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<?application progid="SMath Studio Desktop" version="0.96.4909.6802"?>
<regions>
  <settings>
    <identity>
      <id>be8ed228-7b9f-4d88-9521-f6039e697cd5</id>
      <revision>74</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" />
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      <assembly name="Text Region" version="1.9.4909.6785" guid="485d28c5-349a-48b6-93be-12a35a1c1e39" />
      <assembly name="MaximaPlugin" version="1.0.5096.34732" guid="44011c1e-5d0d-4533-8e68-e32b5badce41" />
      <assembly name="Custom Functions" version="1.0.4902.41872" guid="18dadffd-79a3-4cf9-aee1-d66deb0ea720" />
      <assembly name="Maple Wrapper" version="1.0.4972.7570" guid="32dfd679-8cfd-483a-b79a-19d5ea838750" />
      <assembly name="Matlab C++ Math Library" version="1.0.4987.26944" guid="4c2faab1-4d93-4904-8d88-a4e21512d179" />
    </dependences>
  </settings>
  <region id="0" left="18" top="18" width="26" height="26" color="#000000" bgColor="#ffff80" fontSize="10">
    <math>
      <input>
        <e type="operand">M</e>
        <e type="function" preserve="true" args="1">det</e>
      </input>
    </math>
  </region>
  <region id="1" left="81" top="18" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>det(M)</p>
    </text>
  </region>
  <region id="2" left="18" top="54" width="666" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Determinante der Matrix M</p>
    </text>
    <text lang="eng">
      <p>Determinant of the square matrix M. The native SMath version is weak in symbolic
and numeric evaluation. If required, you may let the Maxima plugin handle the 
function.</p>
    </text>
  </region>
  <region id="3" left="18" top="108" width="68" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
        <e type="operand">0</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">0</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="126" top="126" width="68" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
        <e type="function" preserve="true" args="1">det</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
      </result>
    </math>
  </region>
  <region id="5" left="234" top="126" width="98" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
        <e type="function" preserve="true" args="1">rank</e>
      </input>
      <result action="numeric">
        <e type="operand">2</e>
      </result>
    </math>
  </region>
  <region id="6" left="18" top="171" width="68" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">C</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operand">c</e>
        <e type="operand">d</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="7" left="126" top="180" width="110" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">C</e>
        <e type="function" preserve="true" args="1">det</e>
      </input>
      <result action="symbolic">
        <e type="operand">a</e>
        <e type="operand">d</e>
        <e type="operator" args="2">*</e>
        <e type="operand">c</e>
        <e type="operand">b</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
      </result>
    </math>
  </region>
  <region id="8" left="234" top="180" width="98" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">C</e>
        <e type="function" preserve="true" args="1">rank</e>
      </input>
      <result action="symbolic">
        <e type="operand">2</e>
      </result>
    </math>
  </region>
  <region id="9" left="18" top="225" width="98" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">D</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operand">2</e>
        <e type="operand">a</e>
        <e type="operator" args="2">*</e>
        <e type="operand">2</e>
        <e type="operand">b</e>
        <e type="operator" args="2">*</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="10" left="126" top="234" width="59" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">D</e>
        <e type="function" preserve="true" args="1">det</e>
      </input>
      <result action="symbolic">
        <e type="operand">0</e>
      </result>
    </math>
  </region>
  <region id="11" left="234" top="234" width="98" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">D</e>
        <e type="function" preserve="true" args="1">rank</e>
      </input>
      <result action="symbolic">
        <e type="operand">1</e>
      </result>
    </math>
  </region>
  <region id="12" top="270" color="#000000" bgColor="#ffffff">
    <area collapsed="false">
      <title lang="ger">
        <p>Numerische Probleme beim Berechnen der Determinante in SMath</p>
      </title>
      <title lang="eng">
        <p>The native SMath det() has problems with both numeric and symbolic evaluation</p>
      </title>
    </area>
    <region id="13" left="9" top="297" width="518" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand" style="string">none</e>
          <e type="function" preserve="true" args="1">MaximaTakeover</e>
        </input>
        <result action="numeric">
          <e type="operand" style="string">All functions now are native SMath.</e>
        </result>
      </math>
    </region>
    <region id="14" left="18" top="324" width="737" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>Die numerische Berechnung von Determinante und Rang ist nicht robust, da die 
Zwischenergebnisse für die interne Zahlendarstellung zu groß werden. Im Einzelfall 
kann die symbolische Auswertung noch sinnvolle Werte liefern, stößt aber auch an 
Grenzen der Zahlendarstellung. </p>
      </text>
      <text lang="eng">
        <p>The numeric computation of determinant and rank are not robust, because the intermediate
results can become too big for the internal floating point number format. Occasionally,
symbolic optimization can help, but is limited by number format, too.</p>
      </text>
    </region>
    <region id="15" left="18" top="396" width="196" height="188" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">A</e>
          <e type="operand">8</e>
          <e type="operand">0</e>
          <e type="operand">4</e>
          <e type="operand">8</e>
          <e type="operand">8</e>
          <e type="operand">2</e>
          <e type="operand">8</e>
          <e type="operand">3</e>
          <e type="operand">3</e>
          <e type="operand">2</e>
          <e type="operand">5</e>
          <e type="operand">3</e>
          <e type="operand">0</e>
          <e type="operand">7</e>
          <e type="operand">4</e>
          <e type="operand">7</e>
          <e type="operand">5</e>
          <e type="operand">4</e>
          <e type="operand">6</e>
          <e type="operand">7</e>
          <e type="operand">5</e>
          <e type="operand">8</e>
          <e type="operand">4</e>
          <e type="operand">1</e>
          <e type="operand">8</e>
          <e type="operand">3</e>
          <e type="operand">1</e>
          <e type="operand">8</e>
          <e type="operand">6</e>
          <e type="operand">9</e>
          <e type="operand">6</e>
          <e type="operand">3</e>
          <e type="operand">5</e>
          <e type="operand">0</e>
          <e type="operand">0</e>
          <e type="operand">3</e>
          <e type="operand">8</e>
          <e type="operand">9</e>
          <e type="operand">8</e>
          <e type="operand">0</e>
          <e type="operand">5</e>
          <e type="operand">8</e>
          <e type="operand">3</e>
          <e type="operand">5</e>
          <e type="operand">8</e>
          <e type="operand">3</e>
          <e type="operand">4</e>
          <e type="operand">6</e>
          <e type="operand">6</e>
          <e type="operand">5</e>
          <e type="operand">9</e>
          <e type="operand">6</e>
          <e type="operand">7</e>
          <e type="operand">2</e>
          <e type="operand">8</e>
          <e type="operand">9</e>
          <e type="operand">6</e>
          <e type="operand">3</e>
          <e type="operand">9</e>
          <e type="operand">5</e>
          <e type="operand">1</e>
          <e type="operand">9</e>
          <e type="operand">6</e>
          <e type="operand">4</e>
          <e type="operand">5</e>
          <e type="operand">1</e>
          <e type="operand">8</e>
          <e type="operand">0</e>
          <e type="operand">6</e>
          <e type="operand">1</e>
          <e type="operand">9</e>
          <e type="operand">5</e>
          <e type="operand">5</e>
          <e type="operand">5</e>
          <e type="operand">1</e>
          <e type="operand">7</e>
          <e type="operand">5</e>
          <e type="operand">8</e>
          <e type="operand">2</e>
          <e type="operand">4</e>
          <e type="operand">8</e>
          <e type="operand">4</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="operand">9</e>
          <e type="operand">9</e>
          <e type="operand">5</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="operand">6</e>
          <e type="operand">5</e>
          <e type="operand">9</e>
          <e type="operand">3</e>
          <e type="operand">9</e>
          <e type="operand">5</e>
          <e type="operand">1</e>
          <e type="operand">8</e>
          <e type="operand">0</e>
          <e type="operand">7</e>
          <e type="operand">10</e>
          <e type="operand">10</e>
          <e type="function" preserve="true" args="102">mat</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="16" left="225" top="396" width="98" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
      <math error="43">
        <description active="true" position="Top" lang="ger">
          <p>Numerische Optimierung</p>
        </description>
        <description active="true" position="Top" lang="eng">
          <p>numeric optimization</p>
        </description>
        <input>
          <e type="operand">A</e>
          <e type="function" preserve="true" args="1">rank</e>
        </input>
        <result action="numeric">
          <e type="operand">#</e>
        </result>
      </math>
    </region>
    <region id="17" left="225" top="450" width="59" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
      <math error="43">
        <input>
          <e type="operand">A</e>
          <e type="function" preserve="true" args="1">det</e>
        </input>
        <result action="numeric">
          <e type="operand">#</e>
        </result>
      </math>
    </region>
    <region id="18" left="225" top="495" width="106" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <description active="true" position="Top" lang="ger">
          <p>symbolische Optimierung</p>
        </description>
        <description active="true" position="Top" lang="eng">
          <p>symbolic optimization</p>
        </description>
        <input>
          <e type="operand">A</e>
          <e type="function" preserve="true" args="1">rank</e>
        </input>
        <result action="symbolic">
          <e type="operand">10</e>
        </result>
      </math>
    </region>
    <region id="19" left="225" top="531" width="3070" height="50" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">A</e>
          <e type="function" preserve="true" args="1">det</e>
        </input>
        <result action="symbolic">
          <e type="operand">2006726199281670</e>
          <e type="operand">32418090381882800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">16213093592340300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000</e>
          <e type="operand">165724166765075000000000000000000000000000000000000000000000000000000000</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
        </result>
      </math>
    </region>
    <region id="20" left="18" top="594" width="106" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">D</e>
          <e type="function" preserve="true" args="1">Clear</e>
        </input>
        <result action="numeric">
          <e type="operand">1</e>
        </result>
      </math>
    </region>
    <region id="21" left="18" top="630" width="177" height="64" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">D</e>
          <e type="operand">a</e>
          <e type="operand">b</e>
          <e type="operand">c</e>
          <e type="operand">d</e>
          <e type="operand">e</e>
          <e type="operand">f</e>
          <e type="operand">g</e>
          <e type="operand">h</e>
          <e type="operand">j</e>
          <e type="operand">3</e>
          <e type="operand">3</e>
          <e type="function" preserve="true" args="11">mat</e>
          <e type="operator" args="2">*</e>
          <e type="function" preserve="true" args="1">det</e>
        </input>
        <result action="symbolic">
          <e type="operand">D</e>
          <e type="operand">a</e>
          <e type="operand">b</e>
          <e type="operand">c</e>
          <e type="operand">d</e>
          <e type="operand">e</e>
          <e type="operand">f</e>
          <e type="operand">g</e>
          <e type="operand">h</e>
          <e type="operand">j</e>
          <e type="operand">3</e>
          <e type="operand">3</e>
          <e type="function" preserve="true" args="11">mat</e>
          <e type="operator" args="2">*</e>
          <e type="function" preserve="true" args="1">det</e>
        </result>
      </math>
    </region>
    <region id="22" left="216" top="630" width="462" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p>SMath cannot compute the determinant of a scaled matrix
symbolically</p>
      </text>
    </region>
    <region id="23" left="18" top="702" width="569" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>Maple, Matlab und Maxima finden den Wert problemlos.</p>
      </text>
      <text lang="eng">
        <p>Maple, Matlab and Maxima have no problems computing the determinant.</p>
      </text>
    </region>
    <region id="24" left="27" top="738" width="178" height="28" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">A</e>
          <e type="function" preserve="true" args="1">det</e>
          <e type="function" preserve="true" args="1">maple</e>
        </input>
        <result action="symbolic">
          <e type="operand">784894425</e>
        </result>
      </math>
    </region>
    <region id="25" left="27" top="765" width="172" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
      <math decimalPlaces="10" exponentialThreshold="14">
        <input>
          <e type="operand">A</e>
          <e type="function" preserve="true" args="1">mwdet</e>
        </input>
        <result action="numeric">
          <e type="operand">784894425</e>
        </result>
      </math>
    </region>
    <region id="26" left="27" top="792" width="283" height="28" color="#000000" bgColor="#ffffff" fontSize="10">
      <math decimalPlaces="10" exponentialThreshold="13">
        <input>
          <e type="operand">A</e>
          <e type="function" args="1">determinant</e>
          <e type="function" preserve="true" args="1">Maxima</e>
        </input>
        <result action="numeric">
          <e type="operand">784894425</e>
        </result>
      </math>
    </region>
    <region id="27" top="819" color="#000000" bgColor="#ffffff">
      <area terminator="true" />
    </region>
  </region>
  <region id="28" left="18" top="837" width="462" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Übernahme der Funktion durch Maxima löst das Problem.</p>
    </text>
    <text lang="eng">
      <p>Takeover of the function by Maxima solves the problems.</p>
    </text>
  </region>
  <region id="29" left="18" top="864" width="774" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand" style="string">all</e>
        <e type="function" preserve="true" args="1">MaximaTakeover</e>
      </input>
      <result action="numeric">
        <e type="operand" style="string">The functions int(), diff(), det(), lim() and sum() now use Maxima.</e>
      </result>
    </math>
  </region>
  <region id="30" left="18" top="900" width="423" height="64" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">D</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operand">c</e>
        <e type="operand">d</e>
        <e type="operand">e</e>
        <e type="operand">f</e>
        <e type="operand">g</e>
        <e type="operand">h</e>
        <e type="operand">j</e>
        <e type="operand">3</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="11">mat</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">det</e>
      </input>
      <result action="symbolic">
        <e type="operand">D</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
        <e type="operand">b</e>
        <e type="operand">d</e>
        <e type="operand">j</e>
        <e type="operator" args="2">*</e>
        <e type="operand">f</e>
        <e type="operand">g</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="operator" args="1">-</e>
        <e type="operand">a</e>
        <e type="operand">e</e>
        <e type="operand">j</e>
        <e type="operator" args="2">*</e>
        <e type="operand">f</e>
        <e type="operand">h</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="operator" args="2">+</e>
        <e type="operand">c</e>
        <e type="operand">d</e>
        <e type="operand">h</e>
        <e type="operator" args="2">*</e>
        <e type="operand">e</e>
        <e type="operand">g</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="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="31" left="18" top="972" width="125" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
        <e type="function" preserve="true" args="1">det</e>
      </input>
      <result action="symbolic">
        <e type="operand">784894425</e>
      </result>
    </math>
  </region>
  <region id="32" left="18" top="1008" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin Maxima.sm">Maxima</p>
    </text>
  </region>
  <region id="33" left="18" top="1026" width="151" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Section matrix operations.sm">Rechnen mit Matrizen und Vektoren</p>
    </text>
    <text lang="eng">
      <p href="Section matrix operations.sm">Matrix operations</p>
    </text>
  </region>
  <region id="34" left="18" top="1044" width="127" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Function index.sm">Funktionsindex</p>
    </text>
    <text lang="eng">
      <p href="Function index.sm">Function index</p>
    </text>
  </region>
  <region id="35" left="18" top="1062" 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="36" left="18" top="1098" width="450" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p italic="true">$Author: mkraska $
$Date: 2013-12-15 01:35:16 +0100 (So, 15. Dez 2013) $ </p>
    </text>
  </region>
</regions>