📄 ch11_1_2.htm
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<TITLE> 数学式的化简 </TITLE>
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<H1>11.1.2 数学式的化简</H1>
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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：
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<FONT COLOR=#FF0000 FACE="Times New Roman">collect(S)</FONT>
聚集<FONT COLOR=#FF0000 FACE="Times New Roman">S</FONT>的系数
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<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
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<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
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<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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<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
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<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
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我们来看一些例子
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<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>
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<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>
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<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>
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<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">;
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> factor(S1)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">(x-1)*(x^2+x+1)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>> expand(S2)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">x^2-6*x+25+y^2-8*y</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>collect(S2)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">x^2-6*x+9+(y-4)^2</FONT>
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<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>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">y^2-8*y+(x-3)62+16</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>simplify(S3)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">a^2*b^(7/2)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">>>simple(S4)</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">ans=</FONT>
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<FONT COLOR=#FF0000 FACE="Times New Roman">7/11*x/y</FONT><HR>
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