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        <e type="operand">1</e>
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        <e type="operator" args="2">+</e>
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        <p>sanity check</p>
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        <e type="operand">11.977</e>
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      <p bold="true">... Augment algo command line </p>
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        <p>wild algo style @ top of work sheet</p>
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        <e type="operand">#</e>
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      <p bold="true">value maths</p>
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      <p bold="true">demanded composition</p>
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      <p bold="true">Advanced Project Explorer ...</p>
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        <p>collapse in utilities ... extend varnames at will.</p>
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        <p>Tools, Options, Calculation: Decimals &amp; Threshold   ►  15 ... to fully benefit result round(●,n)</p>
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        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="operand">u</e>
        <e type="operand">v</e>
        <e type="operand">ω</e>
        <e type="operand">Ω</e>
        <e type="function" args="6">code</e>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">y</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="operator" args="2">-</e>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="operator" args="2">+</e>
        <e type="operand">u</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="operand">v</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">7</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="9">mat</e>
        <e type="operator" args="2">:</e>
        <e type="operand">j</e>
        <e type="operand">n</e>
        <e type="function" args="2">result</e>
        <e type="operand">2</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
        <e type="operand">7</e>
        <e type="operand" style="unit">mm</e>
        <e type="operator" args="2">*</e>
        <e type="operand">e</e>
        <e type="operand">10</e>
        <e type="operand" preserve="false" style="unit">'L</e>
        <e type="operator" args="2">*</e>
        <e type="operand">_</e>
        <e type="operand">_</e>
        <e type="operand">code</e>
        <e type="function" args="7">algo</e>
        <e type="operand">j</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">n</e>
        <e type="function" preserve="true" args="2">round</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>
      </input>
    </math>
  </region>
  <region id="20" left="306" top="954" width="251" height="128" color="#ffff00" bgColor="#010101" fontSize="12">
    <text lang="eng">
      <p>in-situ command line0. fabricate code vector1. user codes/select 'j'2. decimals ... 'n'3. ,_,_ ... ignored4. recover units</p>
    </text>
  </region>
  <region id="21" left="18" top="1134" width="226" height="51" color="#000000" bgColor="#ebebeb" fontSize="10">
    <math decimalPlaces="12">
      <input>
        <e type="operand">1</e>
        <e type="operand">6</e>
        <e type="function" args="2">result</e>
      </input>
      <result action="numeric">
        <e type="operand">0.167332</e>
        <e type="operand" style="unit">m</e>
        <e type="operand">3</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="22" left="324" top="1134" width="206" height="50" color="#000000" bgColor="#ebebeb" fontSize="10">
    <math decimalPlaces="6">
      <input>
        <e type="operand">2</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">7</e>
        <e type="operator" args="2">*</e>
        <e type="operand" style="unit">mm</e>
        <e type="operator" args="2">*</e>
      </input>
      <result action="numeric">
        <e type="operand">0.009899</e>
        <e type="operand" style="unit">m</e>
        <e type="operand">3</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="23" left="324" top="1188" width="157" height="24" color="#000000" bgColor="#ebebeb" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
        <e type="operand">7</e>
        <e type="operand" style="unit">mm</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
      </input>
      <result action="numeric">
        <e type="operand">2.007</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="24" left="18" top="1224" width="244" height="27" color="#000000" bgColor="#e1ff80" fontSize="10">
    <math>
      <input>
        <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="operand">u</e>
        <e type="operand">2</e>
        <e type="operator" args="2">:</e>
        <e type="operand">v</e>
        <e type="operand">1.23456789</e>
        <e type="operator" args="2">:</e>
        <e type="operand">1</e>
        <e type="operand">4</e>
        <e type="function" preserve="true" args="6">mat</e>
      </input>
    </math>
  </region>
  <region id="25" left="18" top="1260" width="360" height="135" color="#000000" bgColor="#e1ff80" fontSize="10">
    <math decimalPlaces="15">
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="operand">u</e>
        <e type="operand">v</e>
        <e type="operand">ω</e>
        <e type="operand">Ω</e>
        <e type="function" args="6">code</e>
      </input>
      <result action="numeric">
        <e type="operand">2.82842712474618</e>
        <e type="operand">2.82842712474618</e>
        <e type="operand">4</e>
        <e type="operand">0</e>
        <e type="operand">4</e>
        <e type="operand">0.693147180559945</e>
        <e type="operand">1.11111110605556</e>
        <e type="operand">7</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="9">mat</e>
      </result>
    </math>
  </region>
  <region id="26" left="9" top="1404" width="632" height="41" color="#000000" bgColor="#ebebeb" fontSize="20">
    <text lang="eng">
      <p bold="true">Algo or part of algo ... other style. </p>
    </text>
  </region>
  <region id="27" left="9" top="1449" width="152" height="27" color="#000000" bgColor="#ebebeb" fontSize="10">
    <math fractionType="auto" decimalPlaces="6">
      <description active="true" position="Right" lang="eng">
        <p>Generatrix Conjugate</p>
      </description>
      <input>
        <e type="operand">v</e>
        <e type="function" preserve="true" args="1">Conjugate</e>
        <e type="operand">v</e>
        <e type="function" preserve="true" args="1">Re</e>
        <e type="operand">v</e>
        <e type="function" preserve="true" args="1">Im</e>
        <e type="operand">i</e>
        <e type="operator" args="1">-</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="28" left="369" top="1449" width="280" height="48" color="#000000" bgColor="#ebebeb" fontSize="12">
    <text lang="eng">
      <p>Hypersine was designed jmGfor Mathsoft Collaboratory.</p>
    </text>
  </region>
  <region id="29" left="9" top="1485" width="255" height="63" color="#000000" bgColor="#ebffeb" fontSize="10">
    <math decimalPlaces="6">
      <input>
        <e type="operand">p</e>
        <e type="operand">x</e>
        <e type="function" args="2">f</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="bracket">(</e>
        <e type="operand">p</e>
        <e type="operand">π</e>
        <e type="operator" args="2">/</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">^</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="bracket">(</e>
        <e type="operand">p</e>
        <e type="operand">π</e>
        <e type="operator" args="2">/</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">^</e>
        <e type="function" args="1">Conjugate</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="30" left="279" top="1494" width="51" height="35" color="#000000" bgColor="#ffffff">
    <picture>
      <raw format="png" encoding="base64">iVBORw0KGgoAAAANSUhEUgAAACsAAAAbCAYAAADlJ3ZtAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAABwSURBVFhH7dPRCoAwCIVh3/9BfQ0j6sKGNDQPLHY+ELoI+Rmb2EJEnjmqen9dGFvFWBTGojAWhbEoUawfnmwVY1EYi8JYlGns+cNK401PNlqQmU7paxAFvU2nz3c2CvTTqf2B/SoWab/YcUlVbo/ZAZtj7dW3FdbsAAAAAElFTkSuQmCC</raw>
    </picture>
  </region>
  <region id="31" left="369" top="1512" width="150" height="27" color="#000000" bgColor="#ebffeb" fontSize="10">
    <math>
      <description active="true" position="Right" lang="eng">
        <p>'b' ►  </p>
      </description>
      <input>
        <e type="operand">b</e>
        <e type="operand">0.875</e>
        <e type="operator" args="2">:</e>
        <e type="operand">k</e>
        <e type="operand">0.75</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>
      </input>
    </math>
  </region>
  <region id="32" left="594" top="1512" width="99" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">b</e>
        <e type="operand">1</e>
        <e type="operator" args="2">≥</e>
        <e type="bracket">(</e>
        <e type="operand">b</e>
        <e type="operand">1</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">|</e>
      </input>
    </math>
  </region>
  <region id="33" left="369" top="1548" width="138" height="34" color="#000000" bgColor="#ebffeb" fontSize="10">
    <math>
      <input>
        <e type="operand">b</e>
        <e type="operand">k</e>
        <e type="operand">x</e>
        <e type="function" args="3">Φ</e>
        <e type="operand">b</e>
        <e type="operand">k</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="34" left="9" top="1557" width="43" height="24" color="#000000" bgColor="#ffff80" fontSize="10">
    <math decimalPlaces="6">
      <description active="true" position="Right" lang="eng">
        <p>populate Hypersine</p>
      </description>
      <input>
        <e type="operand">p</e>
        <e type="operand">8</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="35" left="9" top="1593" width="132" height="24" color="#000000" bgColor="#ffff80" fontSize="10">
    <math>
      <description active="true" position="Right" lang="eng">
        <p>shift ◄  ... ►  </p>
      </description>
      <input>
        <e type="operand">shift</e>
        <e type="operand">0.75</e>
        <e type="operand" style="unit">rad</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="36" left="369" top="1593" width="161" height="24" color="#000000" bgColor="#ebffeb" fontSize="10">
    <math>
      <input>
        <e type="operand">0.75</e>
        <e type="operand" style="unit">rad</e>
        <e type="operator" args="2">*</e>
      </input>
      <contract>
        <e type="operand" style="unit">°</e>
      </contract>
      <result action="numeric">
        <e type="operand">42.9718</e>
      </result>
    </math>
  </region>
  <region id="37" left="9" top="1629" width="282" height="69" color="#000000" bgColor="#ffff80" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">plot</e>
        <e type="operand">p</e>
        <e type="operand">x</e>
        <e type="operand">shift</e>
        <e type="operator" args="2">+</e>
        <e type="function" args="2">f</e>
        <e type="operand">b</e>
        <e type="operand">k</e>
        <e type="operand">x</e>
        <e type="function" args="3">Φ</e>
        <e type="operator" args="2">*</e>
        <e type="operand">b</e>
        <e type="operand">k</e>
        <e type="operand">x</e>
        <e type="function" args="3">Φ</e>
        <e type="operand">b</e>
        <e type="operand">k</e>
        <e type="operand">x</e>
        <e type="function" args="3">Φ</e>
        <e type="operator" args="1">-</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>
      </input>
    </math>
  </region>
  <region id="38" left="333" top="1629" width="363" height="158" color="#000000" bgColor="#ffff80" fontSize="10">
    <plot type="2d" render="lines" scale_x="2.06914866998438" scale_y="1.61051" scale_z="3.33238462449655" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="0" transpose_y="0" transpose_z="0">
      <description active="false" position="Right" lang="eng">
        <p>General form ...suggestive project(x)More NOT offered.Φ(b,k,x) ... governs</p>
      </description>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">plot</e>
      </input>
    </plot>
  </region>
  <region id="39" left="576" top="1818" width="164" height="31" color="#000000" bgColor="#ebebeb" fontSize="14">
    <text lang="eng">
      <p bold="true">jmG: 20230206</p>
    </text>
  </region>
  <region id="40" left="306" top="1827" width="264" height="19" color="#000000" bgColor="#ffffff">
    <picture>
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    </picture>
  </region>
</regions>