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      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
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    <text lang="eng">
      <p>function or vector of functions to find roots for</p>
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    <text lang="ger">
      <p>Ausdruck oder Vektor von Ausdrüchen, deren Nullstellen zu suchen sind</p>
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        <e type="operand">x</e>
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    <text lang="eng">
      <p>variable or vector of variables to solve for</p>
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    <text lang="ger">
      <p>Unabhängige Variable oder Vektor unabhängiger Variablen.</p>
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    <text lang="eng">
      <p>initial guess for the variable</p>
    </text>
    <text lang="ger">
      <p>Startwert oder Vektor von Startwerten</p>
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    <text lang="eng">
      <p>Solves f for x starting from x.0 </p>
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    <text lang="ger">
      <p>Sucht eine Lösung für die Funktion f ausgehend vom Startwert x.0.</p>
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        <e type="operand">3</e>
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        <e type="operand">27</e>
        <e type="operand">x</e>
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        <e type="operand">x</e>
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      <input>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">x</e>
        <e type="operand">10</e>
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        <e type="operand">5.4862</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
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        <e type="operand">x</e>
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        <e type="operand">0.64</e>
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        <e type="function" args="1">f</e>
        <e type="operand">x</e>
        <e type="operand">4</e>
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      <result action="numeric">
        <e type="operand">5.49</e>
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  <region id="14" left="18" top="306" width="464" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Function for investigation of the convergence behaviour</p>
    </text>
    <text lang="ger">
      <p>Funktion zur Untersuchung des Konvergenzverhaltens</p>
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  <region id="15" left="18" top="333" width="211" height="37" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">x.0</e>
        <e type="function" args="1">L</e>
        <e type="operand">y</e>
        <e type="function" args="1">f</e>
        <e type="operand">y</e>
        <e type="operand">x.0</e>
        <e type="function" preserve="true" args="3">roots</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">line</e>
        <e type="operator" args="2">:</e>
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  <region id="16" left="18" top="369" width="240" height="158" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="points" scale_x="0.891" scale_y="1.406408618241" scale_z="1.39234453205859" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="6" transpose_y="0" transpose_z="0">
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        <e type="operand">x</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
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    <text lang="eng">
      <p>The diagram shows how the obtained solution (y)
depends on the value of the initial guess (x) </p>
    </text>
    <text lang="ger">
      <p>Das Diagramm zeigt, wie die gefundene Lösung (y) vom 
Startwert (x) abhängt.</p>
    </text>
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      <input>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">2.5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">Taylor</e>
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        <e type="operand">1</e>
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  <region id="19" left="270" top="567" width="431" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Examination of the tangent at x.0 shows why for x.0
between solutions 2 and 3, solution 1 is obtained.</p>
    </text>
    <text lang="ger">
      <p>Untersuchung der Tangente bei x.0 zeigt, warum bei einem
x.0 zwischen Lösungen 2 und 3 die Lösung 1 gefunden wird.</p>
    </text>
  </region>
  <region id="20" top="702" color="#000000" bgColor="#ffffff">
    <area collapsed="false">
      <title lang="eng">
        <p>Bug: roots() behaves differently for equivalent expressions</p>
      </title>
      <title lang="ger">
        <p>Fehler: Unterschiedliches Verhalten bei äquivalenten Ausdrücken</p>
      </title>
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          <e type="operand">A</e>
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          <e type="operand">108</e>
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          <e type="operand">2</e>
          <e type="operand">A</e>
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          <e type="operand">156</e>
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          <e type="operand">1</e>
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        <input>
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          <e type="operand">A</e>
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          <e type="operand">108</e>
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          <e type="operand">2</e>
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          <e type="function" preserve="true" args="4">mat</e>
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          <e type="operand">#</e>
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      <math>
        <input>
          <e type="operand">f.2</e>
          <e type="operand">A</e>
          <e type="operand">B</e>
          <e type="operand">2</e>
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          <e type="operand">96</e>
          <e type="operand">12</e>
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      </math>
    </region>
    <region id="25" left="18" top="846" width="307" height="46" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <description active="true" position="Top" lang="eng">
          <p>symbolic optimization</p>
        </description>
        <input>
          <e type="operand">f.1</e>
          <e type="operand">f.2</e>
          <e type="operator" args="2">-</e>
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          <e type="operand">0</e>
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          <e type="operand">3</e>
          <e type="operand">B</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">-</e>
          <e type="operand">3</e>
          <e type="operand">52</e>
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          <e type="operator" args="2">+</e>
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          <e type="operand">A</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">-</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
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    <region id="26" left="342" top="846" width="277" height="46" color="#000000" bgColor="#ffffff" fontSize="10">
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        <description active="true" position="Top" lang="eng">
          <p>symbolic optimization</p>
        </description>
        <input>
          <e type="operand">0</e>
          <e type="operand">2</e>
          <e type="operand">78</e>
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          <e type="operand">A</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">3</e>
          <e type="operand">B</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">-</e>
          <e type="operand">3</e>
          <e type="operand">52</e>
          <e type="operand">B</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
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          <e type="operand">A</e>
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          <e type="operand">0</e>
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    <region id="27" left="18" top="918" width="405" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p>Intermediate assignment to a variable does help.</p>
      </text>
    </region>
    <region id="28" left="18" top="945" width="91" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">f.3</e>
          <e type="operand">f.1</e>
          <e type="operand">f.2</e>
          <e type="operator" args="2">-</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="29" left="126" top="945" width="71" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">f.3</e>
        </input>
        <result action="symbolic">
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">mat</e>
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    </region>
    <region id="30" top="981" color="#000000" bgColor="#ffffff">
      <area terminator="true" />
    </region>
  </region>
  <region id="31" left="18" top="1008" width="127" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p href="Function index.sm">Function index</p>
    </text>
    <text lang="ger">
      <p href="Function index.sm">Funktionsindex</p>
    </text>
  </region>
  <region id="32" left="18" top="1026" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p href="Handbook.sm">Contents</p>
    </text>
    <text lang="ger">
      <p href="Handbook.sm">Inhalt</p>
    </text>
  </region>
  <region id="33" left="18" top="1062" width="450" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p italic="true">$Author: mkraska $
$Date: 2013-08-17 23:58:19 +0200 (Sa, 17. Aug 2013) $ </p>
    </text>
  </region>
</regions>