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      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
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  <region id="0" left="18" top="18" width="218" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p bold="true">Matrix handling</p>
    </text>
    <text lang="ger">
      <p bold="true">Manipulation von Matrizen</p>
    </text>
  </region>
  <region id="1" left="423" top="27" width="185" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p href="Chapter Matrices.sm">Vectors and Matrices</p>
    </text>
    <text lang="ger">
      <p href="Chapter Matrices.sm">Vektoren und Matrizen</p>
    </text>
  </region>
  <region id="2" left="18" top="54" width="185" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p bold="true">Determine the size</p>
    </text>
    <text lang="ger">
      <p bold="true">Abmessungen ermitteln</p>
    </text>
  </region>
  <region id="3" left="27" top="81" width="68" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
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        <e type="operand">A</e>
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        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="operand">4</e>
        <e type="operand">5</e>
        <e type="operand">6</e>
        <e type="operand">3</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="8">mat</e>
        <e type="operator" args="2">:</e>
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  <region id="4" left="99" top="99" width="98" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
        <e type="function" preserve="true" args="1">cols</e>
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        <e type="operand">2</e>
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    <math>
      <input>
        <e type="operand">A</e>
        <e type="function" preserve="true" args="1">rows</e>
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      <result action="numeric">
        <e type="operand">3</e>
      </result>
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  <region id="6" left="306" top="99" width="114" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
        <e type="function" preserve="true" args="1">length</e>
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      <result action="numeric">
        <e type="operand">6</e>
      </result>
    </math>
  </region>
  <region id="7" left="18" top="144" width="342" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p bold="true">Access to columns and rows</p>
    </text>
    <text lang="ger">
      <p bold="true">Zugriff auf Zeilen, Spalten und Elemente</p>
    </text>
  </region>
  <region id="8" left="18" top="171" width="68" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="operand">4</e>
        <e type="operand">5</e>
        <e type="operand">6</e>
        <e type="operand">3</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="8">mat</e>
        <e type="operator" args="2">:</e>
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    </math>
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  <region id="9" left="90" top="171" width="123" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">col</e>
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      <result action="numeric">
        <e type="operand">1</e>
        <e type="operand">3</e>
        <e type="operand">5</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
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    </math>
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  <region id="10" left="225" top="171" width="68" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="operand">4</e>
        <e type="operand">5</e>
        <e type="operand">6</e>
        <e type="operand">3</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="8">mat</e>
        <e type="operator" args="2">:</e>
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    </math>
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  <region id="11" left="306" top="189" width="139" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">row</e>
      </input>
      <result action="numeric">
        <e type="operand">5</e>
        <e type="operand">6</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="4">mat</e>
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    </math>
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  <region id="12" left="18" top="243" width="251" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p bold="true">Access to individual elements</p>
    </text>
    <text lang="ger">
      <p bold="true">Zugriff auf einzelne Elemente</p>
    </text>
  </region>
  <region id="13" left="18" top="270" width="554" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>A single Element index is generated by [. A second index is added using argument 
separator character (; or ,)  </p>
    </text>
    <text lang="ger">
      <p>Einzelne Indizes werden mit [ erzeugt, ein zweiter
Index kann mit dem Argumenttrennzeichen (; oder ,) erzeugt werden.</p>
    </text>
  </region>
  <region id="14" left="18" top="315" width="81" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="3">el</e>
      </input>
      <result action="numeric">
        <e type="operand">2</e>
      </result>
    </math>
  </region>
  <region id="15" left="234" top="315" width="226" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Display of individual elements</p>
    </text>
    <text lang="ger">
      <p>Anzeige einzelner Elemente</p>
    </text>
  </region>
  <region id="16" left="18" top="351" width="79" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">el</e>
        <e type="operand">10</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="17" left="117" top="351" width="86" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
      </input>
      <result action="numeric">
        <e type="operand">10</e>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="operand">4</e>
        <e type="operand">5</e>
        <e type="operand">6</e>
        <e type="operand">3</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="8">mat</e>
      </result>
    </math>
  </region>
  <region id="18" left="234" top="351" width="267" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Assignment to individual Elements</p>
    </text>
    <text lang="ger">
      <p>Zuweisung auf einzelne Elemente</p>
    </text>
  </region>
  <region id="19" left="18" top="414" width="71" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">A</e>
        <e type="operand">3</e>
        <e type="operand">4</e>
        <e type="function" preserve="true" args="3">el</e>
        <e type="operand">1</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="20" left="234" top="414" width="480" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>If the adressed element in an assignment does not yet 
exist, then the matrix is extended dynamically.</p>
    </text>
    <text lang="ger">
      <p>Ist das adressierte Element in einer Zuweisung noch nicht
vorhanden, wird die Matrix dynamisch erweitert.</p>
    </text>
  </region>
  <region id="21" left="117" top="423" width="118" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
      </input>
      <result action="numeric">
        <e type="operand">10</e>
        <e type="operand">2</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">3</e>
        <e type="operand">4</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">5</e>
        <e type="operand">6</e>
        <e type="operand">0</e>
        <e type="operand">1</e>
        <e type="operand">3</e>
        <e type="operand">4</e>
        <e type="function" preserve="true" args="14">mat</e>
      </result>
    </math>
  </region>
  <region id="22" left="18" top="486" width="169" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p bold="true">Linear indexing</p>
    </text>
    <text lang="ger">
      <p bold="true">Lineare Indizierung</p>
    </text>
  </region>
  <region id="23" left="18" top="513" width="569" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Matrix elements can be accessed by a single index. 
This does not work for assignment. </p>
    </text>
    <text lang="ger">
      <p>Matrixelemente können mit einem einzelnen Index angesprochen  werden 
(nur lesender Zugriff, keine Zuweisung)</p>
    </text>
  </region>
  <region id="24" left="18" top="558" width="75" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">A</e>
        <e type="operand">10</e>
        <e type="function" preserve="true" args="2">el</e>
      </input>
      <result action="numeric">
        <e type="operand">6</e>
      </result>
    </math>
  </region>
  <region id="25" left="135" top="558" width="342" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>linear indexing is row-wise.</p>
    </text>
    <text lang="ger">
      <p>Lineare Indizierung erfolgt zeilenweise.</p>
    </text>
  </region>
  <region id="26" left="18" top="585" width="65" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math error="68">
      <input>
        <e type="operand">A</e>
        <e type="operand">10</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">0</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="27" left="135" top="585" width="530" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Linear indexing does not work in assignment targets.</p>
    </text>
    <text lang="ger">
      <p>Lineare Indizierung funktioniert nicht als Ziel einer Zuweisung</p>
    </text>
  </region>
  <region id="28" left="18" top="630" width="193" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p bold="true">Augmenting of matrices</p>
    </text>
    <text lang="ger">
      <p bold="true">Erweitern von Matrizen</p>
    </text>
  </region>
  <region id="29" left="18" top="657" width="9" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p />
    </text>
  </region>
  <region id="30" left="18" top="657" width="535" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Join two matrices A and B of equal number of rows to a new matrix with the same number 
of rows.</p>
    </text>
    <text lang="ger">
      <p>Erweitern einer Matrix A durch eine Matrix B gleicher Zeilenzahl</p>
    </text>
  </region>
  <region id="31" left="18" top="693" width="222" height="64" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="operand">4</e>
        <e type="operand">5</e>
        <e type="operand">6</e>
        <e type="operand">3</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="8">mat</e>
        <e type="operand">1</e>
        <e type="operand">3</e>
        <e type="operand">5</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
        <e type="function" preserve="true" args="2">augment</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="operand">3</e>
        <e type="operand">4</e>
        <e type="operand">3</e>
        <e type="operand">5</e>
        <e type="operand">6</e>
        <e type="operand">5</e>
        <e type="operand">3</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="11">mat</e>
      </result>
    </math>
  </region>
  <region id="32" left="18" top="765" width="552" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Generation of a matrix column by column in a loop</p>
    </text>
    <text lang="ger">
      <p>So können Sie eine Matrix spaltenweise in einer Schleife aufbauen:</p>
    </text>
  </region>
  <region id="33" left="27" top="801" width="128" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">M</e>
        <e type="operand">2</e>
        <e type="operand">0</e>
        <e type="function" preserve="true" args="2">matrix</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="34" left="297" top="801" width="401" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Initialize the matrix with 2 rows and 0 columns</p>
    </text>
    <text lang="ger">
      <p>Initialisieren einer leeren zweizeiligen Matrix </p>
    </text>
  </region>
  <region id="35" left="18" top="828" width="227" height="72" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">0</e>
        <e type="operand">π</e>
        <e type="operand">π</e>
        <e type="operand">4</e>
        <e type="operator" args="2">/</e>
        <e type="function" preserve="true" args="3">range</e>
        <e type="operand">M</e>
        <e type="operand">M</e>
        <e type="operand">x</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="4">mat</e>
        <e type="function" preserve="true" args="1">transpose</e>
        <e type="function" preserve="true" args="2">augment</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">for</e>
      </input>
    </math>
  </region>
  <region id="36" left="297" top="837" width="238" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>create and add more columns</p>
    </text>
    <text lang="ger">
      <p>Hinzufügen weiterer  Spalten</p>
    </text>
  </region>
  <region id="37" left="18" top="918" width="290" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">M</e>
      </input>
      <result action="numeric">
        <e type="operand">0</e>
        <e type="operand">0.7854</e>
        <e type="operand">1.5708</e>
        <e type="operand">2.3562</e>
        <e type="operand">3.1416</e>
        <e type="operand">0</e>
        <e type="operand">0.7071</e>
        <e type="operand">1</e>
        <e type="operand">0.7071</e>
        <e type="operand">0</e>
        <e type="operand">2</e>
        <e type="operand">5</e>
        <e type="function" preserve="true" args="12">mat</e>
      </result>
    </math>
  </region>
  <region id="38" left="9" top="972" width="177" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p bold="true">Stacking of matrices</p>
    </text>
    <text lang="ger">
      <p bold="true">Stapeln von Matrizen</p>
    </text>
  </region>
  <region id="39" left="9" top="999" width="350" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Stacking of matrices of equal column number</p>
    </text>
    <text lang="ger">
      <p>Stapeln von Matrizen gleicher Spaltenzahl</p>
    </text>
  </region>
  <region id="40" left="18" top="1026" width="205" height="98" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="operand">4</e>
        <e type="operand">5</e>
        <e type="operand">6</e>
        <e type="operand">3</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="8">mat</e>
        <e type="operand">1</e>
        <e type="operand">4</e>
        <e type="operand">3</e>
        <e type="operand">8</e>
        <e type="operand">2</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="6">mat</e>
        <e type="function" preserve="true" args="2">stack</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="operand">4</e>
        <e type="operand">5</e>
        <e type="operand">6</e>
        <e type="operand">1</e>
        <e type="operand">4</e>
        <e type="operand">3</e>
        <e type="operand">8</e>
        <e type="operand">5</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="12">mat</e>
      </result>
    </math>
  </region>
  <region id="41" left="18" top="1143" width="544" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Generation of a matrix row by row in a loop</p>
    </text>
    <text lang="ger">
      <p>So können Sie eine Matrix zeilenweise in einer Schleife aufbauen:</p>
    </text>
  </region>
  <region id="42" left="18" top="1170" width="128" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">M</e>
        <e type="operand">0</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">matrix</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="43" left="288" top="1170" width="401" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Initialize the matrix with 0 rows and 2 columns</p>
    </text>
    <text lang="ger">
      <p>Initialisieren einer leeren zweizeiligen Matrix </p>
    </text>
  </region>
  <region id="44" left="18" top="1197" width="198" height="63" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">0</e>
        <e type="operand">π</e>
        <e type="operand">π</e>
        <e type="operand">4</e>
        <e type="operator" args="2">/</e>
        <e type="function" preserve="true" args="3">range</e>
        <e type="operand">M</e>
        <e type="operand">M</e>
        <e type="operand">x</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="4">mat</e>
        <e type="function" preserve="true" args="2">stack</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">for</e>
      </input>
    </math>
  </region>
  <region id="45" left="288" top="1206" width="238" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>create and add more rows</p>
    </text>
    <text lang="ger">
      <p>Hinzufügen weiterer  Spalten</p>
    </text>
  </region>
  <region id="46" left="18" top="1260" width="160" height="98" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">M</e>
      </input>
      <result action="numeric">
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">0.7854</e>
        <e type="operand">0.7071</e>
        <e type="operand">1.5708</e>
        <e type="operand">1</e>
        <e type="operand">2.3562</e>
        <e type="operand">0.7071</e>
        <e type="operand">3.1416</e>
        <e type="operand">0</e>
        <e type="operand">5</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="12">mat</e>
      </result>
    </math>
  </region>
  <region id="47" left="189" top="1260" width="157" height="84" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="3.38357101722668" scale_y="3.38357101722668" scale_z="3.38357101722668" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-61" transpose_y="-22" transpose_z="0">
      <input>
        <e type="operand">M</e>
      </input>
    </plot>
  </region>
  <region id="48" left="18" top="1368" width="210" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p bold="true">Access to submatrices</p>
    </text>
    <text lang="ger">
      <p bold="true">Zugriff auf Teilmatrizen</p>
    </text>
  </region>
  <region id="49" left="18" top="1395" width="661" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Get a continuous submatrix by row and column indices</p>
    </text>
    <text lang="ger">
      <p>Zusammenhängende Teilmatrix anhand der Zeilen- und Spaltennummern herausgreifen</p>
    </text>
  </region>
  <region id="50" left="18" top="1422" width="341" height="64" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">5</e>
        <e type="operand">11</e>
        <e type="operand">17</e>
        <e type="operand">11</e>
        <e type="operand">25</e>
        <e type="operand">39</e>
        <e type="operand">17</e>
        <e type="operand">39</e>
        <e type="operand">61</e>
        <e type="operand">3</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="11">mat</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="5">submatrix</e>
      </input>
      <result action="numeric">
        <e type="operand">11</e>
        <e type="operand">17</e>
        <e type="operand">25</e>
        <e type="operand">39</e>
        <e type="operand">2</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="6">mat</e>
      </result>
    </math>
  </region>
  <region id="51" left="18" top="1512" width="185" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p href="Chapter Matrices.sm">Vectors and Matrices</p>
    </text>
    <text lang="ger">
      <p href="Chapter Matrices.sm">Vektoren und Matrizen</p>
    </text>
  </region>
  <region id="52" left="18" top="1530" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p href="Handbook.sm">Contents</p>
    </text>
    <text lang="ger">
      <p href="Handbook.sm">Inhalt</p>
    </text>
  </region>
  <region id="53" left="18" top="1566" width="450" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p italic="true">$Author: mkraska $
$Date: 2013-08-21 00:22:17 +0200 (Mi, 21. Aug 2013) $ </p>
    </text>
  </region>
</regions>