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      <author>Lee Curtis Snook</author>
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      <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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        <content>
          <p>I manually entered the values from the calculated matrix below and plotted the graph.</p>
        </content>
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          <e type="operand">M</e>
          <e type="operand">1</e>
          <e type="operand">0</e>
          <e type="operand">1</e>
          <e type="operand">3.1416</e>
          <e type="operand">3.9348</e>
          <e type="operator" args="1">-</e>
          <e type="operand">3.1416</e>
          <e type="operand">3.9348</e>
          <e type="operator" args="1">-</e>
          <e type="operand">2.0261</e>
          <e type="operator" args="1">-</e>
          <e type="operand">.1239</e>
          <e type="operand">2.0261</e>
          <e type="operator" args="1">-</e>
          <e type="operand">.1239</e>
          <e type="operand">0.524</e>
          <e type="operand">1.2114</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0.524</e>
          <e type="operand">1.2114</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0.0752</e>
          <e type="operator" args="1">-</e>
          <e type="operand">.976</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0.0752</e>
          <e type="operator" args="1">-</e>
          <e type="operand">.976</e>
          <e type="operator" args="1">-</e>
          <e type="operand">.0069</e>
          <e type="operand">10</e>
          <e type="operand">2</e>
          <e type="function" args="22">mat</e>
          <e type="operator" args="2">:</e>
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        <input>
          <e type="operand">M</e>
        </input>
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      <text lang="eng" fontFamily="Arial" fontSize="10">
        <content>
          <p>Matrix 1</p>
        </content>
      </text>
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    <region left="45" top="261" width="168" height="38" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Arial" fontSize="10">
        <content>
          <p>M matrix values manually <br />entered from Matrix 2</p>
        </content>
      </text>
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    <region left="585" top="297" width="20" height="24" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">q</e>
        </input>
      </math>
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    <region left="0" top="333" width="511" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Arial" fontSize="10">
        <content>
          <p>----------------------------------------------------------------------------------------------------------------</p>
        </content>
      </text>
    </region>
    <region left="9" top="360" width="352" height="23" color="#000000" fontSize="10">
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        <content>
          <p>I now want the same plot using the following calculations;</p>
        </content>
      </text>
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        <input>
          <e type="operand">α</e>
          <e type="operand">π</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" args="3">mat</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
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    <region left="225" top="396" width="99" height="27" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">α</e>
        </input>
        <result action="numeric">
          <e type="operand">3.1416</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" args="3">mat</e>
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      </math>
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        <input>
          <e type="operand">q</e>
          <e type="operand">0</e>
          <e type="operand">9</e>
          <e type="operand">1</e>
          <e type="function" args="3">range</e>
          <e type="operator" args="2">:</e>
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      <text lang="eng" fontFamily="Arial" fontSize="10">
        <content>
          <p>The result is similar to M matrix above only with the i terms</p>
        </content>
      </text>
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    <region left="0" top="468" width="46" height="24" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">α</e>
          <e type="operand">π</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
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    <region left="0" top="504" width="176" height="72" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">α</e>
          <e type="operand">q</e>
          <e type="function" args="2">P</e>
          <e type="operand">i</e>
          <e type="operand">α</e>
          <e type="operator" args="2">*</e>
          <e type="bracket">(</e>
          <e type="operand">n</e>
          <e type="operator" args="2">^</e>
          <e type="operand">n</e>
          <e type="operator" args="1">!</e>
          <e type="operator" args="2">/</e>
          <e type="function" args="1">vectorize</e>
          <e type="operand">n</e>
          <e type="operand">0</e>
          <e type="operand">q</e>
          <e type="function" args="4">sum</e>
          <e type="operator" args="2">:</e>
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      </math>
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      <math>
        <input>
          <e type="operand">α</e>
          <e type="operand">q</e>
          <e type="function" args="2">P</e>
          <e type="function" args="1">vectorize</e>
        </input>
        <result action="numeric">
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="operand">3.1416</e>
          <e type="operand">i</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operand">3.9348</e>
          <e type="operator" args="1">-</e>
          <e type="operand">3.1416</e>
          <e type="operand">i</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operand">3.9348</e>
          <e type="operator" args="1">-</e>
          <e type="operand">2.0261</e>
          <e type="operand">i</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">-</e>
          <e type="operand">0.1239</e>
          <e type="operand">2.0261</e>
          <e type="operand">i</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">-</e>
          <e type="operand">0.1239</e>
          <e type="operand">0.524</e>
          <e type="operand">i</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operand">1.2114</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0.524</e>
          <e type="operand">i</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operand">1.2114</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0.0752</e>
          <e type="operand">i</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">-</e>
          <e type="operand">0.976</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0.0752</e>
          <e type="operand">i</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">-</e>
          <e type="operand">0.976</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0.0069</e>
          <e type="operand">i</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operand">10</e>
          <e type="operand">1</e>
          <e type="function" args="12">mat</e>
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        <content>
          <p>Doesn't Plot</p>
        </content>
      </text>
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          <e type="operand">α</e>
          <e type="operand">q</e>
          <e type="function" args="2">P</e>
          <e type="function" args="1">vectorize</e>
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    <region left="414" top="702" width="61" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Arial" fontSize="10">
        <content>
          <p>Matrix 2</p>
        </content>
      </text>
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    <region left="18" top="1017" width="290" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Arial" fontSize="10">
        <content>
          <p>Seting x and y to the real and imaginary terms:</p>
        </content>
      </text>
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        <input>
          <e type="operand">α</e>
          <e type="operand">q</e>
          <e type="function" args="2">x</e>
          <e type="operand">α</e>
          <e type="operand">q</e>
          <e type="function" args="2">P</e>
          <e type="function" args="1">vectorize</e>
          <e type="function" args="1">Re</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
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        <input>
          <e type="operand">α</e>
          <e type="operand">q</e>
          <e type="function" args="2">y</e>
          <e type="operand">α</e>
          <e type="operand">q</e>
          <e type="function" args="2">P</e>
          <e type="function" args="1">vectorize</e>
          <e type="function" args="1">Im</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
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      <math>
        <input>
          <e type="operand">α</e>
          <e type="operand">q</e>
          <e type="function" args="2">x</e>
        </input>
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          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="operand">3.9348</e>
          <e type="operator" args="1">-</e>
          <e type="operand">3.9348</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0.1239</e>
          <e type="operand">0.1239</e>
          <e type="operand">1.2114</e>
          <e type="operator" args="1">-</e>
          <e type="operand">1.2114</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0.976</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0.976</e>
          <e type="operator" args="1">-</e>
          <e type="operand">10</e>
          <e type="operand">1</e>
          <e type="function" args="12">mat</e>
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          <e type="operand">α</e>
          <e type="operand">q</e>
          <e type="function" args="2">y</e>
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          <e type="operand">0</e>
          <e type="operand">3.1416</e>
          <e type="operand">3.1416</e>
          <e type="operand">2.0261</e>
          <e type="operator" args="1">-</e>
          <e type="operand">2.0261</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0.524</e>
          <e type="operand">0.524</e>
          <e type="operand">0.0752</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0.0752</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0.0069</e>
          <e type="operand">10</e>
          <e type="operand">1</e>
          <e type="function" args="12">mat</e>
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        <content>
          <p>Doesn't plot</p>
        </content>
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          <e type="operand">α</e>
          <e type="operand">q</e>
          <e type="function" args="2">x</e>
          <e type="operand">α</e>
          <e type="operand">q</e>
          <e type="function" args="2">y</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" args="4">sys</e>
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        <content>
          <p>Maybe I need to concatinate the x(α;q) matrix with the y(α;q) matrix but I don't know how<br />The result show look like matrix M in the first example which does plot.<br /></p>
        </content>
      </text>
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