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  <region id="0" top="18" color="#000000" bgColor="#ffffff">
    <area collapsed="true">
      <title lang="ger">
        <p>hatch</p>
      </title>
    </area>
    <region id="1" left="36" top="36" width="449" height="274" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
      <math decimalPlaces="4">
        <description active="true" position="Top" lang="ger">
          <p>Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den Funktionen f(x) und g(x) im Bereich von x1 bis x2 mit 2*n Linien.</p>
        </description>
        <description active="true" position="Top" lang="eng">
          <p>Generates a matrix for 2*n vertical lines (hatching) between functions f(x) and g(x)in x-range from x1 to x2</p>
        </description>
        <input>
          <e type="operand">f</e>
          <e type="operand">g</e>
          <e type="operand">x.1</e>
          <e type="operand">x.2</e>
          <e type="operand">N</e>
          <e type="function" args="5">hatch</e>
          <e type="operand">dx</e>
          <e type="operand">x.2</e>
          <e type="operand">x.1</e>
          <e type="operator" args="2">-</e>
          <e type="operand">N</e>
          <e type="operator" args="2">/</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">:</e>
          <e type="operand">h</e>
          <e type="operand">x.1</e>
          <e type="operand">x.1</e>
          <e type="function" args="1">f</e>
          <e type="operand">x.1</e>
          <e type="operand">x.1</e>
          <e type="function" args="1">g</e>
          <e type="operand">2</e>
          <e type="operand">2</e>
          <e type="function" preserve="true" args="6">mat</e>
          <e type="operator" args="2">:</e>
          <e type="operand">x</e>
          <e type="operand">x.1</e>
          <e type="operand">x.2</e>
          <e type="operand">dx</e>
          <e type="operator" args="2">-</e>
          <e type="operand">x.1</e>
          <e type="operand">dx</e>
          <e type="operator" args="2">+</e>
          <e type="function" preserve="true" args="3">range</e>
          <e type="operand">h</e>
          <e type="operand">h</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operand">2</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">+</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operand">2</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">+</e>
          <e type="function" args="1">g</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operand">2</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">+</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operand">2</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">+</e>
          <e type="function" args="1">f</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operator" args="2">+</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operator" args="2">+</e>
          <e type="function" args="1">f</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operator" args="2">+</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operator" args="2">+</e>
          <e type="function" args="1">g</e>
          <e type="operand">4</e>
          <e type="operand">2</e>
          <e type="function" preserve="true" args="10">mat</e>
          <e type="function" preserve="true" args="2">stack</e>
          <e type="operator" args="2">:</e>
          <e type="function" preserve="true" args="3">for</e>
          <e type="operand">h</e>
          <e type="operand">4</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="6">line</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
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  <region id="3" left="18" top="414" width="388" height="147" border="true" color="#000000" bgColor="#ffe1e1" fontSize="10">
    <math decimalPlaces="4">
      <description active="true" position="Top" lang="eng">
        <p>a useful substract algo style collapse in utilities</p>
      </description>
      <input>
        <e type="operand">fnct</e>
        <e type="operand">n</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operand">c</e>
        <e type="operand">d</e>
        <e type="function" args="6">∫</e>
        <e type="operand">Δ</e>
        <e type="operand">dummy</e>
        <e type="operand">x</e>
        <e type="function" args="1">fnct</e>
        <e type="operand">n</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">x</e>
        <e type="operand">c</e>
        <e type="operand">d</e>
        <e type="function" preserve="true" args="4">int</e>
        <e type="operand">x</e>
        <e type="function" args="1">fnct</e>
        <e type="operand">n</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">x</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="function" preserve="true" args="4">int</e>
        <e type="function" preserve="true" args="3">at</e>
        <e type="operator" args="2">:</e>
        <e type="operand">Δ</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
        <e type="operator" args="2">:</e>
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    <math decimalPlaces="4">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">fnct</e>
        <e type="operand">x</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">erf</e>
        <e type="function" preserve="true" args="1">vectorize</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">Gamma</e>
        <e type="function" preserve="true" args="1">vectorize</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">sys</e>
        <e type="operator" args="2">:</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="function" preserve="true" args="1">Gamma</e>
        <e type="function" preserve="true" args="1">vectorize</e>
        <e type="operator" args="2">:</e>
        <e type="operand">x</e>
        <e type="function" args="1">g</e>
        <e type="operand">0</e>
        <e type="operator" args="2">:</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
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    <math decimalPlaces="4">
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">Gamma</e>
        <e type="function" preserve="true" args="1">vectorize</e>
        <e type="operand">x</e>
        <e type="operand">2.5</e>
        <e type="operand">4</e>
        <e type="function" preserve="true" args="4">int</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">Gamma</e>
        <e type="function" preserve="true" args="1">vectorize</e>
        <e type="operand">x</e>
        <e type="operand">0.5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">int</e>
        <e type="operator" args="2">-</e>
      </input>
      <result action="numeric">
        <e type="operand">3.7196</e>
      </result>
    </math>
  </region>
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    <plot type="2d" render="lines" scale_x="1" scale_y="2.5937424601" scale_z="2.5937424601" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="0" transpose_y="0" transpose_z="0">
      <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">x</e>
        <e type="function" args="1">g</e>
        <e type="operand">0.5</e>
        <e type="operand">1</e>
        <e type="operand">20</e>
        <e type="function" args="5">hatch</e>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">x</e>
        <e type="function" args="1">g</e>
        <e type="operand">2.5</e>
        <e type="operand">4</e>
        <e type="operand">30</e>
        <e type="function" args="5">hatch</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">sys</e>
      </input>
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    <math decimalPlaces="4">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">fnct</e>
        <e type="operand">1</e>
        <e type="operand">2.5</e>
        <e type="operand">4</e>
        <e type="operand">0.5</e>
        <e type="operand">1</e>
        <e type="function" args="6">∫</e>
        <e type="operand">x</e>
        <e type="function" args="1">fnct</e>
        <e type="operand">2</e>
        <e type="operand">2.5</e>
        <e type="operand">4</e>
        <e type="operand">0.5</e>
        <e type="operand">1</e>
        <e type="function" args="6">∫</e>
        <e type="operand">x</e>
        <e type="function" args="1">fnct</e>
        <e type="operand">3</e>
        <e type="operand">2.5</e>
        <e type="operand">4</e>
        <e type="operand">0.5</e>
        <e type="operand">1</e>
        <e type="function" args="6">∫</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
      </input>
      <result action="numeric">
        <e type="operand">54</e>
        <e type="operand">1.1493</e>
        <e type="operand">3.7196</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
      </result>
    </math>
  </region>
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    <text lang="eng">
      <p>OBSERVE: erf(x), Gamma(x) are not scalar functions in Smath. Thus,the integrand must be vectorized.</p>
    </text>
  </region>
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