a00100.html

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

          <td class="md"></td>
          <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" nowrap>V &amp;&nbsp;</td>
          <td class="mdname" nowrap> <em>e</em></td>
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<p>
evaluates polynomial value <em>p(a)</em>, and computes <img class="formulaInl" alt="$\frac{p(x)}{(x - a)}$" src="form_22.png"> .<p>
Evaluates <img class="formulaInl" alt="$p(a)$" src="form_23.png"> and polynomial <img class="formulaInl" alt="$q(x)=\frac{p(x)-p(a)}{(x - a)}$" src="form_24.png"> at the same time by Horner's recurence.<p>
It can be shown that <img class="formulaInl" alt="$p(x)=q(x)(x - a)+p(a)$" src="form_25.png"> , which essentially means that <img class="formulaInl" alt="$p(a)$" src="form_23.png"> is the remainder of <img class="formulaInl" alt="$\frac{p(x)}{(x - a)}$" src="form_22.png"> . For the special case where <img class="formulaInl" alt="$a$" src="form_26.png"> is a root of <img class="formulaInl" alt="$p(x)$" src="form_21.png"> (i.e. <img class="formulaInl" alt="$p(a)=0$" src="form_27.png"> ), this operation is called <em>deflation</em>. That is, on exit <img class="formulaInl" alt="$q(x)$" src="form_28.png"> will have all the roots of <img class="formulaInl" alt="$p(x)$" src="form_21.png"> , except for the root <img class="formulaInl" alt="$a$" src="form_26.png"> .<p>
No error checking is performed, so any validation for overflow, or underflow is the responsibility of the caller.<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>[in]</tt>&nbsp;</td><td valign="top"><em>a</em>&nbsp;</td><td>parameter of <img class="formulaInl" alt="$p(a)$" src="form_23.png"> . </td></tr>
    <tr><td valign="top"><tt>[out]</tt>&nbsp;</td><td valign="top"><em>q</em>&nbsp;</td><td>on exit contains the quotient <img class="formulaInl" alt="$q(x)=\frac{p(x)-p(a)}{(x - a)}$" src="form_24.png"> . </td></tr>
    <tr><td valign="top"><tt>[out]</tt>&nbsp;</td><td valign="top"><em>e</em>&nbsp;</td><td>round-off error to be expected in the calculation of <img class="formulaInl" alt="$p(a)$" src="form_23.png"> </td></tr>
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<dl compact><dt><b>Returns:</b></dt><dd><img class="formulaInl" alt="$p(a)$" src="form_23.png"> , the remainder of <img class="formulaInl" alt="$\frac{p(x)}{(x - a)}$" src="form_22.png"> .</dd></dl>
<dl compact><dt><b>See also:</b></dt><dd>Polynomial&lt;T&gt;::evalAndDeflate(const U&amp; x, Polynomial&lt;U&gt;&amp; q) const<br>
 Polynomial&lt;T&gt;::evalAndDeflate(const U&amp; x, Polynomial&lt;U&gt;&amp; q, V&amp; e) const<br>
 <a class="el" href="a00100.html#g0a6fc89686a91e3c8c99923a7b0247e3">evalAndDeflate(const Polynomial&lt;T&gt;&amp; p, const U&amp; x, Polynomial&lt;U&gt;&amp; q)</a> </dd></dl>

<p>
Definition at line <a class="el" href="a00107.html#l01011">1011</a> of file <a class="el" href="a00107.html">Polynomial.h</a>.    </td>
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<a class="anchor" name="g0a6fc89686a91e3c8c99923a7b0247e3"></a><!-- doxytag: member="Polynomial.h::evalAndDeflate" ref="g0a6fc89686a91e3c8c99923a7b0247e3" args="(const Polynomial&lt; T &gt; &amp;p, const U &amp;a, 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 evalAndDeflate           </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>const U &amp;&nbsp;</td>
          <td class="mdname" nowrap> <em>a</em>, </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>
evaluates polynomial value <em>p(a)</em>, and computes <img class="formulaInl" alt="$\frac{p(x)}{(x - a)}$" src="form_22.png"> .<p>
Evaluates <img class="formulaInl" alt="$p(a)$" src="form_23.png"> and polynomial <img class="formulaInl" alt="$q(x)=\frac{p(x)-p(a)}{(x - a)}$" src="form_24.png"> at the same time by Horner's recurence.<p>
It can be shown that <img class="formulaInl" alt="$p(x)=q(x)(x - a)+p(a)$" src="form_25.png"> , which essentially means that <img class="formulaInl" alt="$p(a)$" src="form_23.png"> is the remainder of <img class="formulaInl" alt="$\frac{p(x)}{(x - a)}$" src="form_22.png"> . For the special case where <img class="formulaInl" alt="$a$" src="form_26.png"> is a root of <img class="formulaInl" alt="$p(x)$" src="form_21.png"> (i.e. <img class="formulaInl" alt="$p(a)=0$" src="form_27.png"> ), this operation is called <em>deflation</em>. That is, on exit <img class="formulaInl" alt="$q(x)$" src="form_28.png"> will have all the roots of <img class="formulaInl" alt="$p(x)$" src="form_21.png"> , except for the root <img class="formulaInl" alt="$a$" src="form_26.png"> .<p>
No error checking is performed, so any validation for overflow, or underflow is the responsibility of the caller.<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>[in]</tt>&nbsp;</td><td valign="top"><em>a</em>&nbsp;</td><td>parameter of <img class="formulaInl" alt="$p(a)$" src="form_23.png"> . </td></tr>
    <tr><td valign="top"><tt>[out]</tt>&nbsp;</td><td valign="top"><em>q</em>&nbsp;</td><td>on exit contains the quotient <img class="formulaInl" alt="$q(x)=\frac{p(x)-p(a)}{(x - a)}$" src="form_24.png"> . </td></tr>
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<dl compact><dt><b>Returns:</b></dt><dd><img class="formulaInl" alt="$p(a)$" src="form_23.png"> , the remainder of <img class="formulaInl" alt="$\frac{p(x)}{(x - a)}$" src="form_22.png"> .</dd></dl>
<dl compact><dt><b>See also:</b></dt><dd>Polynomial&lt;T&gt;::evalAndDeflate(const U&amp; x, Polynomial&lt;U&gt;&amp; q) const<br>
 Polynomial&lt;T&gt;::evalAndDeflate(const U&amp; x, Polynomial&lt;U&gt;&amp; q, V&amp; e) const<br>
 <a class="el" href="a00100.html#g2fe3a1cb7b5ae7739c3f228758d9f1fd">evalAndDeflate(const Polynomial&lt;T&gt;&amp; p, const U&amp; x, Polynomial&lt;U&gt;&amp; q, V&amp; e)</a> </dd></dl>

<p>
Definition at line <a class="el" href="a00107.html#l00954">954</a> of file <a class="el" href="a00107.html">Polynomial.h</a>.    </td>
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<a class="anchor" name="gcc297191b953d7df4ecad642e13e7911"></a><!-- doxytag: member="Polynomial.h::evalAndDerive" ref="gcc297191b953d7df4ecad642e13e7911" args="(const Polynomial&lt; T &gt; &amp;p, const U &amp;x, U &amp;ppx, U &amp;pppx)" --><p>
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template&lt;class T, class U&gt; </td>
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          <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>const U &amp;&nbsp;</td>
          <td class="mdname" nowrap> <em>x</em>, </td>
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          <td class="md" nowrap>U &amp;&nbsp;</td>
          <td class="mdname" nowrap> <em>ppx</em>, </td>
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          <td class="md"></td>
          <td class="md" nowrap>U &amp;&nbsp;</td>
          <td class="mdname" nowrap> <em>pppx</em></td>
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          <td class="md">)&nbsp;</td>
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<p>
evaluates <img class="formulaInl" alt="$p(x)$" src="form_21.png"> , first derivate <img class="formulaInl" alt="$p'(x)$" src="form_30.png"> , and second derivative <img class="formulaInl" alt="$p''(x)$" src="form_31.png"> at the same time.<p>
Evaluates efficiently <img class="formulaInl" alt="$p(x)$" src="form_21.png"> , first derivate <img class="formulaInl" alt="$p'(x)$" src="form_30.png"> , and second derivative <img class="formulaInl" alt="$p''(x)$" src="form_31.png"> at the same time.<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>[in]</tt>&nbsp;</td><td valign="top"><em>x</em>&nbsp;</td><td>variable to evaluate. </td></tr>
    <tr><td valign="top"><tt>[out]</tt>&nbsp;</td><td valign="top"><em>ppx</em>&nbsp;</td><td>on exit contains <img class="formulaInl" alt="$p'(x)$" src="form_30.png"> . </td></tr>
    <tr><td valign="top"><tt>[out]</tt>&nbsp;</td><td valign="top"><em>pppx</em>&nbsp;</td><td>on exit contains <img class="formulaInl" alt="$p''(x)$" src="form_31.png"> . </td></tr>
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<dl compact><dt><b>Returns:</b></dt><dd>The value of <img class="formulaInl" alt="$p(x)$" src="form_21.png"> .</dd></dl>
<dl compact><dt><b>See also:</b></dt><dd><a class="el" href="a00100.html#gc143079d7e07a2b902831ec539e45fc6">evalAndDerive(const Polynomial&lt;T&gt;&amp; p, const U&amp; x, U&amp; ppx)</a> </dd></dl>

<p>
Definition at line <a class="el" href="a00107.html#l01141">1141</a> of file <a class="el" href="a00107.html">Polynomial.h</a>.    </td>
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<a class="anchor" name="gc143079d7e07a2b902831ec539e45fc6"></a><!-- doxytag: member="Polynomial.h::evalAndDerive" ref="gc143079d7e07a2b902831ec539e45fc6" args="(const Polynomial&lt; T &gt; &amp;p, const U &amp;x, U &amp;ppx)" --><p>
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template&lt;class T, class U&gt; </td>
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