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<regions>
  <settings>
    <identity>
      <id>b4bea744-d848-4b3d-857a-5b18c99fc903</id>
      <revision>11</revision>
    </identity>
    <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="1" orientation="Portrait" width="850" height="1100" />
      <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 />
    </pageModel>
    <dependences>
      <assembly name="SMath Studio Desktop" version="0.97.5346.24640" guid="a37cba83-b69c-4c71-9992-55ff666763bd" />
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      <assembly name="Special Functions" version="1.11.5346.31403" guid="2814e667-4e12-48b1-8d51-194e480eabc5" />
      <assembly name="X-Y Plot Region (Chart2DLib)" version="0.1.5151.38078" guid="c12231ec-4873-43c1-a7d0-a167ebd17066" />
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  </settings>
  <region id="0" left="27" top="36" width="216" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">f</e>
        <e type="operand">3</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">-</e>
        <e type="operand">2</e>
        <e type="operand">y</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
        <e type="operand">y</e>
        <e type="operand">4</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="1" left="333" top="45" width="76" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">level</e>
        <e type="operand">2</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="2" left="27" top="72" width="287" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">f_1</e>
        <e type="operand">3</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">-</e>
        <e type="operand">2</e>
        <e type="operand">y</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
        <e type="operand">y</e>
        <e type="operand">4</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">+</e>
        <e type="operand">level</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="3" left="333" top="81" width="78" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Y</e>
        <e type="operand">0</e>
        <e type="operand">3</e>
        <e type="operand">0</e>
        <e type="operand">3</e>
        <e type="operator" args="1">-</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>
      </input>
    </math>
  </region>
  <region id="4" left="441" top="99" width="96" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">datum</e>
        <e type="operand">0</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="5" left="27" top="108" width="287" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">f_2</e>
        <e type="operand">3</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">-</e>
        <e type="operand">2</e>
        <e type="operand">y</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
        <e type="operand">y</e>
        <e type="operand">4</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">+</e>
        <e type="operand">level</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="6" left="27" top="162" width="304" height="208" color="#000000" bgColor="#ffffff" fontSize="10">
    <xyplot width="294" height="200" smoothing="false" points="100">
      <propertiessource index="1" sourcetype="PropertyGrid" />
      <grid gridcolor="LightGray" gridpattern="Solid" gridthickness="1" isxgrid="true" isygrid="true" />
      <xaxes xmin="-4" xmax="4" xtick="1" numberformat="General" decimalplaces="3" />
      <yaxes ymin="-4" ymax="4" ytick="1" numberformat="General" decimalplaces="3" />
      <y2axes isy2axis="false" y2min="-1" y2max="1" y2tick="0.5" numberformat="General" decimalplaces="3" />
      <title2d title="Unknown parametric" titlefont="Times New Roman, 11.25pt" titlefontcolor="Black" />
      <xylabel labelfont="Arial, 10pt" labelfontcolor="Black" tickfont="Courier New, 10pt" tickfontcolor="Black" xlabel="x" ylabel="y" y2label="y2" />
      <legend isbordervisible="true" islegendvisible="false" legendbackcolor="White" legendbordercolor="Black" legendfont="Arial, 8pt" legendposition="NorthEast" textcolor="Black" />
      <traces>
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Blue" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Red" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Green" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Fuchsia" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="DarkOrange" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
      </traces>
      <input>
        <e type="operand">f</e>
        <e type="operand">f_1</e>
        <e type="operand">f_2</e>
        <e type="operand">Y</e>
        <e type="operand">x</e>
        <e type="function" args="1">datum</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="7">sys</e>
      </input>
    </xyplot>
  </region>
  <region id="7" left="369" top="207" width="361" height="31" color="#000000" bgColor="#ffffff" fontSize="14">
    <text lang="eng">
      <p bold="true">Does NOT plot vector functions</p>
    </text>
  </region>
  <region id="8" left="405" top="243" width="280" height="89" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">f</e>
        <e type="operand">3</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">-</e>
        <e type="operand">2</e>
        <e type="operand">y</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
        <e type="operand">y</e>
        <e type="operand">4</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">+</e>
        <e type="operand">3</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">-</e>
        <e type="operand">2</e>
        <e type="operand">y</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
        <e type="operand">y</e>
        <e type="operand">4</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">+</e>
        <e type="operand">level</e>
        <e type="operator" args="2">-</e>
        <e type="operand">3</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">-</e>
        <e type="operand">2</e>
        <e type="operand">y</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
        <e type="operand">y</e>
        <e type="operand">4</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">+</e>
        <e type="operand">level</e>
        <e type="operator" args="2">+</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="9" left="36" top="486" width="177" height="52" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="operand">μ</e>
        <e type="function" args="3">ψ</e>
        <e type="operand">μ</e>
        <e type="operand">y</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operand">y</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
        <e type="bracket">(</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="10" left="243" top="495" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operand">1</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="11" left="315" top="495" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">R</e>
        <e type="operand">1</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="12" left="369" top="495" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">μ</e>
        <e type="operand">0</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="13" left="36" top="540" width="269" height="61" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">φ</e>
        <e type="operand">a</e>
        <e type="operand">y</e>
        <e type="operand">R</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operand">y</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operand">y</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="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">x</e>
        <e type="operand">y</e>
        <e type="operand">μ</e>
        <e type="function" args="3">ψ</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="14" left="396" top="558" width="101" height="24" color="#000000" bgColor="#80ffff" fontSize="10">
    <math>
      <input>
        <e type="operand">level</e>
        <e type="operand">0.25</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="15" left="36" top="603" width="251" height="61" color="#000000" bgColor="#ffff80" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">Doublet</e>
        <e type="operand">y</e>
        <e type="operand">R</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="1">-</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="operand">y</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">x</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operand">y</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="16" left="306" top="603" width="321" height="61" color="#000000" bgColor="#ffff80" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">Doublet_1</e>
        <e type="operand">y</e>
        <e type="operand">R</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="1">-</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="operand">y</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">x</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operand">y</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
        <e type="operand">level</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="17" left="306" top="666" width="321" height="61" color="#000000" bgColor="#ffff80" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">Doublet_2</e>
        <e type="operand">y</e>
        <e type="operand">R</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="1">-</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="operand">y</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">x</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operand">y</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
        <e type="operand">level</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="18" left="36" top="702" width="200" height="208" color="#000000" bgColor="#ffffff" fontSize="10">
    <xyplot width="190" height="200" smoothing="false" points="100">
      <propertiessource index="1" sourcetype="PropertyGrid" />
      <grid gridcolor="LightGray" gridpattern="Solid" gridthickness="1" isxgrid="true" isygrid="true" />
      <xaxes xmin="-2" xmax="2" xtick="1" numberformat="General" decimalplaces="3" />
      <yaxes ymin="-2" ymax="2" ytick="1" numberformat="General" decimalplaces="3" />
      <y2axes isy2axis="false" y2min="-1" y2max="1" y2tick="0.5" numberformat="General" decimalplaces="3" />
      <title2d title="Doublet StreamLines" titlefont="Times New Roman, 11.25pt" titlefontcolor="Black" />
      <xylabel labelfont="Arial, 10pt" labelfontcolor="Black" tickfont="Courier New, 10pt" tickfontcolor="Black" xlabel="x" ylabel="y" y2label="y2" />
      <legend isbordervisible="true" islegendvisible="false" legendbackcolor="White" legendbordercolor="Black" legendfont="Arial, 8pt" legendposition="NorthEast" textcolor="Black" />
      <traces>
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Blue" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Red" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Green" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
      </traces>
      <input>
        <e type="operand">Doublet</e>
        <e type="operand">Doublet_1</e>
        <e type="operand">Doublet_2</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">sys</e>
      </input>
    </xyplot>
  </region>
  <region id="19" left="405" top="729" width="43" height="24" color="#000000" bgColor="#80ffff" fontSize="10">
    <math>
      <input>
        <e type="operand">β</e>
        <e type="operand">0</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="20" left="306" top="756" width="308" height="30" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">y</e>
        <e type="function" args="1">F</e>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">Doublet</e>
        <e type="operand">β</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="2">solve</e>
        <e type="function" preserve="true" args="1">maple</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="21" left="306" top="792" width="195" height="208" color="#000000" bgColor="#ffffff" fontSize="10" showInputData="False">
    <xyplot width="185" height="200" smoothing="false" points="100">
      <propertiessource index="1" sourcetype="PropertyGrid" />
      <grid gridcolor="LightGray" gridpattern="Solid" gridthickness="1" isxgrid="true" isygrid="true" />
      <xaxes xmin="-2" xmax="2" xtick="1" numberformat="General" decimalplaces="3" />
      <yaxes ymin="-2" ymax="2" ytick="1" numberformat="General" decimalplaces="3" />
      <y2axes isy2axis="false" y2min="-1" y2max="1" y2tick="0.5" numberformat="General" decimalplaces="3" />
      <title2d title="Doublet Eclusive Circle" titlefont="Times New Roman, 11.25pt" titlefontcolor="Black" />
      <xylabel labelfont="Arial, 10pt" labelfontcolor="Black" tickfont="Courier New, 10pt" tickfontcolor="Black" xlabel="x" ylabel="y" y2label="y2" />
      <legend isbordervisible="true" islegendvisible="false" legendbackcolor="White" legendbordercolor="Black" legendfont="Arial, 8pt" legendposition="NorthEast" textcolor="Black" />
      <traces>
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Blue" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Red" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Green" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Fuchsia" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
      </traces>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">F</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" preserve="true" args="1">Re</e>
        <e type="operand">x</e>
        <e type="function" args="1">F</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" preserve="true" args="1">Re</e>
        <e type="operand">x</e>
        <e type="function" args="1">F</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" preserve="true" args="1">Im</e>
        <e type="operand">x</e>
        <e type="function" args="1">F</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" preserve="true" args="1">Im</e>
        <e type="operand">4</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="6">sys</e>
      </input>
    </xyplot>
  </region>
</regions>