Maple’s Evaluation Rules 教授 : 蔡桂宏 博士 學生 : 林佳慧 學號 : 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 equal sign?  Compare 『 % 』 with 『 eval(x,n) 』  Another mean about the command’s output in 『 ‘ ’ 』  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 evaluation  『 ’’’ 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( expression 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

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 unevaluated function call. Case 1 Case 2

Evaluating function call (continue) Compare this:

A no evaluation rule Purpose:  There have many examples of how unevaluations 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) x 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 』