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      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
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      <title lang="eng">
        <p>     hatch/fill     </p>
      </title>
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        <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>
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          <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>
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          <e type="bracket">(</e>
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          <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>
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          <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>
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    <text lang="eng">
      <p bold="true">Fourier Quantum [2 slits momentum distribution]</p>
    </text>
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        <e type="operand">x</e>
        <e type="function" args="1">Ψ</e>
        <e type="operand">1</e>
        <e type="operand">10</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">/</e>
        <e type="operand">7.5</e>
        <e type="operator" args="1">-</e>
        <e type="operand">x</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operand">x</e>
        <e type="operand">2.5</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operand">2.5</e>
        <e type="operand">x</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operand">x</e>
        <e type="operand">7.5</e>
        <e type="operator" args="2">≤</e>
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        <e type="operand">0</e>
        <e type="function" preserve="true" args="3">cases</e>
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        <e type="operand">x</e>
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        <e type="operator" args="2">:</e>
        <e type="operand">x</e>
        <e type="function" args="1">g</e>
        <e type="operand">0</e>
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        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
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      <description active="true" position="Top" lang="eng">
        <p>A neat fill exclusive plot</p>
      </description>
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        <e type="operand">f</e>
        <e type="operand">g</e>
        <e type="operand">7.5</e>
        <e type="operator" args="1">-</e>
        <e type="operand">7.5</e>
        <e type="operand">60</e>
        <e type="function" args="5">hatch</e>
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  <region id="7" left="360" top="540" width="306" height="139" border="true" color="#000000" bgColor="#ffffe1">
    <writer lang="eng"><![CDATA[<span style="font-family: 'Arial'; font-size: 10pt; font-weight: normal; font-style: normal; color: Black; background-color: Transparent; text-align: left; line-height: 115%">
<div><span style="font-family: 'Times New Roman'"><span style="font-size: 14pt"><strong><span style="color: Red">Key points in this document</span></strong></span><span style="font-size: 11pt"><span style="color: Red"><strong>:</strong></span></span></span></div>
<div><span style="font-family: 'Times New Roman'"><span style="font-size: 11pt"><strong>1. </strong>A neat 2D plot exclusive</span></span></div>
<div><span style="font-family: 'Times New Roman'"><span style="font-size: 11pt"><strong>2. </strong>'v' is <strong>scalar</strong> wrt integral</span></span></div>
<div><span style="font-family: 'Times New Roman'"><span style="font-size: 11pt"><strong>3.</strong> <strong>Vectorize</strong> operates on the &quot;scalar Integral.</span></span></div>
<div><span style="font-family: 'Times New Roman'"><span style="font-size: 11pt"><strong>4. X_Y</strong> plot augment both scalar <span style="color: Blue">augment</span></span></span><span style="color: Blue">(<span style="font-family: 'Times New Roman'"><span style="font-size: 11pt">v</span></span>,<span style="font-size: 14pt">∫</span>(<span style="font-family: 'Times New Roman'"><span style="font-size: 11pt">v</span></span>))</span>.</div>
<div><span style="font-family: 'Times New Roman'"><span style="font-size: 11pt"><strong>5.</strong> <strong>W</strong> region accepts </span></span><span style="font-size: 14pt"> ∫</span></div></span>]]></writer>
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      <description active="true" position="Top" lang="eng">
        <p>Momentum distribution @ the slit Screen</p>
      </description>
      <input>
        <e type="operand">u</e>
        <e type="function" args="1">P</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">/</e>
        <e type="operand">i</e>
        <e type="operand">u</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">exp</e>
        <e type="operand">x</e>
        <e type="function" args="1">Ψ</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="operand">10</e>
        <e type="operator" args="1">-</e>
        <e type="operand">10</e>
        <e type="function" preserve="true" args="4">int</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">abs</e>
        <e type="bracket">(</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">:</e>
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      <input>
        <e type="operand">t0</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="1">time</e>
        <e type="operator" args="2">:</e>
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      <input>
        <e type="operand">v</e>
        <e type="operand">3</e>
        <e type="operator" args="1">-</e>
        <e type="operand">3</e>
        <e type="operand">2.95</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="3">range</e>
        <e type="operator" args="2">:</e>
        <e type="operand">v</e>
        <e type="function" args="1">∫</e>
        <e type="operand">v</e>
        <e type="function" args="1">P</e>
        <e type="function" preserve="true" args="1">vectorize</e>
        <e type="operator" args="2">:</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
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  <region id="11" left="522" top="774" width="218" height="56" border="true" color="#ff0000" bgColor="#ffffe1" fontSize="10">
    <text lang="eng">
      <p bold="true">For an export, you must copy/paste the data table.....augment(v,∫(v)).....</p>
    </text>
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        <e type="function" preserve="true" args="2">augment</e>
        <e type="operand">0</e>
        <e type="operand">2</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">2</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="6">mat</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
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        <e type="function" preserve="true" args="1">time</e>
        <e type="operand">t0</e>
        <e type="operator" args="2">-</e>
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        <e type="operand" style="unit">min</e>
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        <e type="operand">1.1</e>
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        <e type="operand">v</e>
        <e type="function" args="1">∫</e>
        <e type="function" preserve="true" args="2">augment</e>
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        <e type="operand">3</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.016</e>
        <e type="operand">2.95</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.009</e>
        <e type="operand">2.9</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.003</e>
        <e type="operand">2.85</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0</e>
        <e type="operand">2.8</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0</e>
        <e type="operand">2.75</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.002</e>
        <e type="operand">2.7</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.004</e>
        <e type="operand">2.65</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.004</e>
        <e type="operand">2.6</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.003</e>
        <e type="operand">2.55</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0.001</e>
        <e type="operand">10</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="22">mat</e>
      </result>
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