Maple’s Evaluation Rules

教授 :蔡桂宏 博士學生 :林佳慧 學號 :95356062

95503 統資軟體課程講義

Program

Full evaluation

Levels of evaluation

Delayed evaluation

Program (continue)

Last name evaluation

Evaluating function definitions

Evaluating function calls

A no evaluation rule

Program (continue)

Evaluating concatenated names

Evaluating indexed names

Online help for evaluation rules

Full evaluation

Introducing the kinds of the data styles by normal programming ：

文字 - 字元：『’’』或『 ’’　’’ 』 數字 - 整數和浮點數： 5 、 5.0 邏輯值（ boolean ）：『 true 』或『 false 』

What is full evaluation? 一口氣計算完畢

Full evaluation(Continue)There are exceptions to this rule:

delayed evaluation levels evaluation last name evaluation

1. Compare 『 : 』和『；』

2. Maple 語法的結尾是用『 : 』和『；』

3. 交換變數

f := x -> f(x)

f(x) 的資料會隨著變數 x 的值改變而變

Solve 語法：

solve( 函數，變數）

此處只有一個變數 (x)

Plot 語法：

plot( 函數，變數 1 range ，變數 2 range ）

Seq 語法：

seq( 數學式， i= 下界．．上界 )

Levels of evaluation

Purpose: How do we use the command?

The command in levels of evaluation

eval(expression ， level ）

Delayed evaluation

Purpose ： see the command’s output Compare 『 Delay 』 of evaluation with

『 Level 』 of evaluation Compare 『 eval(x) 』 with 『 eval(x,n) 』 What happened to the single quote in left equal

sign

Delayed evaluation What happened to the double quote in left eq

ual sign? Compare 『 % 』 with 『 eval(x,n) 』 Another mean about the command’s output i

n 『‘　’』 Explain the function output in 『 rand( ) 』 Compare some different in 『 plot( ) 』

Delayed evaluation

What is delayed evaluation?

沒有立即要計算變數時使用

Delayed evaluation(continue)The command’s output ：

『’變數’』 : one delayed evaluation 『’’變數’’』 : a doubly delayed eval

uation 『’’’變數’’’』 : a trebly delayed

evaluation

expression

X unassigned

function

EX.1 C is a delayed parameter

EX.2 We can use delayed evaluation to prevent Maple from making the function call.

EX.3 Compare them…

Delayed evaluation(continue)Compare 『 Delay 』 of evaluation with 『 Level 』 of evaluation

『 Delay 』 - 由原來的表示式看 delay 幾次

『 Level 』 - 『 eval(x,n) 』 : 程式由前面開始找到 x 後，逐行由上往下顯示

eval(x) 是 eval(eval(x,2))

Delayed evaluation(continue)Compare 『 eval(x) 』 with 『 eval(x,n) 』

The call eval(x) means: Two delayed evaluations.(the same of the eval(eval(x,2)) ) or evaluate x

The call eval(x,n) means: To evaluate the n level of the name x

evaluate a

討論 eval(y,1)

Delayed evaluation(continue)What happened to the single quote in left equal sign

The first x has its evaluation dealyed and the second x is evaluated right away

Delayed evaluation(continue)What happened to the double quote in left equal sign

The first x has its evaluation dealyed and the second x is one delayed evaluated of x

Delayed evaluation(continue) the command’s output in 『 % 』、 『 %% 』

『 % 』 :last expression 『 %% 』 : second last expression

i.e 『 %%% 』 : third last expression

Delayed evaluation(continue)Compare 『 % 』 with 『 eval(x,n) 』

『 % 』 : 由此指令往前找一行 『 eval(x,n) 』 : 程式由前面開始找到

x 後，逐行由上往下顯示

Delayed evaluation(continue)Another mean about the command’s output in 『‘　’』 :

It can get automatic simplification It is a very safe way to define y It is an often used trick in Maple Explain the command’s output in 『 plot( exp

ression in independent variable x ,the range of the x) 』

『‘ u+u ‘ 』 doesn’t evaluate to 2u, it simplifies to 2u.

『 u+u 』 is evaluated by u=5.

『’ u+u’ 』 is a simplistic action.

Delayed evaluation(continue)Explain the function output in 『 rand( ) 』 :

It can generate a random interger

You can find there do not return

a random fracion.

We can try it again by the common as following:

Another way to generate a random fraction:

Delayed evaluation(continue)Compare some different as following:

plot(x^2,x=-5..5); v.s

plot(x^2,'x'=-5..5); plot('x'^2,'x'=-5..5); v.s

plot('x'^2, x=-5..5);

There have the same output

There have the same output

Last name evaluation

Define: Maple 在計算函數時 , 最後一步計算時的變數

Last name is f

Last name is k(w)

此處未使用 last name evaluation

Evaluating function definitions

Purpose: Learning how Maple evaluates function

calls

If we define f as an expression in x.

Now define g as a Maple function.

c is a parameter in the definition of g along with x.

Evaluating function definitions (continue)

How do we define Maple function? use 『 -> 』 use 『 unapply 』 command

Exercise: Explain each the following three sequences of commands.

Evaluating function call

If f is the name of a Maple function, then an expression of the form

f(any-maple-expression) f was defined using by 『 -> 』

Here is an example of a function and several function calls

Evaluating function call (continue)

Some of the function call: Case 1 : above this page Case 2 : unevaluated function call

g(2) is an unevaluat

ed function

call.

Case 1

Case 2

Evaluating function call (continue)

Compare this:

A no evaluation rule

Purpose: There have many examples of how unevalu

ations are used Explain the command in 『 assigned( ) 』 What is recursion ？

assign(x=n);

x;

Why?Because x:=‘x’

A no evaluation rule(continue) Explain the command in 『 assigned( ) 』 : The assigned function returns true if n has a

value other than its own name, and returns false

這裡是因為遞迴(x:=‘x’) 所引起

A no evaluation rule(continue)

What is recursion? x=‘x’ f(0)=1

f(1)=1

f(x+2)=f(x+1)+f(x)

EX. f(5)=8

f(x) 1 1 2 3 5 8

x 0 1 2 3 4 5

電腦記憶體 x的地方放 x的位置

Evaluating concatenated names

Purpose: find Maple’s rules for evaluating

concatenated names

What is a concatenated name? the concatenated name’s command is 『 || 』

evaln(expression)

使用 w||eval(x,n)有無括號之差別

The next exercise shows that Maple does allow the use of parentheses for grouping around the right pair of vertical lines.

Evaluating indexed names

Purpose: To understand what indexed name is it

Compare 『 x||1:=0 』 with 『 x[1]:=0 』 『 x||1:=0 』 : Maple evaluates x||1 to the

name x1 『 x[1]:=0 』 : x[1] is a name. Maple does

not need to evaluate it

Online help for evaluation rules

Purpose: Finding many ways to call for help

Online help for evaluation rules (continue)

Ways: 『 ? 』 『 F1 』 (version 9) 『 Help/Search 』