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📄 第六节 mathematica编程基础.htm

📁 Mathematica软件包的介绍
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      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">为</SPAN><SPAN       
      lang=EN-US>False</SPAN></font></b></P></TD></TR>      
  <TR>      
    <TD       
    style="BORDER-BOTTOM: windowtext 0.75pt solid; BORDER-LEFT: windowtext 0.75pt solid; BORDER-RIGHT: windowtext 0.75pt solid; BORDER-TOP: medium none; PADDING-BOTTOM: 0cm; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; PADDING-TOP: 0cm; WIDTH: 213.05pt; mso-border-top-alt: solid windowtext .75pt"       
    vAlign=top width=284>      
      <P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN       
      lang=EN-US><font size="4"><b>For[start,test,incr,body]</b></font></SPAN></P></TD>      
    <TD       
    style="BORDER-BOTTOM: windowtext 0.75pt solid; BORDER-LEFT: medium none; BORDER-RIGHT: windowtext 0.75pt solid; BORDER-TOP: medium none; PADDING-BOTTOM: 0cm; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; PADDING-TOP: 0cm; WIDTH: 213.05pt; mso-border-left-alt: solid windowtext .75pt; mso-border-top-alt: solid windowtext .75pt"       
    vAlign=top width=284>      
      <P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN       
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><b><font size="4">以</font></b></SPAN><b><font size="4"><SPAN       
      lang=EN-US>start</SPAN><SPAN       
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">为开始，重复计算</SPAN><SPAN       
      lang=EN-US>body</SPAN><SPAN       
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">和</SPAN><SPAN       
      lang=EN-US>incr, </SPAN><SPAN         
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">直到</SPAN><SPAN         
      lang=EN-US>test</SPAN><SPAN         
      style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">为</SPAN><SPAN         
      lang=EN-US>False</SPAN></font></b></P></TD></TR></TBODY></TABLE>        
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN lang=EN-US>For</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">语句是</SPAN><SPAN        
lang=EN-US>Mathematica</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">系统的循环语句之一。当程序执行到</SPAN><SPAN        
lang=EN-US>For</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">语句时，</SPAN><SPAN        
lang=EN-US>For</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">语句首先执行</SPAN><SPAN        
lang=EN-US>start</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">部分，然后判定</SPAN><SPAN        
lang=EN-US>test</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">部分是否成立。一般</SPAN><SPAN        
lang=EN-US>start</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">部分是给</SPAN><SPAN        
lang=EN-US>test</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">部分中的变量赋初值，如（</SPAN><SPAN        
lang=EN-US>1</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">）式中的</SPAN><SPAN        
lang=EN-US>I=1</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN><SPAN        
lang=EN-US>I</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">称为循环控制变量，变量赋初值后才能判定</SPAN><SPAN        
lang=EN-US>I&lt;=1000</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">是否成立（此时</SPAN><SPAN        
lang=EN-US>I</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">为</SPAN><SPAN        
lang=EN-US>1</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN><SPAN        
lang=EN-US>1&lt;=1000</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">成立）。由于</SPAN><SPAN        
lang=EN-US>test</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">部分成立（即</SPAN><SPAN        
lang=EN-US>test</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">运算结果为</SPAN><SPAN        
lang=EN-US>True</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">），则执行</SPAN><SPAN        
lang=EN-US>body</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">部分，即</SPAN><SPAN        
lang=EN-US>S=S+I^2</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，然后执行</SPAN><SPAN        
lang=EN-US>incr</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，一般</SPAN><SPAN        
lang=EN-US>incr</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">部分是改变循环控制变量的值（</SPAN><SPAN        
lang=EN-US>I=I+1</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">），</SPAN><SPAN        
lang=EN-US>I</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">的改变量可以为任何有意义的值，该值称为步长。然后再判定</SPAN><SPAN        
lang=EN-US>test</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">是否成立，如成立再执行</SPAN><SPAN        
lang=EN-US>body,incr,</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">然后判定</SPAN><SPAN        
lang=EN-US>test</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">部分，如此循环直到</SPAN><SPAN        
lang=EN-US>test</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">不成立（</SPAN><SPAN        
lang=EN-US>I=1001</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">），接着会继续运行</SPAN><SPAN        
lang=EN-US>For</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">后的语句。</SPAN></b></font></P>       
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN lang=EN-US><b><font size="4">Do</font></b></SPAN><b><font size="4"><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">和</SPAN><SPAN        
lang=EN-US>While</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">语句同样可以描述</SPAN><SPAN        
lang=EN-US>For</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">语句表示的内容。（</SPAN><SPAN        
lang=EN-US>1</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">）式使用</SPAN><SPAN        
lang=EN-US>Do</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">语句可写为：</SPAN><SPAN        
lang=EN-US>S=0</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">；</SPAN><SPAN        
lang=EN-US>Do[S=S+I^2</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，</SPAN><SPAN        
lang=EN-US>{I,1,1000,1}]; Print[s];Do</SPAN><SPAN         
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">语句中的</SPAN><SPAN         
lang=EN-US>{I,1,1000,1}</SPAN><SPAN         
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">部分还可写成</SPAN><SPAN         
lang=EN-US>{I,1,1000}</SPAN><SPAN         
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">或</SPAN><SPAN         
lang=EN-US>{I,1000}</SPAN><SPAN         
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，分别表示默认步长为</SPAN><SPAN         
lang=EN-US>1</SPAN><SPAN         
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，默认循环控制变量的初始值为</SPAN><SPAN         
lang=EN-US>1</SPAN><SPAN         
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">。</SPAN></font></b></P>        
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">使用</SPAN><SPAN        
lang=EN-US>While</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">语句可写为：</SPAN><SPAN        
lang=EN-US>S=0</SPAN><SPAN        
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">；</SPAN><SPAN        
lang=EN-US>While[I&lt;=1000,S=S+I^2;I=I+1]; Print[s];</SPAN></b></font></P>      
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%">　</P>      
<P class=MsoNormal style="line-height: 200%"><SPAN       
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><b><font color="#FF0000" size="5">四、<a name="条件结构">条件结构</a></font></b></SPAN></P>     
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">有时候在计算过程中，需要根据某些条件执行不同的语句，这就用到了条件语句，条件语句并不重复执行。</SPAN><SPAN      
lang=EN-US>Mathematica</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">系统有两个很有用的条件语句</SPAN><SPAN      
lang=EN-US>If</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">和</SPAN><SPAN      
lang=EN-US>Which,</SPAN><SPAN      
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">它们的用法格式如下表：</SPAN></b></font></P>     
<TABLE border=1 cellPadding=0 cellSpacing=0
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