Maple高级编程指南：经典全面解析

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《Maple高级编程指南》是一本专为Maple用户撰写的经典教程，由Maplesoft，Waterloo Maple Inc.的一个部门，即Maplesoft出版于1996年至2008年期间。作者包括M.B. Monagan、K.O. Geddes、K.M. Heal、G.Labahn、S.M. Vorkoetter、J.McCarron以及P.DeMarco等，他们在软件开发和Maple技术领域具有深厚的背景。本书主要关注Maple的高级编程技巧和功能，这是针对那些希望进一步提升Maple使用能力，特别是进行复杂计算、符号计算、数值分析和图形处理的用户。 Maple是一款强大的数学软件，它提供了一套完整的工具集，用于解决各种数学问题，包括代数、微积分、线性代数、概率统计等。Maple Advanced Programming Guide详细介绍了如何利用Maple的高级特性进行编程，如脚本编写、函数设计、算法实现、程序优化，以及如何与其他编程语言（如Java）集成使用。书中还涉及了Maple的工作流程，如交互式环境、命令行操作以及LaTeX文件的导入和导出，这对于理解和提高Maple的生产力至关重要。在版权方面，Maple、Maplelet和Maplesoft都是Waterloo Maple Inc.的注册商标，所有权利受到保护。读者在使用软件时必须遵守许可协议，不可未经允许复制或传播软件，否则可能触犯法律。同时，书中提到的Windows是Microsoft Corporation的注册商标，而Java和相关标志则是Sun Microsystems, Inc.在美国和其他国家的商标或注册商标。本书的出版旨在提供一个全面的学习资源，帮助读者掌握Maple的高级编程技术，无论是对学术研究者、工程师，还是教育工作者来说，都是一个提升专业技能的重要参考资料。通过阅读《Maple高级编程指南》，读者将能够深入理解Maple的强大功能，并有效地将其应用到实际工作和学习场景中。由于文档是基于特定版本的Maple编写的，因此部分内容可能只适用于该版本，但基本原则和技巧对于后续版本也有指导价值。最后，本书的印刷版拥有加拿大ISBN号码978-1-897310-47-2，包含了丰富的章节内容和实用指南。

6 • Chapter 1: Procedures, Variables, and Extending Maple

environment, the map command is used to apply an operation to the

elements of a structure. For example, you can divide each element of a

list by a number, such as 8.

lst := [8, 4, 2, 16]:

map( x->x/8, lst);

[1,

, 2]

Consider a variation on the map command, which appears in the fol-

lowing pro cedure.

Example This new procedure divides each element of a list by the ﬁrst

element of that list.

nest := proc(x::list)

local v;

v := x[1];

map( y -> y/v, x );

end proc:

nest(lst);

[1,

, 2]

The procedure nest contains a second procedure, map, which in this

case is the Maple command map. Maple applies its lexical scoping rules,

which declare the v within the call to map as the same v as in the outer

procedure, nest.

Scoping Rules

This section explains Maple scoping rules. You will learn how Maple de-

termines which variables are local to a procedure and which are global.

You must have a basic understanding of Maple evaluation rules for pa-

rameters, and for local and global variables. For more information, refer

to chapter 6 of the

Introductory Programming Guide.

Local Versus Global Variables

In general, when writing a procedure, you should explicitly declare which

variables are global and which are local. Declaring the scope of the vari-

ables makes your procedure easier to read and debug. However, sometimes

declaring the variables is not the best method. In the previous nest pro-

cedure, the variable in the map command is deﬁned by the surrounding

8 • Chapter 1: Procedures, Variables, and Extending Maple

The Quick-Sort Algorithm

Sorting a few numbers is quick using any method, but sorting large

amounts of data can be very time consuming; thus, ﬁnding eﬃcient meth-

ods is important.

The following quick-sort algorithm is a classic algorithm. The key to

understanding this algorithm is to understand the operation of partition-

ing. This involves choosing any one number from the array that you are

about to sort. Then, you reposition the numbers in the array that are less

than the number that you chose to one end of the array and reposition

numbers that are greater to the other end. Lastly, you insert the chosen

number between these two groups.

At the end of the partitioning, you have not yet entirely sorted the

array, because the numbers less than or greater than the one you chose

may still be in their original order. This procedure divides the array into

two smaller arrays which are easier to sort than the original larger one.

The partitioning operation has thus made the work of sorting much eas-

ier. You can bring the array one step closer in the sorting process by

partitioning each of the two smaller arrays. This operation produces four

smaller arrays. You sort the entire array by rep eatedly partitioning the

smaller arrays.

Example

The partition procedure uses an array to store the list because you can

change the elements of an array directly. Thus, you can sort the array in

place and not waste any space generating extra copies.

The quicksort procedure is easier to understand if you look at the

procedure partition in isolation ﬁrst. This procedure accepts an array

of numbers and two integers. The two integers are element numbers of the

array, indicating the portion of the array to partition. While you could

possibly choose any of the numbers in the array to partition around, this

procedure chooses the last element of the section of the array for that

purpose, namely A[n]. The intentional omission of global and local

statements shows which variables Maple recognizes as local and which

are global by default. It is recommended, however, that you not make

this omission in your pro cedures.

partition := proc(A::array(1, numeric),

m::posint, n::posint)

i := m;

j := n;

x := A[j];

while i<j do

if A[i]>x then

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