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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="316" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p bold="true">Functions for creating matrices</p>
    </text>
    <text lang="ger">
      <p bold="true">Funktionen zur Erzeugung von Matrizen</p>
    </text>
  </region>
  <region id="1" left="540" top="18" 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="540" top="36" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p href="Mathematik.sm">Mathematics</p>
    </text>
    <text lang="ger">
      <p href="Mathematik.sm">Mathematik</p>
    </text>
  </region>
  <region id="3" left="540" top="54" 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="4" left="18" top="72" width="127" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p underline="true">Identity matrix</p>
    </text>
    <text lang="ger">
      <p underline="true">Einheitsmatrix</p>
    </text>
  </region>
  <region id="5" left="207" top="99" width="172" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
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        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">1</e>
        <e type="operand">3</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="11">mat</e>
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  </region>
  <region id="6" left="36" top="108" width="156" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="1">identity</e>
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      <result action="numeric">
        <e type="operand">1</e>
        <e type="operand">0</e>
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        <e type="operand">1</e>
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        <e type="operand">2</e>
        <e type="function" preserve="true" args="6">mat</e>
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  <region id="7" left="18" top="162" width="323" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p underline="true">Matrix or vector of all zeros</p>
    </text>
    <text lang="ger">
      <p underline="true">Mit Nullen besetzte Matrix oder Vektor</p>
    </text>
  </region>
  <region id="8" left="36" top="198" width="115" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="1">Zeros</e>
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      <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="9" left="153" top="198" width="171" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">Zeros</e>
      </input>
      <result action="numeric">
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="8">mat</e>
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    </math>
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    <math>
      <input>
        <e type="operand">2</e>
        <e type="operand">4</e>
        <e type="function" preserve="true" args="2">matrix</e>
      </input>
      <result action="numeric">
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">2</e>
        <e type="operand">4</e>
        <e type="function" preserve="true" args="10">mat</e>
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    </math>
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  <region id="11" left="36" top="297" width="199" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">0</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">matrix</e>
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      <result action="numeric">
        <e type="operand">0</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="2">mat</e>
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  <region id="12" left="279" top="297" width="418" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>matrix with zero rows, rows can be added using stack()</p>
    </text>
    <text lang="ger">
      <p>Matrix mit null Zeilen, Zeilen können mit stack() 
hinzugefügt werden</p>
    </text>
  </region>
  <region id="13" left="36" top="342" width="199" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">3</e>
        <e type="operand">0</e>
        <e type="function" preserve="true" args="2">matrix</e>
      </input>
      <result action="numeric">
        <e type="operand">3</e>
        <e type="operand">0</e>
        <e type="function" preserve="true" args="2">mat</e>
      </result>
    </math>
  </region>
  <region id="14" left="279" top="342" width="407" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>matrix with zero columns and three columns, columns 
can be added using augment()</p>
    </text>
    <text lang="ger">
      <p>Matrix mit null Spalten und drei Zeilen. Spalten
können mit augment() hinzugefügt werden.</p>
    </text>
  </region>
  <region id="15" left="18" top="396" width="323" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p underline="true">Matrix or vector of all ones</p>
    </text>
    <text lang="ger">
      <p underline="true">Mit Einsen besetzte Matrix oder Vektor</p>
    </text>
  </region>
  <region id="16" left="36" top="432" width="107" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="1">Ones</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
        <e type="operand">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="17" left="153" top="432" width="163" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">Ones</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="8">mat</e>
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    </math>
  </region>
  <region id="18" left="18" top="486" width="266" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p underline="true">Diagonal matrix from vector</p>
    </text>
    <text lang="ger">
      <p underline="true">Diagonalmatrix aus einem Vektor</p>
    </text>
  </region>
  <region id="19" left="36" top="522" width="246" height="88" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
        <e type="operand">3</e>
        <e type="operand" style="unit">N</e>
        <e type="operator" args="2">*</e>
        <e type="operand">5</e>
        <e type="operand" style="unit">kg</e>
        <e type="operator" args="2">*</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="1">diag</e>
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      <result action="numeric">
        <e type="operand">1</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
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        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">3</e>
        <e type="operand" style="unit">kg</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
        <e type="operand" style="unit">s</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">0</e>
        <e type="operand">0</e>
        <e type="operand">0</e>
        <e type="operand">5</e>
        <e type="operand" style="unit">kg</e>
        <e type="operator" args="2">*</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="20" left="18" top="612" width="407" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p underline="true">Vectors with equidistant ranges of values</p>
    </text>
    <text lang="ger">
      <p underline="true">Vektoren mit auf- oder absteigenden Zahlenwerten</p>
    </text>
  </region>
  <region id="21" left="288" top="639" width="42" height="35" color="#000000" bgColor="#ffffff">
    <picture>
      <raw format="png" encoding="base64"> </raw>
    </picture>
  </region>
  <region id="22" left="36" top="648" width="74" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="operand">1</e>
        <e type="operand">5</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="23" left="126" top="648" width="62" height="98" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</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">5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="7">mat</e>
      </result>
    </math>
  </region>
  <region id="24" left="333" top="648" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>x:rang</p>
    </text>
  </region>
  <region id="25" left="396" top="648" width="37" height="24" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Tab</p>
    </text>
  </region>
  <region id="26" left="432" top="648" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>1</p>
    </text>
  </region>
  <region id="27" left="450" top="648" width="20" height="24" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>→</p>
    </text>
  </region>
  <region id="28" left="468" top="648" width="24" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>5 </p>
    </text>
  </region>
  <region id="29" left="36" top="756" width="111" height="98" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="operand">2</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="2">range</e>
      </input>
      <result action="numeric">
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="operand">0</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="operand">2</e>
        <e type="operator" args="1">-</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="7">mat</e>
      </result>
    </math>
  </region>
  <region id="30" left="144" top="765" width="144" height="80" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">0.5</e>
        <e type="operand">3.5</e>
        <e type="function" preserve="true" args="2">range</e>
      </input>
      <result action="numeric">
        <e type="operand">0.5</e>
        <e type="operand">1.5</e>
        <e type="operand">2.5</e>
        <e type="operand">3.5</e>
        <e type="operand">4</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="6">mat</e>
      </result>
    </math>
  </region>
  <region id="31" left="36" top="864" width="666" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>For ranges with step not equal to one, the function range() is used with tree 
arguments.</p>
    </text>
    <text lang="ger">
      <p>Für Wertebereiche mit anderem Schritt als 1 muss die Funktion range(3) mit drei 
Argumenten benutzt werden:</p>
    </text>
  </region>
  <region id="32" left="288" top="900" width="207" height="112" color="#000000" bgColor="#ffffff">
    <picture>
      <raw format="png" encoding="base64"> </raw>
    </picture>
  </region>
  <region id="33" left="99" top="909" width="56" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x.2</e>
        <e type="operand">π</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="34" left="36" top="918" width="52" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x.1</e>
        <e type="operand">0</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="35" left="171" top="918" width="67" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x.n</e>
        <e type="operand">2</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="36" left="36" top="954" width="160" height="98" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x.1</e>
        <e type="operand">x.n</e>
        <e type="operand">x.2</e>
        <e type="function" preserve="true" args="3">range</e>
      </input>
      <contract>
        <e type="operand">π</e>
      </contract>
      <result action="numeric">
        <e type="operand">0</e>
        <e type="operand">0.5</e>
        <e type="operand">1</e>
        <e type="operand">1.5</e>
        <e type="operand">2</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="7">mat</e>
      </result>
    </math>
  </region>
  <region id="37" left="288" top="1017" width="42" height="35" color="#000000" bgColor="#ffffff">
    <picture>
      <raw format="png" encoding="base64"> </raw>
    </picture>
  </region>
  <region id="38" left="333" top="1026" width="49" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>rang </p>
    </text>
  </region>
  <region id="39" left="378" top="1026" width="20" height="24" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>↓</p>
    </text>
  </region>
  <region id="40" left="396" top="1026" width="37" height="24" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Tab</p>
    </text>
  </region>
  <region id="41" left="432" top="1026" width="37" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>x.1</p>
    </text>
  </region>
  <region id="42" left="468" top="1026" width="20" height="24" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>→</p>
    </text>
  </region>
  <region id="43" left="486" top="1026" width="37" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>x.n</p>
    </text>
  </region>
  <region id="44" left="522" top="1026" width="20" height="24" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>→</p>
    </text>
  </region>
  <region id="45" left="540" top="1026" width="37" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>x.2</p>
    </text>
  </region>
  <region id="46" left="18" top="1062" width="333" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p underline="true">Random matrices</p>
    </text>
    <text lang="ger">
      <p underline="true">Matrizen und Vektoren mit Zufallszahlen</p>
    </text>
  </region>
  <region id="47" left="36" top="1098" width="365" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Real random numbers between zero and one</p>
    </text>
    <text lang="ger">
      <p>Reelle Zufallszahlen zwischen Null und Eins</p>
    </text>
  </region>
  <region id="48" left="45" top="1125" width="164" height="98" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">5</e>
        <e type="function" preserve="true" args="1">Random</e>
      </input>
      <result action="numeric">
        <e type="operand">0.4164</e>
        <e type="operand">0.872</e>
        <e type="operand">0.3432</e>
        <e type="operand">0.2504</e>
        <e type="operand">0.4633</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="7">mat</e>
      </result>
    </math>
  </region>
  <region id="49" left="234" top="1125" width="302" height="98" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">5</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">Random</e>
      </input>
      <result action="numeric">
        <e type="operand">0.6884</e>
        <e type="operand">0.7595</e>
        <e type="operand">0.7327</e>
        <e type="operand">0.2641</e>
        <e type="operand">0.8121</e>
        <e type="operand">0.9427</e>
        <e type="operand">0.061</e>
        <e type="operand">0.5981</e>
        <e type="operand">0.8842</e>
        <e type="operand">0.3488</e>
        <e type="operand">0.3602</e>
        <e type="operand">0.4835</e>
        <e type="operand">0.0662</e>
        <e type="operand">0.4854</e>
        <e type="operand">0.3258</e>
        <e type="operand">5</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="17">mat</e>
      </result>
    </math>
  </region>
  <region id="50" left="36" top="1224" width="431" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>integer random numbers in specified intervals</p>
    </text>
    <text lang="ger">
      <p>Ganzzahlige Zufallszahlen in angebbaren Intervallen</p>
    </text>
  </region>
  <region id="51" left="45" top="1251" width="189" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">3</e>
        <e type="operand">5</e>
        <e type="operator" args="1">-</e>
        <e type="operand">5</e>
        <e type="function" preserve="true" args="3">Random.N</e>
      </input>
      <result action="numeric">
        <e type="operand">4</e>
        <e type="operand">4</e>
        <e type="operand">3</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
      </result>
    </math>
  </region>
  <region id="52" left="234" top="1251" width="272" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">3</e>
        <e type="operand">3</e>
        <e type="operand">5</e>
        <e type="operator" args="1">-</e>
        <e type="operand">5</e>
        <e type="function" preserve="true" args="4">Random.N</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
        <e type="operand">5</e>
        <e type="operator" args="1">-</e>
        <e type="operand">0</e>
        <e type="operand">2</e>
        <e type="operator" args="1">-</e>
        <e type="operand">3</e>
        <e type="operator" args="1">-</e>
        <e type="operand">2</e>
        <e type="operand">4</e>
        <e type="operand">4</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</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="53" left="18" top="1332" 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="54" left="18" top="1350" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p href="Mathematik.sm">Mathematics</p>
    </text>
    <text lang="ger">
      <p href="Mathematik.sm">Mathematik</p>
    </text>
  </region>
  <region id="55" left="18" top="1368" 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="56" left="18" top="1404" 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>