a00099.html

This library defines basic operation on polynomials, and contains also 3 different roots (zeroes)-fi

       
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<p>
returns optimal scale for polynomial.<p>
Computes an optimal scale factor for polynomial <em>p</em>. Thus ensuring that evaluating the polynomial will not result in overflow or underflow.<p>
<dl compact><dt><b>Parameters:</b></dt><dd>
  <table border="0" cellspacing="2" cellpadding="0">
    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>p</em>&nbsp;</td><td>a polynomial.</td></tr>
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<dl compact><dt><b>See also:</b></dt><dd>U <a class="el" href="a00099.html#g663581aef6853ed86df03a35505c9ebd">scalePoly(Polynomial&lt;T&gt;&amp; p, const Polynomial&lt;U&gt;&amp; q)</a>; </dd></dl>

<p>
Definition at line <a class="el" href="a00107.html#l01253">1253</a> of file <a class="el" href="a00107.html">Polynomial.h</a>.    </td>
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<a class="anchor" name="g1ca5c1a34fcdcadb083a25ecf0e1a995"></a><!-- doxytag: member="Polynomial.h::modulus" ref="g1ca5c1a34fcdcadb083a25ecf0e1a995" args="(const Polynomial&lt; T &gt; &amp;p, Polynomial&lt; U &gt; &amp;q)" --><p>
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template&lt;class T, class U&gt; </td>
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          <td class="md" nowrap valign="top">void modulus           </td>
          <td class="md" valign="top">(&nbsp;</td>
          <td class="md" nowrap valign="top">const <a class="el" href="a00090.html">Polynomial</a>&lt; T &gt; &amp;&nbsp;</td>
          <td class="mdname" nowrap> <em>p</em>, </td>
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          <td class="md" nowrap align="right"></td>
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          <td class="md" nowrap><a class="el" href="a00090.html">Polynomial</a>&lt; U &gt; &amp;&nbsp;</td>
          <td class="mdname" nowrap> <em>q</em></td>
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          <td class="md">)&nbsp;</td>
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<p>
computes the modulus of polynomial <em>p</em>.<p>
Computes the modulus of polynomial <em>p</em>, such as for polynomial:<p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[p(x)=a_0+a_1{x}+a_2{x^2}+...+a_n{x^n}\]" src="form_33.png">
<p>
<p>
the resulting polynomial <em>q</em> will be :<p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[q(x)=|a_0|+|a_1|{x}+|a_2|{x^2}+...+|a_n|{x^n}\]" src="form_34.png">
<p>
<p>
<dl compact><dt><b>Parameters:</b></dt><dd>
  <table border="0" cellspacing="2" cellpadding="0">
    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>p</em>&nbsp;</td><td>a polynomial. </td></tr>
    <tr><td valign="top"><tt>[out]</tt>&nbsp;</td><td valign="top"><em>q</em>&nbsp;</td><td>the modulus polynomial p. </td></tr>
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<p>
Definition at line <a class="el" href="a00107.html#l01315">1315</a> of file <a class="el" href="a00107.html">Polynomial.h</a>.    </td>
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<a class="anchor" name="g663581aef6853ed86df03a35505c9ebd"></a><!-- doxytag: member="Polynomial.h::scalePoly" ref="g663581aef6853ed86df03a35505c9ebd" args="(Polynomial&lt; T &gt; &amp;p, const Polynomial&lt; U &gt; &amp;q)" --><p>
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template&lt;class T, class U&gt; </td>
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          <td class="md" nowrap valign="top">U scalePoly           </td>
          <td class="md" valign="top">(&nbsp;</td>
          <td class="md" nowrap valign="top"><a class="el" href="a00090.html">Polynomial</a>&lt; T &gt; &amp;&nbsp;</td>
          <td class="mdname" nowrap> <em>p</em>, </td>
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          <td class="md" nowrap align="right"></td>
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          <td class="md" nowrap>const <a class="el" href="a00090.html">Polynomial</a>&lt; U &gt; &amp;&nbsp;</td>
          <td class="mdname" nowrap> <em>q</em></td>
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          <td class="md">)&nbsp;</td>
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<p>
rescales a polynomial using an optimal scale.<p>
Computes an optimal scale factor for polynomial <em>p</em>. Thus ensuring that evaluating the polynomial will not result in overflow or underflow, then scales the polynomial <em>p</em>.<p>
<dl compact><dt><b>Parameters:</b></dt><dd>
  <table border="0" cellspacing="2" cellpadding="0">
    <tr><td valign="top"><tt>[in,out]</tt>&nbsp;</td><td valign="top"><em>p</em>&nbsp;</td><td>a polynomial. </td></tr>
    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>q</em>&nbsp;</td><td>the modulus polynomial of p.</td></tr>
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</dl>
<dl compact><dt><b>See also:</b></dt><dd><a class="el" href="a00099.html#g663581aef6853ed86df03a35505c9ebd">scalePoly(Polynomial&lt;T&gt;&amp; p, const Polynomial&lt;U&gt;&amp; q)</a><br>
 <a class="el" href="a00099.html#g1ca5c1a34fcdcadb083a25ecf0e1a995">modulus(const Polynomial&lt;T&gt;&amp; p, Polynomial&lt;U&gt;&amp; q)</a> </dd></dl>

<p>
Definition at line <a class="el" href="a00107.html#l01293">1293</a> of file <a class="el" href="a00107.html">Polynomial.h</a>.    </td>
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<a class="anchor" name="gff48f345e1c619a7fcfef4fec02674f8"></a><!-- doxytag: member="polyzero.h::zerosGeometricMean" ref="gff48f345e1c619a7fcfef4fec02674f8" args="(const Polynomial&lt; std::complex&lt; T &gt; &gt; &amp;p)" --><p>
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template&lt;class T&gt; </td>
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          <td class="md" nowrap valign="top">T zerosGeometricMean           </td>
          <td class="md" valign="top">(&nbsp;</td>
          <td class="md" nowrap valign="top">const <a class="el" href="a00090.html">Polynomial</a>&lt; std::complex&lt; T &gt; &gt; &amp;&nbsp;</td>
          <td class="mdname1" valign="top" nowrap> <em>p</em>          </td>
          <td class="md" valign="top">&nbsp;)&nbsp;</td>
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<p>
returns the geometric mean for zeros of a polynomial.<p>
See <a class="el" href="a00099.html#ga911d353ac1900e9da22160a11d8b350">zerosGeometricMean(const Polynomial&lt;T&gt;&amp; p)</a> for more details. 
<p>
Definition at line <a class="el" href="a00108.html#l00306">306</a> of file <a class="el" href="a00108.html">polyzero.h</a>.    </td>
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<a class="anchor" name="ga911d353ac1900e9da22160a11d8b350"></a><!-- doxytag: member="polyzero.h::zerosGeometricMean" ref="ga911d353ac1900e9da22160a11d8b350" args="(const Polynomial&lt; T &gt; &amp;p)" --><p>
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template&lt;class T&gt; </td>
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          <td class="md" nowrap valign="top">T zerosGeometricMean           </td>
          <td class="md" valign="top">(&nbsp;</td>
          <td class="md" nowrap valign="top">const <a class="el" href="a00090.html">Polynomial</a>&lt; T &gt; &amp;&nbsp;</td>
          <td class="mdname1" valign="top" nowrap> <em>p</em>          </td>
          <td class="md" valign="top">&nbsp;)&nbsp;</td>
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<p>
returns the geometric mean for zeros of a polynomial.<p>
Returns the geometric mean for zeros of a polynomial.<p>
According to Vieta's theorem, the geometric mean <img class="formulaInl" alt="$G$" src="form_50.png"> for the zeros of a polynomial can be simplified to the result of the equation:<p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[G_p=\left[\frac{|a_0|}{|a_n|}\right]^{\frac{1}{n}}, p(x)=a_0+a_1{x}+a_2{x^2}+...+a_n{x^n}, a_n\neq 0\]" src="form_51.png">
<p>
<p>
<dl compact><dt><b>Parameters:</b></dt><dd>
  <table border="0" cellspacing="2" cellpadding="0">
    <tr><td valign="top"><tt>[in]</tt>&nbsp;</td><td valign="top"><em>p</em>&nbsp;</td><td>polynomial being evaluated. template parameter <em>T</em> can be any real or complex IEEE floating-point type.</td></tr>
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</dl>
<dl compact><dt><b>See also:</b></dt><dd><a class="el" href="a00090.html">Polynomial</a><br>
 <a class="el" href="a00099.html#g4c00b88d043d1f70cdcb4d2cec66b55e">cauchyLowerBound()</a> </dd></dl>

<p>
Definition at line <a class="el" href="a00108.html#l00293">293</a> of file <a class="el" href="a00108.html">polyzero.h</a>.    </td>
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