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  <settings>
    <identity>
      <id>cc9460d7-d8df-4591-8d7a-6a9e3fd99d8d</id>
      <revision>19</revision>
    </identity>
    <calculation>
      <precision>4</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <fractions>decimal</fractions>
    </calculation>
    <pageModel active="true" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
      <paper id="9" orientation="Portrait" width="827" height="1169" />
      <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="0.96.4909.6802" guid="a37cba83-b69c-4c71-9992-55ff666763bd" />
      <assembly name="Text Region" version="1.9.4909.6785" guid="485d28c5-349a-48b6-93be-12a35a1c1e39" />
      <assembly name="MaximaPlugin" version="1.0.5115.5713" guid="44011c1e-5d0d-4533-8e68-e32b5badce41" />
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      <assembly name="Picture Region" version="1.9.4909.6762" guid="06b5df04-393e-4be7-9107-305196fcb861" />
      <assembly name="Nonlinear Solvers" version="1.0.9999.5" guid="618b7e96-330a-406a-b055-9e577672f0b8" />
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  <region id="0" left="18" top="18" width="385" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p bold="true">Programming example: Unit-proof linear solver </p>
    </text>
  </region>
  <region id="1" left="504" top="18" width="103" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Kapitel Programmierung.sm">Programmierung</p>
    </text>
    <text lang="eng">
      <p href="Kapitel Programmierung.sm">Programming</p>
    </text>
  </region>
  <region id="2" left="504" top="36" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Handbook.sm">Inhalt</p>
    </text>
    <text lang="eng">
      <p href="Handbook.sm">Contents</p>
    </text>
  </region>
  <region id="3" left="18" top="63" width="452" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand" style="string">cleanup</e>
        <e type="function" preserve="true" args="1">MaximaControl</e>
      </input>
      <result action="numeric">
        <e type="operand" style="string">Maxima was re-initialized</e>
      </result>
    </math>
  </region>
  <region id="4" left="18" top="108" width="415" height="155" color="#000000" bgColor="#ffffff">
    <picture readOnly="false">
      <raw format="png" encoding="base64"> </raw>
    </picture>
  </region>
  <region id="5" left="108" top="270" width="122" height="42" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">M.Aq</e>
        <e type="operand">3</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operand">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="6" left="18" top="279" width="77" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">F</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="7" left="243" top="279" width="86" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">R.q</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="8" left="153" top="324" width="234" height="51" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">Gl</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">M.Aq</e>
        <e type="operand">F</e>
        <e type="operand" preserve="false" style="unit">l.0</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">F.B</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="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
        <e type="operand">0</e>
        <e type="operator" args="2">≡</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="9" left="18" top="342" width="126" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Moment about A</p>
    </text>
  </region>
  <region id="10" left="18" top="378" width="127" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Vertical force</p>
    </text>
  </region>
  <region id="11" left="153" top="378" width="184" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">Gl</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">F</e>
        <e type="operand">R.q</e>
        <e type="operator" args="2">+</e>
        <e type="operand">F.A</e>
        <e type="operator" args="2">-</e>
        <e type="operand">F.B</e>
        <e type="operator" args="2">-</e>
        <e type="operand">0</e>
        <e type="operator" args="2">≡</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="12" left="18" top="414" width="257" height="96" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Gl</e>
        <e type="operand">F.A</e>
        <e type="operand">F.B</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
        <e type="function" preserve="true" args="2">Solve</e>
      </input>
      <result action="none">
        <e type="operand">F.A</e>
        <e type="operand">2</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operand">3</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">F.B</e>
        <e type="operand">4</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operand">3</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">*</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>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">mat</e>
      </result>
    </math>
  </region>
  <region id="13" left="288" top="423" width="417" height="72" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>The function Solve is part of the Maxima plugin.
It requires the unknown variables to be specified 
(because it can solve systems with symbolic 
coefficients and right hand side).</p>
    </text>
  </region>
  <region id="14" left="18" top="513" width="244" height="60" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Gl</e>
        <e type="operand">F</e>
        <e type="operand">F</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
        <e type="function" preserve="true" args="2">FindRoot</e>
      </input>
      <result action="numeric">
        <e type="operand">0.5</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand">1</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="15" left="288" top="513" width="447" height="88" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>The function FindRoot is Part of the NonlinearSolvers
plugin. It requires initial values for the unknowns
to be specified. The solution may depend on these 
values and the returned values may not satisfy the
equations as we shall see further down.</p>
    </text>
  </region>
  <region id="16" left="18" top="567" width="277" height="60" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Gl</e>
        <e type="operand">F</e>
        <e type="operand">F</e>
        <e type="operator" args="1">-</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
        <e type="function" preserve="true" args="2">FindRoot</e>
      </input>
      <result action="numeric">
        <e type="operand">0.6667</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand">1.3333</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="17" left="18" top="639" width="726" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>We want to create a function which just needs the system to be solved, i.e. no variable 
names and no initial guesses.</p>
    </text>
  </region>
  <region id="18" top="693" color="#000000" bgColor="#ffffff">
    <area collapsed="false">
      <title lang="ger">
        <p>LinSolve</p>
      </title>
      <title lang="eng">
        <p>linsolve</p>
      </title>
    </area>
    <region id="19" left="27" top="720" width="698" height="406" color="#000000" bgColor="#ffffff" fontSize="10">
      <math optimize="2">
        <description active="true" position="Top" lang="ger">
          <p>Löst ein lineares Gleichungssystem, gegeben als Vektor von Gleichungen, nach allen
unbekannten Variablen auf. Für symbolische Ergebnisse definieren Sie bekannte Größen
mit eigenen Maßeinheiten.</p>
        </description>
        <description active="true" position="Top" lang="eng">
          <p>Solves a linear system, given as a vector of equations, for any unknown variable. 
Use custom units for parametric (symbolic) solutions.</p>
        </description>
        <input>
          <e type="operand">sys#</e>
          <e type="function" args="1">linsolve</e>
          <e type="operand" style="string">subtract right hand sides of equations</e>
          <e type="operand">n#</e>
          <e type="operand">sys#</e>
          <e type="function" preserve="true" args="1">length</e>
          <e type="operator" args="2">:</e>
          <e type="operand">i#</e>
          <e type="operand">1</e>
          <e type="operand">n#</e>
          <e type="function" preserve="true" args="2">range</e>
          <e type="operand">Nsys#</e>
          <e type="operand">i#</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="operand">sys#</e>
          <e type="operand">i#</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="function" preserve="true" args="1">num2str</e>
          <e type="operand" style="string">≡</e>
          <e type="operand" style="string">-(</e>
          <e type="function" preserve="true" args="3">strrep</e>
          <e type="operand" style="string">)</e>
          <e type="function" preserve="true" args="2">concat</e>
          <e type="function" preserve="true" args="1">str2num</e>
          <e type="operator" args="2">:</e>
          <e type="operand">sys#</e>
          <e type="operand">i#</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="function" preserve="true" args="1">num2str</e>
          <e type="function" preserve="true" args="1">trace</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="4">line</e>
          <e type="function" preserve="true" args="3">for</e>
          <e type="operand" style="string">Compute Jacobi matrix and it's determinant</e>
          <e type="operand">u#</e>
          <e type="operand">Nsys#</e>
          <e type="function" preserve="true" args="1">Unknowns</e>
          <e type="operator" args="2">:</e>
          <e type="operand">J#</e>
          <e type="operand">Nsys#</e>
          <e type="operand">u#</e>
          <e type="function" preserve="true" args="2">Jacob</e>
          <e type="operator" args="2">:</e>
          <e type="operand">d#</e>
          <e type="operand">J#</e>
          <e type="function" preserve="true" args="1">det</e>
          <e type="operator" args="2">:</e>
          <e type="operand" style="string">compute right hand side of linear system</e>
          <e type="operand">i#</e>
          <e type="operand">1</e>
          <e type="operand">n#</e>
          <e type="function" preserve="true" args="2">range</e>
          <e type="operand">RHS#</e>
          <e type="operand">i#</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="operand">Nsys#</e>
          <e type="operand">i#</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="operator" args="1">-</e>
          <e type="operand">J#</e>
          <e type="operand">i#</e>
          <e type="operand">j#</e>
          <e type="function" preserve="true" args="3">el</e>
          <e type="operand">u#</e>
          <e type="operand">j#</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="operator" args="2">*</e>
          <e type="bracket">(</e>
          <e type="operand">j#</e>
          <e type="operand">1</e>
          <e type="operand">n#</e>
          <e type="function" preserve="true" args="4">sum</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" style="string">multiply inverse jacobi matrix by rhs</e>
          <e type="operand">i#</e>
          <e type="operand">1</e>
          <e type="operand">n#</e>
          <e type="function" preserve="true" args="2">range</e>
          <e type="operand">r#</e>
          <e type="operand">i#</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="operand">J#</e>
          <e type="operand">j#</e>
          <e type="operand">i#</e>
          <e type="function" preserve="true" args="3">alg</e>
          <e type="operand">d#</e>
          <e type="operator" args="2">/</e>
          <e type="operand">RHS#</e>
          <e type="operand">j#</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="operator" args="2">*</e>
          <e type="bracket">(</e>
          <e type="operand">j#</e>
          <e type="operand">1</e>
          <e type="operand">n#</e>
          <e type="function" preserve="true" args="4">sum</e>
          <e type="operator" args="2">:</e>
          <e type="function" preserve="true" args="3">for</e>
          <e type="operand">r#</e>
          <e type="operand">12</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="14">line</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="20" left="540" top="954" width="96" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">RHS</e>
          <e type="operand">J</e>
          <e type="operand">u</e>
          <e type="operator" args="2">*</e>
          <e type="operand">G</e>
          <e type="operator" args="2">-</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="21" left="540" top="1044" width="73" height="33" color="#000000" bgColor="#ffffff" fontSize="10">
      <math optimize="2">
        <input>
          <e type="operand">J</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="operator" args="2">^</e>
          <e type="operand">RHS</e>
          <e type="operator" args="2">*</e>
        </input>
      </math>
    </region>
    <region id="22" left="18" top="1188" width="519" height="50" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <description active="true" position="Top" lang="ger">
          <p>Residual(sys): Berechnet den Residuenvektor des Gleichungssystems sys. Die Lösung muss den 
Unbekannten schon zugewiesen sein. Geeignet zur Prüfung von Lösungsverfahren mit eingebetteter
Ergebniszuweisung.</p>
        </description>
        <description active="true" position="Top" lang="eng">
          <p>Residual(sys): Computes the residual vector of system of equations sys. All variables must
be assigned. Suitable to check solutions with embedded assignment.</p>
        </description>
        <input>
          <e type="operand">sys#</e>
          <e type="function" args="1">Residual</e>
          <e type="operand" style="string">subtract right hand sides of equations</e>
          <e type="operand">Nsys#</e>
          <e type="operand">sys#</e>
          <e type="function" preserve="true" args="1">num2str</e>
          <e type="operand" style="string">≡</e>
          <e type="operand" style="string">-</e>
          <e type="function" preserve="true" args="3">strrep</e>
          <e type="function" preserve="true" args="1">str2num</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>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="23" left="18" top="1332" width="608" height="158" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <description active="true" position="Top" lang="ger">
          <p>Residual(sys,L): Berechnet den Residuenvektor des Gleichungssystems sys für die Lösung L, die
den Unbekannten nicht vorab zugewiesen wurde. Dies erfolgt innerhalb der Funktion. Geeignet zur 
Prüfung von Lösungsverfahren ohne eingebettete Ergebniszuweisung.</p>
        </description>
        <description active="true" position="Top" lang="eng">
          <p>Residual(sys,L): Computes the residual vector of system of equations sys for a given solution L. 
The solution is assigned to the unknowns and the residual is evaluated. Suitable to check 
solutions without embedded assignment.</p>
        </description>
        <input>
          <e type="operand">sys#</e>
          <e type="operand">L#</e>
          <e type="function" args="2">Residual</e>
          <e type="operand" style="string">subtract right hand sides of equations</e>
          <e type="operand">n#</e>
          <e type="operand">sys#</e>
          <e type="function" preserve="true" args="1">length</e>
          <e type="operator" args="2">:</e>
          <e type="operand">u#</e>
          <e type="operand">sys#</e>
          <e type="function" preserve="true" args="1">Unknowns</e>
          <e type="operator" args="2">:</e>
          <e type="operand" style="string">Assign solution to unknowns</e>
          <e type="operand">i#</e>
          <e type="operand">1</e>
          <e type="operand">n#</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="function" preserve="true" args="1">num2str</e>
          <e type="operand" style="string">:</e>
          <e type="operand">L#</e>
          <e type="operand">i#</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="function" preserve="true" args="1">num2str</e>
          <e type="function" preserve="true" args="3">concat</e>
          <e type="function" preserve="true" args="1">str2num</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">line</e>
          <e type="function" preserve="true" args="3">for</e>
          <e type="operand">Nsys#</e>
          <e type="operand">sys#</e>
          <e type="function" preserve="true" args="1">num2str</e>
          <e type="operand" style="string">≡</e>
          <e type="operand" style="string">-</e>
          <e type="function" preserve="true" args="3">strrep</e>
          <e type="function" preserve="true" args="1">str2num</e>
          <e type="operator" args="2">:</e>
          <e type="operand">6</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="8">line</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="24" top="1539" color="#000000" bgColor="#ffffff">
      <area terminator="true" />
    </region>
  </region>
  <region id="25" left="18" top="1575" width="431" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p underline="true">Expression for the residual of the unsolved system:</p>
    </text>
  </region>
  <region id="26" left="18" top="1611" width="277" height="81" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Gl</e>
        <e type="function" args="1">Residual</e>
      </input>
      <result action="symbolic">
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operand">4</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand">3</e>
        <e type="operand">F.B</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">2</e>
        <e type="operator" args="2">/</e>
        <e type="operand">F.A</e>
        <e type="operand">F.B</e>
        <e type="operator" args="2">+</e>
        <e type="operand">2</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">l.0</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="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="27" left="324" top="1620" width="157" height="60" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Gl</e>
        <e type="function" preserve="true" args="1">Unknowns</e>
      </input>
      <result action="symbolic">
        <e type="operand">F.A</e>
        <e type="operand">F.B</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="28" left="18" top="1701" width="529" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p underline="true">Check of solutions without embedded assignment with Residual(2)</p>
    </text>
  </region>
  <region id="29" left="36" top="1737" width="366" height="69" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Gl</e>
        <e type="operand">Gl</e>
        <e type="operand">F</e>
        <e type="operand">F</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
        <e type="function" preserve="true" args="2">FindRoot</e>
        <e type="function" args="2">Residual</e>
      </input>
      <result action="numeric">
        <e type="operand">0.5</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand">0.5</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="30" left="423" top="1755" width="167" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Should be all zeros</p>
    </text>
  </region>
  <region id="31" left="36" top="1809" width="439" height="78" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Gl</e>
        <e type="operand">Gl</e>
        <e type="operand">F</e>
        <e type="operand">F</e>
        <e type="operator" args="1">-</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
        <e type="function" preserve="true" args="2">FindRoot</e>
        <e type="function" args="2">Residual</e>
      </input>
      <result action="numeric">
        <e type="operand">5</e>
        <e type="operand">10</e>
        <e type="operand">15</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand">3.1666</e>
        <e type="operand">10</e>
        <e type="operand">15</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="32" left="36" top="1881" width="235" height="60" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Gl</e>
        <e type="function" args="1">linsolve</e>
      </input>
      <result action="numeric">
        <e type="operand">0.6667</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand">1.3333</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="33" left="270" top="1890" width="258" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Gl</e>
        <e type="operand">Gl</e>
        <e type="function" args="1">linsolve</e>
        <e type="function" args="2">Residual</e>
      </input>
      <result action="numeric">
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="34" left="18" top="1953" width="504" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p underline="true">Check of solutions with embedded assignment with Residual(1)</p>
    </text>
  </region>
  <region id="35" left="18" top="1980" width="307" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Gl</e>
        <e type="operand">F.A</e>
        <e type="operand">F</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">F.B</e>
        <e type="operand">F</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">mat</e>
        <e type="function" preserve="true" args="2">FindRoot</e>
      </input>
      <result action="numeric">
        <e type="operand">0.6667</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand">1.3333</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="36" left="333" top="1980" width="287" height="78" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Gl</e>
        <e type="function" args="1">Residual</e>
      </input>
      <result action="numeric">
        <e type="operand">5</e>
        <e type="operand">10</e>
        <e type="operand">15</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand">3.1666</e>
        <e type="operand">10</e>
        <e type="operand">15</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="37" left="18" top="2052" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Handbook.sm">Inhalt</p>
    </text>
    <text lang="eng">
      <p href="Handbook.sm">Contents</p>
    </text>
  </region>
  <region id="38" left="18" top="2088" width="450" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p italic="true">$Author: mkraska $
$Date: 2014-01-03 00:31:00 +0100 (Fr, 03. Jan 2014) $ </p>
    </text>
  </region>
</regions>