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    <identity>
      <id>be8ed228-7b9f-4d88-9521-f6039e697cd5</id>
      <revision>25</revision>
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    <calculation>
      <precision>4</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <fractions>decimal</fractions>
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    <pageModel active="true" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
      <paper id="9" orientation="Portrait" width="827" height="1169" />
      <margins left="39" right="39" top="39" bottom="39" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
      <backgrounds />
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    <dependences>
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  <region id="0" left="18" top="18" width="138" height="34" color="#000000" bgColor="#ffff80" fontSize="10">
    <math>
      <input>
        <e type="operand">f</e>
        <e type="operand">x.0</e>
        <e type="operand">n</e>
        <e type="function" preserve="true" args="3">Taylor</e>
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  <region id="1" left="18" top="54" width="202" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Part of plugin</p>
    </text>
    <text lang="ger">
      <p>Bestandteil des Plugins</p>
    </text>
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  <region id="2" left="234" top="54" width="152" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin Nonlinear Solvers.sm">Nonlinear Solvers</p>
    </text>
  </region>
  <region id="3" left="0" top="72" width="9" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p />
    </text>
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  <region id="4" left="18" top="81" width="649" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Taylor-series expansion of expression f about point x.0 up to order n</p>
    </text>
    <text lang="ger">
      <p>Taylor-Reihenentwicklung des Ausdrucks f um den Entwicklungspunkt x.0 bis zur 
Ordnung n</p>
    </text>
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  <region id="5" left="27" top="126" width="240" height="158" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="3.57406813465074" scale_y="3.28197257543686" scale_z="6.33167971869" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-4" transpose_y="-52" transpose_z="0">
      <input>
        <e type="operand">e</e>
        <e type="operand">x</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operand">e</e>
        <e type="operand">x</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operand">0</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">Taylor</e>
        <e type="operand">e</e>
        <e type="operand">x</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operand">0</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="3">Taylor</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">sys</e>
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  <region id="6" left="270" top="126" width="240" height="158" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="2.67134145110602" scale_y="2.75311161931118" scale_z="4.73244433246283" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-38" transpose_y="-10" transpose_z="0">
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operand">0</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">Taylor</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operand">0.5</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">Taylor</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operand">π</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">Taylor</e>
        <e type="operand">4</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="6">sys</e>
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    </plot>
  </region>
  <region id="7" left="27" top="378" width="595" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>The series expansion uses the built-in capability for symbolic derivatives.
That's why you can get symbolic results</p>
    </text>
    <text lang="ger">
      <p>Die Reihenentwicklung benutzt die Fähigkeit von SMath zur symbolischen 
Ableitungsbildung. Daher kann man auch symbolische Ergebnisse bekommen.</p>
    </text>
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  <region id="8" left="27" top="423" width="259" height="52" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <description active="true" position="Top" lang="eng">
        <p>Optimization&gt; Symbolic</p>
      </description>
      <description active="true" position="Top" lang="ger">
        <p>Optimierung&gt; Symbolisch</p>
      </description>
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operand">0</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="3">Taylor</e>
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      <result action="symbolic">
        <e type="operand">x</e>
        <e type="operand">6</e>
        <e type="operand">x</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operand">6</e>
        <e type="operator" args="2">/</e>
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  <region id="9" top="504" color="#000000" bgColor="#ffffff">
    <area collapsed="false">
      <title lang="ger">
        <p>Bug</p>
      </title>
    </area>
    <region id="10" left="27" top="522" width="706" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p>SMath does not know the symbolic derivative of hyperbolic secans and cosecans. 
Therefore their series expansions fail.</p>
      </text>
      <text lang="ger">
        <p>SMath beherrscht nicht die symbolische Ableitung für den Secans Hyperbolicus und den 
Cosecans Hyperbolicus. Daher scheitern auch die entsprechenden Reihenentwicklungen.</p>
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      <math>
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          <e type="operand">x</e>
          <e type="function" preserve="true" args="1">sech</e>
          <e type="operand">x</e>
          <e type="function" preserve="true" args="2">diff</e>
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        <result action="symbolic">
          <e type="operand">x</e>
          <e type="function" preserve="true" args="1">sech</e>
          <e type="operand">x</e>
          <e type="function" preserve="true" args="2">diff</e>
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      </math>
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      <math error="84">
        <input>
          <e type="operand">x</e>
          <e type="function" preserve="true" args="1">sech</e>
          <e type="operand">0</e>
          <e type="operand">4</e>
          <e type="function" preserve="true" args="3">Taylor</e>
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        <result action="symbolic">
          <e type="operand">#</e>
        </result>
      </math>
    </region>
    <region id="13" left="288" top="594" width="199" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">x</e>
          <e type="function" preserve="true" args="1">csch</e>
          <e type="operand">x</e>
          <e type="function" preserve="true" args="2">diff</e>
        </input>
        <result action="symbolic">
          <e type="operand">x</e>
          <e type="function" preserve="true" args="1">csch</e>
          <e type="operand">x</e>
          <e type="function" preserve="true" args="2">diff</e>
        </result>
      </math>
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    <region id="14" left="27" top="603" width="207" height="28" color="#000000" bgColor="#ffffff" fontSize="10">
      <math error="84">
        <input>
          <e type="operand">x</e>
          <e type="function" preserve="true" args="1">csch</e>
          <e type="operand">0</e>
          <e type="operand">4</e>
          <e type="function" preserve="true" args="3">Taylor</e>
        </input>
        <result action="symbolic">
          <e type="operand">#</e>
        </result>
      </math>
    </region>
    <region id="15" top="639" color="#000000" bgColor="#ffffff">
      <area terminator="true" />
    </region>
  </region>
  <region id="16" left="18" top="666" width="152" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin Nonlinear Solvers.sm">Nonlinear Solvers</p>
    </text>
  </region>
  <region id="17" left="18" top="693" 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="18" left="18" top="711" width="61" 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="19" left="18" top="756" width="450" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p italic="true">$Author: mkraska $
$Date: 2013-08-13 11:18:41 +0200 (Di, 13. Aug 2013) $ </p>
    </text>
  </region>
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