📄 第六节 mathematica编程基础.htm
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style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">的值，如果使用顺序结构求这个表达式，需要计算</SPAN><SPAN
lang=EN-US>1000</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">次求平方，然后进行累加。写起来极其繁琐。仔细分析一下就可发现，这是一种对一千个数求平方的重复计算。为了简化这个计算程序，我们可以设置一个变量</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'">，让他从</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'">开始，每次加</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'">，一直变到</SPAN><SPAN
lang=EN-US>1000</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">。每次都计算</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'">的平方值并累加起来赋给另一个变量</SPAN><SPAN
lang=EN-US>S</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">。这样上面的想法可写成程序为：</SPAN></b></font></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><font size="4"><b><SPAN
lang=EN-US>S=0;For[I=1,I<=1000,I=I+1,S=S+I^2]; Print[s];<SPAN
style="mso-spacerun: yes">
</SPAN>(1)</SPAN></b></font></P>
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style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><b><font size="4">所谓循环结构实际上是指对同一个程序段重复执行若干次。被重复执行的部分称为循环体。如上述程序中：</font></b></SPAN><b><font size="4"><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'">。循环体往往有若干条语句组成，它们之间以分号隔开。在进行复杂的运算时，常常要用到循环结构，如计算中的迭代、递归等。一般程序语言都提供了描述重复执行的循环控制结构，</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'">系统也不例外。系统提供的循环结构及相关的控制函数参见下表：</SPAN></font></b></P>
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style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><font size="4"><b>表示符号</b></font></SPAN></P></TD>
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style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><font size="4"><b>含义</b></font></SPAN></P></TD></TR>
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<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><font size="4"><b>Do[expr,{i,imin,imax,di}]</b></font></SPAN></P></TD>
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<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">当</font></b></SPAN><b><font size="4"><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'">从</SPAN><SPAN
lang=EN-US>imin</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">以增量</SPAN><SPAN
lang=EN-US>di</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">依次增加到</SPAN><SPAN
lang=EN-US>imax</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">时，重复计算</SPAN><SPAN
lang=EN-US>expr</SPAN></font></b></P></TD></TR>
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<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><font size="4"><b>Nest[f,expr,n]</b></font></SPAN></P></TD>
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<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">对表达式</font></b></SPAN><b><font size="4"><SPAN
lang=EN-US>expr</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">用</SPAN><SPAN
lang=EN-US>n</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">次函数</SPAN><SPAN
lang=EN-US>f</SPAN></font></b></P></TD></TR>
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<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><font size="4"><b>FixedPoint[f,expr,SameTest->Comp]</b></font></SPAN></P></TD>
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<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>expr</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">开始，重复使用</SPAN><SPAN
lang=EN-US>f,</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">直到结果为</SPAN><SPAN
lang=EN-US>False</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">时</SPAN></font></b></P></TD></TR>
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<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><font size="4"><b>While[test,body]</b></font></SPAN></P></TD>
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<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">当</font></b></SPAN><b><font size="4"><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>True</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">时，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'">直到</SPAN><SPAN
lang=EN-US>test</SPAN><SPAN
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