📄 ch11_1_2.htm
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<title> 数学式的化简 </title>
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<font COLOR="#0000FF">
<h1>11.1.2 数学式的化简</h1>
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<p>以下的函数适用来简化数学式，如展开、化简或聚集数学式。相关的指令有：
</p>
<p><font COLOR="#FF0000" FACE="Times New Roman">collect(S)</font> 聚集<font COLOR="#FF0000" FACE="Times New Roman">S</font>的系数 </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">collect(S,</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">v</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">)</font> 聚集<font COLOR="#FF0000" FACE="Times New Roman">S</font>的系数，是以<font COLOR="#FF0000" FACE="Times New Roman">v</font>为独立变数 </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">expand(S) </font>将<font COLOR="#FF0000" FACE="Times New Roman">S</font>表示式展开 </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">factor(S)</font> 还原<font COLOR="#FF0000" FACE="Times New Roman">S</font>的因式<font FACE="Times New Roman">(factorization)</font>
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<p><font COLOR="#FF0000" FACE="Times New Roman">simple(S)</font> 如果可能的话，将<font COLOR="#FF0000" FACE="Times New Roman">S</font>表示式再做简化 </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">simplify(S)</font> 利用<font FACE="Times New Roman">Maple</font>简化法则化简<font COLOR="#FF0000" FACE="Times New Roman">S</font>表示式 <br>
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<p>我们来看一些例子 </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>> S1 = </font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">x^3-1</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">;</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>> S2 = </font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">(x-3)^2+(y-4)^2</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">;</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>> S3 = </font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">sqrt(a^4*b^7)</font><font COLOR="#FF0000">'</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>> S4 = </font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">14*x^2/(22*x*y)</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">; <br>
</font></p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>> factor(S1)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">(x-1)*(x^2+x+1)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>> expand(S2)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">x^2-6*x+25+y^2-8*y</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>>collect(S2)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">x^2-6*x+9+(y-4)^2</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>>collect(S2,</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">y</font><font COLOR="#FF0000">'</font><font COLOR="#FF0000" FACE="Times New Roman">)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">y^2-8*y+(x-3)62+16</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>>simplify(S3)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">a^2*b^(7/2)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>>simple(S4)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">ans=</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">7/11*x/y</font></p>
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