﻿<?xml version="1.0" encoding="utf-8" standalone="yes"?>
<?application progid="SMath Studio Desktop" version="0.98.6179.21440"?>
<regions>
  <settings>
    <identity>
      <id>6d126df8-1c2e-4cb0-80ca-54597b4d3bf3</id>
      <revision>5</revision>
    </identity>
    <calculation>
      <precision>4</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <fractions>decimal</fractions>
    </calculation>
    <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>
    <dependencies>
      <assembly name="SMath Studio Desktop" version="0.98.6179.21440" guid="a37cba83-b69c-4c71-9992-55ff666763bd" />
      <assembly name="Math Region" version="0.98.6179.21440" guid="02f1ab51-215b-466e-a74d-5d8b1cf85e8d" />
      <assembly name="Custom Functions" version="1.1.6281.4594" guid="18dadffd-79a3-4cf9-aee1-d66deb0ea720" />
      <assembly name="3D Plot Region (Chart3DLib)" version="0.1.5997.41808" guid="2427d808-1e5e-4ae0-88bf-bc271664a3ab" />
      <assembly name="Special Functions" version="1.11.6179.21442" guid="2814e667-4e12-48b1-8d51-194e480eabc5" />
      <assembly name="Text Region" version="1.10.6179.21446" guid="485d28c5-349a-48b6-93be-12a35a1c1e39" />
      <assembly name="Plot Region" version="1.9.6179.21450" guid="c451c2b5-798b-4f08-b9ec-b90963d1ddaa" />
    </dependencies>
    <mode debug="true" />
  </settings>
  <region id="0" left="9" top="9" width="153" height="31" color="#000000" bgColor="#80ffff" fontSize="14">
    <text lang="eng">
      <p bold="true">3D Utilities</p>
    </text>
  </region>
  <region id="1" left="225" top="9" width="429" height="31" border="true" color="#ff0000" bgColor="#e1ff80" fontSize="14">
    <text lang="eng">
      <p bold="true">Copy/export this stand alone section</p>
    </text>
  </region>
  <region id="2" left="9" top="45" width="454" height="128" border="true" color="#000000" bgColor="#ebebeb" fontSize="10">
    <math optimize="2" fractionType="auto" decimalPlaces="3">
      <input>
        <e type="operand">data</e>
        <e type="operand">char</e>
        <e type="operand">size</e>
        <e type="operand">clr</e>
        <e type="function" args="4">plot</e>
        <e type="operand">k</e>
        <e type="operand">1</e>
        <e type="operand">data</e>
        <e type="function" preserve="true" args="1">rows</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">r3</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">char</e>
        <e type="operator" args="2">:</e>
        <e type="operand">r4</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">size</e>
        <e type="operator" args="2">:</e>
        <e type="operand">r5</e>
        <e type="operand">k</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">clr</e>
        <e type="operator" args="2">:</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">line</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">data</e>
        <e type="operand">r3</e>
        <e type="operand">r4</e>
        <e type="operand">r5</e>
        <e type="function" preserve="true" args="4">augment</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>
      </input>
    </math>
  </region>
  <region id="3" left="54" top="171" width="540" height="195" border="true" color="#000000" bgColor="#ffffe1" fontSize="10">
    <math>
      <description active="true" position="Top" lang="eng">
        <p>Sequential triplet : U, V, Z</p>
      </description>
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">X</e>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">Y</e>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">Z</e>
        <e type="operand">u</e>
        <e type="operand">v</e>
        <e type="function" args="5">Sr</e>
        <e type="operand">count</e>
        <e type="operand">1</e>
        <e type="operator" args="2">:</e>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">u</e>
        <e type="function" preserve="true" args="1">rows</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">j</e>
        <e type="operand">1</e>
        <e type="operand">v</e>
        <e type="function" preserve="true" args="1">rows</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">U</e>
        <e type="operand">count</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">u</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">v</e>
        <e type="operand">j</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" args="2">X</e>
        <e type="function" preserve="true" args="1">eval</e>
        <e type="operator" args="2">:</e>
        <e type="operand">V</e>
        <e type="operand">count</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">u</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">v</e>
        <e type="operand">j</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" args="2">Y</e>
        <e type="function" preserve="true" args="1">eval</e>
        <e type="operator" args="2">:</e>
        <e type="operand">Z</e>
        <e type="operand">count</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">u</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">v</e>
        <e type="operand">j</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" args="2">Z</e>
        <e type="function" preserve="true" args="1">eval</e>
        <e type="operator" args="2">:</e>
        <e type="operand">count</e>
        <e type="operand">count</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
        <e type="operand">4</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="6">line</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">U</e>
        <e type="operand">V</e>
        <e type="operand">Z</e>
        <e type="function" preserve="true" args="3">augment</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="4" left="18" top="252" width="264" height="124" border="true" color="#000000" bgColor="#ffffc0" fontSize="10">
    <math>
      <description active="false" position="Top" lang="eng">
        <p>Mesh U, V  within the bounds L, H</p>
      </description>
      <input>
        <e type="operand">L</e>
        <e type="operand">H</e>
        <e type="operand">N</e>
        <e type="function" args="3">xd</e>
        <e type="operand">U</e>
        <e type="operand">0</e>
        <e type="operator" args="2">:</e>
        <e type="operand">dx</e>
        <e type="operand">H</e>
        <e type="operand">L</e>
        <e type="operator" args="2">-</e>
        <e type="operand">N</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">N</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">U</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">L</e>
        <e type="operand">dx</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operand">dx</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">U</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>
  </region>
  <region id="5" left="594" top="360" width="163" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">81</e>
        <e type="operand">6</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>
      </input>
      <result action="numeric">
        <e type="operand">351.6702</e>
      </result>
    </math>
  </region>
  <region id="6" left="333" top="396" width="319" height="72" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operand">1</e>
        <e type="operator" args="2">:</e>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">Φ</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operand">3</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="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">exp</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="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">a</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="1">-</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>
      </input>
    </math>
  </region>
  <region id="7" left="18" top="405" width="179" height="53" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">L</e>
        <e type="operand">10</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">:</e>
        <e type="operand">H</e>
        <e type="operand">10</e>
        <e type="operator" args="2">:</e>
        <e type="operand">N</e>
        <e type="operand">50</e>
        <e type="operator" args="2">:</e>
        <e type="operand">1</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="5">mat</e>
        <e type="operand">U</e>
        <e type="operand">L</e>
        <e type="operand">H</e>
        <e type="operand">N</e>
        <e type="function" args="3">xd</e>
        <e type="operator" args="2">:</e>
        <e type="operand">V</e>
        <e type="operand">U</e>
        <e type="operator" args="2">:</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="4">mat</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
      </input>
    </math>
  </region>
  <region id="8" left="18" top="477" width="144" height="69" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">X</e>
        <e type="operand">x</e>
        <e type="operator" args="2">:</e>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">Y</e>
        <e type="operand">y</e>
        <e type="operator" args="2">:</e>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">Z</e>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">Φ</e>
        <e type="operator" args="2">:</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">sys</e>
      </input>
    </math>
  </region>
  <region id="9" left="333" top="477" width="312" height="75" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">E</e>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">X</e>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">Y</e>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">Z</e>
        <e type="operand">U</e>
        <e type="operand">V</e>
        <e type="function" args="5">Sr</e>
        <e type="operator" args="2">:</e>
        <e type="operand">P1</e>
        <e type="operand">E</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">col</e>
        <e type="operand">E</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">col</e>
        <e type="function" preserve="true" args="2">augment</e>
        <e type="operator" args="2">:</e>
        <e type="operand">P2</e>
        <e type="operand">E</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">col</e>
        <e type="operand">E</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">col</e>
        <e type="function" preserve="true" args="2">augment</e>
        <e type="operator" args="2">:</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">sys</e>
      </input>
    </math>
  </region>
  <region id="10" left="18" top="558" width="51" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <description active="true" position="Right" lang="eng">
        <p>select a trace</p>
      </description>
      <input>
        <e type="operand">n</e>
        <e type="operand">25</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="11" left="18" top="585" width="292" height="36" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <description active="true" position="Right" lang="eng">
        <p>Export the 'n' trace</p>
      </description>
      <input>
        <e type="operand">sub</e>
        <e type="operand">P2</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operand">n</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand">N</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand">n</e>
        <e type="operand">1</e>
        <e type="operand">N</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="bracket">(</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="function" preserve="true" args="3">el</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="12" left="18" top="630" width="277" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">trace</e>
        <e type="operand">sub</e>
        <e type="operand" style="string">o</e>
        <e type="operand">5</e>
        <e type="operand" style="string">black</e>
        <e type="function" args="4">plot</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="13" left="18" top="666" width="395" height="28" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">Electron</e>
        <e type="operand">sub</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">col</e>
        <e type="operand">sub</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">col</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="3">cinterp</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="14" left="18" top="702" width="238" height="45" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">c</e>
        <e type="operand">1</e>
        <e type="operand">10</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">10</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">&amp;</e>
        <e type="operand" style="string" />
        <e type="function" preserve="true" args="3">cases</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="15" left="18" top="738" width="518" height="244" color="#000000" bgColor="#ffffff" fontSize="10" showInputData="False">
    <plot type="2d" render="points" scale_x="0.804992535022966" scale_y="1.64155424909893" scale_z="7.42629326467371" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="0" transpose_y="1" transpose_z="0">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">Electron</e>
        <e type="operand">x</e>
        <e type="function" args="1">c</e>
        <e type="operator" args="2">*</e>
        <e type="operand">P2</e>
        <e type="operand">trace</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">sys</e>
      </input>
    </plot>
  </region>
  <region id="16" left="18" top="1044" width="519" height="269" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot3d width="509" height="261">
      <input>
        <e type="operand">Φ</e>
      </input>
    </plot3d>
  </region>
</regions>