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      <id>be8ed228-7b9f-4d88-9521-f6039e697cd5</id>
      <revision>38</revision>
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    <calculation>
      <precision>4</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <fractions>decimal</fractions>
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      <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>
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    <dependences>
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    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">Dirac</e>
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    <text lang="eng">
      <p>Part of plugin</p>
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    <text lang="ger">
      <p>Bestandteil des Plugins</p>
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    <text lang="ger">
      <p href="Plugin Statistical Tools.sm">Statistical Tools</p>
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  <region id="4" left="18" top="108" width="502" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Dirac distribution, has the value ∞ at x0 (x0 defaults to 0)</p>
    </text>
    <text lang="ger">
      <p>Dirac-Distribution, hat an der Stelle x0 den Wert ∞, Voreinstellung für x0 = 0.</p>
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        <e type="operand">x.0</e>
        <e type="function" args="2">δ</e>
        <e type="operand">x</e>
        <e type="operand">x.0</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">∞</e>
        <e type="operand">0</e>
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        <e type="operator" args="2">:</e>
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    <math>
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        <e type="operand">∞</e>
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    <math>
      <input>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="1">Dirac</e>
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  <region id="8" left="333" top="234" width="115" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">Dirac</e>
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      <result action="numeric">
        <e type="operand">0</e>
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  <region id="9" left="27" top="270" width="130" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">Dirac</e>
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      <result action="symbolic">
        <e type="operand">∞</e>
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  <region id="10" left="189" top="270" width="130" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
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        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">Dirac</e>
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      <result action="symbolic">
        <e type="operand">0</e>
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  <region id="11" left="333" top="270" width="130" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">3</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">Dirac</e>
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      <result action="symbolic">
        <e type="operand">0</e>
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  <region id="12" left="333" top="297" width="204" height="206" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">5</e>
        <e type="operator" args="1">-</e>
        <e type="operand">5</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">Dirac</e>
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        <e type="operand">4</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0</e>
        <e type="operand">3</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0</e>
        <e type="operand">2</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
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        <e type="operand">1</e>
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        <e type="operand">0</e>
        <e type="operand">11</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="24">mat</e>
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    <math>
      <input>
        <e type="operand">5</e>
        <e type="operator" args="1">-</e>
        <e type="operand">5</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="function" preserve="true" args="1">Dirac</e>
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        <e type="operator" args="1">-</e>
        <e type="operand">0</e>
        <e type="operand">3</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0</e>
        <e type="operand">2</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">∞</e>
        <e type="operand">1</e>
        <e type="operand">0</e>
        <e type="operand">2</e>
        <e type="operand">0</e>
        <e type="operand">3</e>
        <e type="operand">0</e>
        <e type="operand">4</e>
        <e type="operand">0</e>
        <e type="operand">5</e>
        <e type="operand">0</e>
        <e type="operand">11</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="24">mat</e>
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  <region id="14" left="18" top="531" width="734" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>The integral of the Dirac distribution equals to one. However, the numeric integration
fails due to usage of the if-statement in the function definition, which the integration
function of SMath cannot handle.</p>
    </text>
    <text lang="ger">
      <p>Das Integral der Dirac-Distribution ist gleich 1, die numerische Integration scheitert,
vermutlich, weil die Funktion intern mit der if-Anweisung definiert wurde, was die
numerische Integrationsroutine in SMath nicht verträgt.</p>
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  <region id="15" left="27" top="594" width="152" height="66" color="#000000" bgColor="#ffffff" fontSize="10">
    <math error="2">
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">Dirac</e>
        <e type="operand">x</e>
        <e type="operand">1</e>
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        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">int</e>
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        <e type="operand">#</e>
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  <region id="16" left="18" top="666" width="707" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Even if defined using boolean expressions, the integral would hardly provide usable
values, either the infinity point is missed, then the integral is equal to zero or
the result is undefined, if inifinity is hit by the function sampling in integration.</p>
    </text>
  </region>
  <region id="17" left="18" top="756" width="152" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin Statistical Tools.sm">Statistical Tools</p>
    </text>
  </region>
  <region id="18" left="18" top="792" 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="19" left="18" top="810" 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="20" left="18" top="846" 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>
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