a00100.html

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

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          <td class="md" nowrap valign="top">U evalAndDerive           </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>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">)&nbsp;</td>
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<p>
evaluates <img class="formulaInl" alt="$p(x)$" src="form_21.png"> and first derivate <img class="formulaInl" alt="$dy=p'(x)$" src="form_29.png"> at the same time.<p>
Evaluates efficiently <img class="formulaInl" alt="$p(x)$" src="form_21.png"> and first derivative <img class="formulaInl" alt="$p'(x)$" src="form_30.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>
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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#gcc297191b953d7df4ecad642e13e7911">evalAndDerive(const Polynomial&lt;T&gt;&amp; p, const U&amp; x, U&amp; ppx, U&amp; pppx)</a> </dd></dl>

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Definition at line <a class="el" href="a00107.html#l01095">1095</a> of file <a class="el" href="a00107.html">Polynomial.h</a>.    </td>
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<a class="anchor" name="g055ddecc1576e178f623b4b8e868cc23"></a><!-- doxytag: member="Polynomial.h::evalDeriveAndDeflate" ref="g055ddecc1576e178f623b4b8e868cc23" args="(const Polynomial&lt; T &gt; &amp;p, const U &amp;x, U &amp;ppx, U &amp;pppx, 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 evalDeriveAndDeflate           </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"></td>
          <td class="md" nowrap>const U &amp;&nbsp;</td>
          <td class="mdname" nowrap> <em>x</em>, </td>
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          <td class="md"></td>
          <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" 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 first derivate <img class="formulaInl" alt="$p'(x)$" src="form_30.png"> , second derivative <img class="formulaInl" alt="$p''(x)$" src="form_31.png"> , and deflates a polynomial 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"> , while deflating 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]</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>
    <tr><td valign="top"><tt>[out]</tt>&nbsp;</td><td valign="top"><em>q</em>&nbsp;</td><td>on exit, contains <img class="formulaInl" alt="$q(z)=\frac{p(z)}{z-x}$" src="form_32.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#gcc297191b953d7df4ecad642e13e7911">evalAndDerive(const Polynomial&lt;T&gt;&amp; p, const U&amp; x, U&amp; ppx, U&amp; ppx)</a> </dd></dl>

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Definition at line <a class="el" href="a00107.html#l01197">1197</a> of file <a class="el" href="a00107.html">Polynomial.h</a>.    </td>
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<a class="anchor" name="g1d2411f2d57ecde3c510c53390e4c611"></a><!-- doxytag: member="Polynomial.h::evalError" ref="g1d2411f2d57ecde3c510c53390e4c611" args="(const Polynomial&lt; T &gt; &amp;p, const U &amp;mx)" --><p>
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template&lt;class T, class U&gt; </td>
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          <td class="md" nowrap valign="top">U evalError           </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>mx</em></td>
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<p>
evaluates round-off error.<p>
Evaluates round_off error in computing <img class="formulaInl" alt="$p(x)$" src="form_21.png"> .<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>mx</em>&nbsp;</td><td>absolute value of x. </td></tr>
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<dl compact><dt><b>Returns:</b></dt><dd>e round-off error to be expected in the calculation 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#g06acec12b7f66f68ea3db5838ac7e072">eval(const Polynomial&lt;T&gt;&amp; p, const U&amp; x, V&amp; e)</a><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><br>
 Polynomial&lt;T&gt;::evalAndDeflate(const U&amp; x, Polynomial&lt;U&gt;&amp; q, V&amp; e) const </dd></dl>

<p>
Definition at line <a class="el" href="a00107.html#l01063">1063</a> of file <a class="el" href="a00107.html">Polynomial.h</a>.    </td>
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