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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.

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Presentation on theme: "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."— Presentation transcript:

1 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

2 Program Full evaluation Levels of evaluation Delayed evaluation

3 Program (continue) Last name evaluation Evaluating function definitions Evaluating function calls A no evaluation rule

4 Program (continue) Evaluating concatenated names Evaluating indexed names Online help for evaluation rules

5 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

6 Full evaluation(Continue) There are exceptions to this rule:  delayed evaluation  levels evaluation  last name evaluation

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9 1.Compare 『 : 』和『;』 2.Maple 語法的結尾是用『 : 』和 『;』 3. 交換變數

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11 f := x -> f(x) f(x) 的資料會隨著變數 x 的值改變而 變

12 Solve 語法: solve( 函數,變數)

13 此處只有一個變數 (x) Plot 語法: plot( 函數,變數 1 range ,變數 2 range )

14 Seq 語法: seq( 數學式, i= 下界..上界 )

15 Levels of evaluation Purpose:  How do we use the command? The command in levels of evaluation eval(expression , level )

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20 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

21 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( ) 』

22 Delayed evaluation What is delayed evaluation? 沒有立即要計算變數時使用

23 Delayed evaluation(continue) The command’s output :  『 ’ 變數 ’ 』 : one delayed evaluation  『 ’’ 變數 ’’ 』 : a doubly delayed evaluation  『 ’’’ 變數 ’’’ 』 : a trebly delayed evaluation

24 expression X unassigned

25 function EX.1 C is a delayed parameter

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

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28 EX.3 Compare them…

29 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

30 eval(x) 是 eval(eval(x,2))

31 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

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33 evaluate a

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35 討論 eval(y,1)

36 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

37 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

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39 Delayed evaluation(continue) the command’s output in 『 % 』、 『 % 』  『 % 』 :last expression  『 % 』 : second last expression i.e 『 %% 』 : third last expression

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42 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

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44 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) 』

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

46 『 u+u 』 is evaluated by u=5. 『 ’u+u’ 』 is a simplistic action.

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50 Delayed evaluation(continue) Explain the function output in 『 rand( ) 』 :  It can generate a random interger

51 You can find there do not return a random fracion. We can try it again by the common as following:

52 Another way to generate a random fraction:

53 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);

54 There have the same output

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56 Last name evaluation Define:  Maple 在計算函數時, 最後一步計算時的 變數

57 Last name is f

58 Last name is k(w) 此處未使用 last name evaluation

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60 Evaluating function definitions Purpose:  Learning how Maple evaluates function calls

61 If we define f as an expression in x. Now define g as a Maple function.

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

63 Evaluating function definitions (continue) How do we define Maple function?  use 『 -> 』  use 『 unapply 』 command

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67 Exercise: Explain each the following three sequences of commands.

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71 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

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74 Evaluating function call (continue) Some of the function call:  Case 1 : above this page  Case 2 : unevaluated function call

75 g(2) is an unevaluated function call. Case 1 Case 2

76 Evaluating function call (continue) Compare this:

77 A no evaluation rule Purpose:  There have many examples of how unevaluations are used  Explain the command in 『 assigned( ) 』  What is recursion ?

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79 assign(x=n); x;

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81 Why? Because x:=‘x’

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83 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

84 這裡是因為遞迴 (x:=‘x’) 所引起

85 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

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87 Evaluating concatenated names Purpose:  find Maple’s rules for evaluating concatenated names What is a concatenated name?  the concatenated name’s command is 『 || 』

88 evaln(expression)

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90 使用 w||eval(x,n) 有無括號之差別

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

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95 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

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106 Online help for evaluation rules Purpose:  Finding many ways to call for help

107 Online help for evaluation rules (continue) Ways:  『 ? 』  『 F1 』 (version 9)  『 Help/Search 』


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