equations exactly, in terms of variables, rather than only computing approximate floating-point numeric answers. Mechanically, Maple represents mathematical expressions internally as symbolic data structures and applies simplification and transformation rules to manipulate them, similar in spirit to Wolfram Language, while also providing a large library of numerical routines for cases where exact symbolic answers are impractical or computationally unnecessary. Its worksheet interface displays typeset mathematical notation directly, so equations render as they would in a printed textbook rather than as plain text expressions, which supports both exploratory research work and polished document-style output suited for teaching. Maple's closest peer is Wolfram Language and Mathematica, both computer algebra systems combining symbolic manipulation with an interactive notebook interface, though the two differ in syntax philosophy and specific library strengths, with Maple often noted by practitioners for particularly strong performance on certain classes of symbolic integration and differential equation problems. It differs more sharply from numerical-only tools like GNU Octave or MATLAB, which are built around matrix computation and simulation rather than exact symbolic manipulation of expressions. In practice, Maple is used in university mathematics and engineering education, in symbolic derivation for physics and control systems research, and in generating verified closed-form solutions that later feed into other simulation or design tools downstream. Its ability to produce exact, checkable algebraic results makes it valuable wherever an approximate numeric answer is insufficient, such as verifying a formula analytically before it is implemented in production code elsewhere. The trade-offs are licensing cost, a smaller general-purpose programming ecosystem than Python, and less prominence outside mathematically intensive fields such as engineering research and academia. Teams whose needs are primarily numerical simulation, machine learning, or general software development typically choose MATLAB, Python with SciPy, or Julia instead, reserving Maple specifically for problems where exact symbolic manipulation is the central requirement rather than a secondary concern. Maple also integrates connectors to some of these other environments, letting a derived formula be exported directly into MATLAB or a compiled language for downstream implementation, which helps bridge the symbolic derivation stage with production numerical code.

Key Features

• Computer algebra system built for exact symbolic mathematics
• Interactive worksheets display typeset mathematical notation directly
• Extensive library covering calculus, algebra, and differential equations
• Combines symbolic manipulation with numerical computation routines
• Strong performance on symbolic integration and equation solving
• Widely used in university mathematics and engineering curricula
• Supports generating verified closed-form solutions for other tools

Use Cases

Alternatives

Frequently Asked Questions

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