Maple简介夏壁灿

2012 年春

Maple 的结构 用户界面 library 介绍

主要内容

关于Maple

Maple 是一个计算机代数系统（ Computer Algebra System, CAS ）。 它提供了一个交互式的问题求解环境，你可以通过编程完成符号、数值和图形计算。 该系统提供一个高级程序设计语言Maple ， Maple 的库函数皆用它实现。 开发：始于 1980 年，加拿大 University of Waterloo 的符号计算小组（ Symbolic Computation Group ） 市场化： 1992 年 Waterloo Maple Software ；1995 年 Waterloo Maple Inc.

Maple的结构

Maple 由 User Interface （用户界面，又称作 Iris ） Kernel （内核） Library （库函数，应用程序包等）

组成。

Maple的结构

Iris 处理输入输出，图形，人机交互

Kernel 翻译，基本而核心的计算，内存管理

library 库函数，应用程序包，在线帮助

Maple的结构

Maple 有多种 User Interface 。包括前面介绍的 standard worksheet 和 classic worksheet 等。

Maple standard worksheetInterface Description

Standard (default) A full-featured graphical user interface that helps you create electronic documents to show all your calculations, assumptions, and any margin of error in your results. You can also hide the computations to allow your reader to focus on the problem setup and final results. The advanced formatting features lets you create the customized document you need. Because the documents are live, you can edit the parameters and, with the click of a button, compute the new results. The Standard interface has two modes: Document mode and Worksheet mode.

Maple classic worksheetClassic A basic worksheet environment for older

computers with limited memory. The Classic interface does not offer all of the graphical user interface features that are available in the Standard interface. The Classic interface has only one mode, Worksheet mode.

Other interfacesCommand-line version

A command-line interface for solving very large complex problems or batch processing with scripts. No graphical user interface features are available.

MapletTM Applications

Graphical user interfaces containing windows, textbox regions, and other visual interfaces, which gives you point-and-click access to the power of Maple. You can perform calculations and plot functions without using the worksheet.

MaplesoftTM Graphing Calculator

A graphical calculator interface to the Maple computational engine. Using it, you can perform simple computations and create customizable, zoomable graphs. This is available on Microsoft®

Windows® only.

Maple 启动（ standard ， classic 或command-line ）后，称作一个 session 。 一个 Maple session 启动时， kernel 也同时载入，而别的函数在需要时通过指令载入。

Classic 和 standard 界面的功能介绍、 interface 命令的使用，改变参数等。

05.mws

library 分为 main library 和 packages

最常用的指令包含在 main library 中，可以通过如下方式直接调用

command(arguments);

Library的使用

比较专门的、不太常用的指令包含在各个 package 中，可以通过“长指令”方式调用

package[command](arguments);

Library的使用

或者在执行载入命令：

with(package):

后，用“短指令”方式调用

command(arguments);

最常使用的指令（非完全）Commandname

Description

plot and plot3d

Create a two-dimensional and three-dimensional plot of functions.

solve Solve one or more equations or inequalities for their unknowns.

fsolve Solve one or more equations using floating-point arithmetic.

eval Evaluate an expression at a given point.

evalf Numerically evaluate expressions.

dsolve Solve ordinary differential equations (ODEs).

int Compute an indefinite or definite integral.

diff Compute an ordinary or partial derivative, as the context dictates.

limit Calculate the limiting value of a function.

sum For symbolic summation. It is used to compute a closed form for an indefinite or definite sum.

assume/is Set variable properties and relationships between variables. Similar functionality is provided by the assuming command.

assuming Compute the value of an expression under assumptions.

simplify Apply simplification rules to an expression.

expand Distribute products over sums.

normal Normalize a rational expression.

convert Convert an expression to a different type or form.

type Type-checking command. In many contexts, it is not necessary to know the exact value of an expression; it suffices to know that an expression belongs to a broad class, or group, of expressions that share some common properties. These classes or groups are known as types.

series Generalized series expansion.

map Apply a procedure to each operand of an expression.

Main library 中指令的完整清单可以从Maple的帮助系统获

得。

最常使用的程序包（非完全）Package Name DescriptionCodeGeneration The package is a collection of commands and subpackages

that enable the translation of Maple code to other programming languages, such as C, Fortran, MATLAB®, Visual Basic®, and Java.

LinearAlgebra The package contains commands to construct and manipulate Matrices and Vectors, and solve linear algebra problems. LinearAlgebra routines operate on three principal data structures: Matrices, Vectors, and scalars.

Optimization The package is a collection of commands for numerically solving optimization problems, which involve finding the minimum or maximum of an objective function possibly subject to constraints.

Physics The package implements computational representations and related operations for most of the objects used in mathematical physics computations.

RealDomain The package provides an environment in which Maple assumes that the basic underlying number system is the field of real numbers instead of the complex number field.

ScientificConstants The package provides access to the values of various physical constants, for example, the velocity of light and the atomic weight of sodium. This package provides the units for each of the constant values, allowing for greater understanding of an equation. The package also provides units-matching for error checking of the solution.

ScientificErrorAnalysis

The package provides representation and construction of numerical quantities that have a central value and an associated uncertainty (or error), which is a measure of the degree of precision to which the quantity's value is known. Various first-order calculations of error analysis can be performed with these quantities.

Statistics The package is a collection of tools for mathematical statistics and data analysis. The package supports a wide range of common statistical tasks such as quantitative and graphical data analysis, simulation, and curve fitting.

Student The package is a collection of subpackages designed to assist with teaching and learning standard undergraduate mathematics. The many commands display functions, computations, and theorems in various ways, including stepping through important computations. The Student package contains the following subpackages: Calculus1 - single-variable calculus

LinearAlgebra - linear algebra

MultivariateCalculus - multivariate calculus

NumericalAnalysis - numerical analysis

Precalculus - precalculus

VectorCalculus - multivariate vector calculus

Units The package contains commands for unit conversion and provides environments for performing calculations with units. It accepts approximately 300 distinct unit names (for example, meters and grams) and over 550 units with various contexts (for example, standard miles and U.S. survey miles). Maple also contains two Units palettes that allow you to enter the unit for an expression quickly.

VectorCalculus The package is a collection of commands that perform multivariate and vector calculus operations. A large set of predefined orthogonal coordinate systems is available. All computations in the package can be performed in any of these coordinate systems. It contains a facility for adding a custom but orthogonal coordinate system and using that new coordinate system for your computations.

完整的 package清单可以从Maple的帮助系统获得。

作业1. 熟悉 classic 的 Maple 界面，以及常用的 Maple

指令。2. 指令 simplify 和 normal 有何异同？如何化简 (24+6*15^(1/2))^(1/2) 和 sqrt(2*x+1-

2*sqrt(x^2+x)) ？3. 给定一个有理系数的一元二次多项式，验证韦

达定理成立。4. 一个自然数 n ，如果它是除 n 以外所有自己因

数的和，则 n 称为完全数 (perfect number) 。请问如何用 Maple 判断一个给定的自然数是否完全数？（提示：注意 numtheory[divisors] 指令）

5. 思考题：怎样得到 10000 以内的所有完全数？