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    <identity>
      <id>be8ed228-7b9f-4d88-9521-f6039e697cd5</id>
      <revision>84</revision>
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    <calculation>
      <precision>4</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <fractions>decimal</fractions>
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    <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 />
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  <region id="0" left="18" top="18" width="303" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Hintergrundinfo zu Operatoren</p>
    </text>
    <text lang="eng">
      <p bold="true">Background information on operators </p>
    </text>
  </region>
  <region id="1" left="567" top="18" width="168" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Section math operators priority.sm">Operatoren, Priorität</p>
    </text>
    <text lang="eng">
      <p href="Section math operators priority.sm">Operators, Priority</p>
    </text>
  </region>
  <region id="2" left="567" top="36" width="103" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Mathematik.sm">Mathematik</p>
    </text>
    <text lang="eng">
      <p href="Mathematik.sm">Mathematics</p>
    </text>
  </region>
  <region id="3" left="567" top="54" 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="4" left="18" top="90" width="655" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Ausdrücke bestehen in SMath aus Konstanten und Variablen, die Argumente von 
Operationen sind. Operationen können durch Funktionen und Operatoren dargestellt werden.</p>
    </text>
    <text lang="eng">
      <p>Expressions in SMath consist of constants and variables which are arguments to 
operations. Operations are represented by functions or operators.</p>
    </text>
  </region>
  <region id="5" left="18" top="135" width="687" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>In SMath erfolgt die offizielle Einstufung anhand der internen Darstellung. Eine 
Funktion hat einen Namen und eine Argumentliste in Klammern, ein Operator wird durch
spezielle Zeichen dargestellt.</p>
    </text>
    <text lang="eng">
      <p>In SMath, the official classification is by internal representation. A function is 
represented by a name, an operator is represented by a symbol.</p>
    </text>
  </region>
  <region id="6" left="18" top="198" width="710" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>There are some operations, which are internally treated as functions but have special
operator formatting in math regions.</p>
    </text>
  </region>
  <region id="7" left="18" top="252" width="152" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p underline="true">Echte Operatoren</p>
    </text>
    <text lang="eng">
      <p underline="true">Genuine operators</p>
    </text>
  </region>
  <region id="8" left="18" top="288" width="299" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Diese können über das Menü eingefügt werden:</p>
    </text>
    <text lang="eng">
      <p>These can be inserted via main menu</p>
    </text>
  </region>
  <region id="9" left="414" top="288" width="144" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Einfügen&gt; Operator</p>
    </text>
    <text lang="eng">
      <p bold="true">Insert&gt; Operator</p>
    </text>
  </region>
  <region id="10" left="27" top="324" width="41" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operator" args="2">≡</e>
      </input>
    </math>
  </region>
  <region id="11" left="108" top="324" width="119" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Boolsches Gleich</p>
    </text>
    <text lang="eng">
      <p>boolean equal</p>
    </text>
  </region>
  <region id="12" left="387" top="324" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>≡</p>
    </text>
  </region>
  <region id="13" left="27" top="351" width="41" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operator" args="2">≠</e>
      </input>
    </math>
  </region>
  <region id="14" left="108" top="351" width="152" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Boolsches Ungleich</p>
    </text>
    <text lang="eng">
      <p>boolean not equal</p>
    </text>
  </region>
  <region id="15" left="387" top="351" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>≠</p>
    </text>
  </region>
  <region id="16" left="27" top="378" width="41" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operator" args="2">|</e>
      </input>
    </math>
  </region>
  <region id="17" left="108" top="378" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Boolsches Oder</p>
    </text>
    <text lang="eng">
      <p>boolean or</p>
    </text>
  </region>
  <region id="18" left="387" top="378" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>|</p>
    </text>
  </region>
  <region id="19" left="27" top="405" width="41" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operator" args="2">¤</e>
      </input>
    </math>
  </region>
  <region id="20" left="108" top="405" width="225" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Boolsches exklusives Oder (XOR)</p>
    </text>
    <text lang="eng">
      <p>boolean exclusive or (XOR)</p>
    </text>
  </region>
  <region id="21" left="387" top="405" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>¤</p>
    </text>
  </region>
  <region id="22" left="27" top="432" width="41" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operator" args="2">&amp;</e>
      </input>
    </math>
  </region>
  <region id="23" left="108" top="432" width="103" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Boolsches Und</p>
    </text>
    <text lang="eng">
      <p>boolean and</p>
    </text>
  </region>
  <region id="24" left="387" top="432" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>&amp;</p>
    </text>
  </region>
  <region id="25" left="27" top="459" width="41" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operator" args="2">&lt;</e>
      </input>
    </math>
  </region>
  <region id="26" left="108" top="459" width="152" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>boolean less than</p>
    </text>
  </region>
  <region id="27" left="387" top="459" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>&lt;</p>
    </text>
  </region>
  <region id="28" left="27" top="486" width="41" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operator" args="2">&gt;</e>
      </input>
    </math>
  </region>
  <region id="29" left="108" top="486" width="177" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>boolean greater than</p>
    </text>
  </region>
  <region id="30" left="387" top="486" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>&gt;</p>
    </text>
  </region>
  <region id="31" left="27" top="513" width="41" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operator" args="2">≤</e>
      </input>
    </math>
  </region>
  <region id="32" left="108" top="513" width="184" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Boolsches Kleiner oder Gleich</p>
    </text>
    <text lang="eng">
      <p>boolean less or equal</p>
    </text>
  </region>
  <region id="33" left="387" top="513" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>≤</p>
    </text>
  </region>
  <region id="34" left="27" top="540" width="41" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operator" args="2">≥</e>
      </input>
    </math>
  </region>
  <region id="35" left="108" top="540" width="209" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Boolsches Größer oder Gleich</p>
    </text>
    <text lang="eng">
      <p>boolean greater or equal</p>
    </text>
  </region>
  <region id="36" left="387" top="540" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>≥</p>
    </text>
  </region>
  <region id="37" left="36" top="567" width="29" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operator" args="1">¬</e>
      </input>
    </math>
  </region>
  <region id="38" left="108" top="567" width="103" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Boolsches Nicht</p>
    </text>
    <text lang="eng">
      <p>boolean not</p>
    </text>
  </region>
  <region id="39" left="387" top="567" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>¬</p>
    </text>
  </region>
  <region id="40" left="27" top="594" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math error="0">
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="41" left="108" top="594" width="98" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Zuweisung</p>
    </text>
    <text lang="eng">
      <p>assignment </p>
    </text>
  </region>
  <region id="42" left="387" top="594" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>:</p>
    </text>
  </region>
  <region id="43" left="36" top="621" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>=</p>
    </text>
  </region>
  <region id="44" left="108" top="621" width="98" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Auswertung</p>
    </text>
    <text lang="eng">
      <p>evaluation </p>
    </text>
  </region>
  <region id="45" left="387" top="621" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>=</p>
    </text>
  </region>
  <region id="46" left="27" top="648" width="41" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operator" args="2">+</e>
      </input>
    </math>
  </region>
  <region id="47" left="108" top="648" width="82" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Addition</p>
    </text>
    <text lang="eng">
      <p>addition </p>
    </text>
  </region>
  <region id="48" left="387" top="648" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>+</p>
    </text>
  </region>
  <region id="49" left="27" top="675" width="41" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operator" args="2">-</e>
      </input>
    </math>
  </region>
  <region id="50" left="108" top="675" width="107" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Subtraktion</p>
    </text>
    <text lang="eng">
      <p>subtraction </p>
    </text>
  </region>
  <region id="51" left="387" top="675" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>-</p>
    </text>
  </region>
  <region id="52" left="27" top="702" width="35" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operator" args="2">*</e>
      </input>
    </math>
  </region>
  <region id="53" left="108" top="702" width="131" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Multiplikation</p>
    </text>
    <text lang="eng">
      <p>multiplication </p>
    </text>
  </region>
  <region id="54" left="387" top="702" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>*</p>
    </text>
  </region>
  <region id="55" left="27" top="720" width="24" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operator" args="2">/</e>
      </input>
    </math>
  </region>
  <region id="56" left="108" top="729" width="82" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Division</p>
    </text>
    <text lang="eng">
      <p>division </p>
    </text>
  </region>
  <region id="57" left="387" top="729" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>/</p>
    </text>
  </region>
  <region id="58" left="27" top="756" width="32" height="33" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operator" args="2">^</e>
      </input>
    </math>
  </region>
  <region id="59" left="108" top="765" width="126" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Potenzieren</p>
    </text>
    <text lang="eng">
      <p>raise to power</p>
    </text>
  </region>
  <region id="60" left="387" top="765" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>^</p>
    </text>
  </region>
  <region id="61" left="27" top="792" width="41" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operator" args="2">±</e>
      </input>
    </math>
  </region>
  <region id="62" left="108" top="792" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Plus/Minus</p>
    </text>
    <text lang="eng">
      <p>plus/minus</p>
    </text>
  </region>
  <region id="63" left="387" top="792" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>±</p>
    </text>
  </region>
  <region id="64" left="27" top="819" width="41" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operator" args="2">%</e>
      </input>
    </math>
  </region>
  <region id="65" left="108" top="819" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Minus/Plus</p>
    </text>
    <text lang="eng">
      <p>minus/plus</p>
    </text>
  </region>
  <region id="66" left="387" top="819" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>%</p>
    </text>
  </region>
  <region id="67" left="27" top="846" width="41" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operator" args="2">†</e>
      </input>
    </math>
  </region>
  <region id="68" left="108" top="846" width="119" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Kreuzprodukt</p>
    </text>
    <text lang="eng">
      <p>cross product</p>
    </text>
  </region>
  <region id="69" left="387" top="846" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>†</p>
    </text>
  </region>
  <region id="70" left="27" top="873" width="27" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operator" args="1">!</e>
      </input>
    </math>
  </region>
  <region id="71" left="108" top="873" width="70" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Fakultät</p>
    </text>
    <text lang="eng">
      <p>faculty</p>
    </text>
  </region>
  <region id="72" left="387" top="873" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>!</p>
    </text>
  </region>
  <region id="73" left="18" top="918" width="463" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p underline="true">Eingebaute SMath-Operatoren, die interne Funktionen darstellen</p>
    </text>
    <text lang="eng">
      <p underline="true">Operators representing internal functions, native SMath</p>
    </text>
  </region>
  <region id="74" left="27" top="954" width="26" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="1">abs</e>
      </input>
    </math>
  </region>
  <region id="75" left="108" top="954" width="224" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Betrag einer Zahl</p>
    </text>
    <text lang="eng">
      <p>absolute value of a number</p>
    </text>
  </region>
  <region id="76" left="396" top="954" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>abs(#)</p>
    </text>
  </region>
  <region id="77" left="108" top="972" width="200" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Determinante einer Matrix</p>
    </text>
    <text lang="eng">
      <p>determinant of a matrix</p>
    </text>
  </region>
  <region id="78" left="396" top="972" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>det(#)</p>
    </text>
  </region>
  <region id="79" left="27" top="999" width="24" height="27" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="1">diff</e>
      </input>
    </math>
  </region>
  <region id="80" left="108" top="999" width="98" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Ableitung</p>
    </text>
    <text lang="eng">
      <p>derivative </p>
    </text>
  </region>
  <region id="81" left="396" top="999" width="70" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>diff(#)</p>
    </text>
  </region>
  <region id="82" left="495" top="999" width="131" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>nicht aktiv </p>
    </text>
    <text lang="eng">
      <p>not functional </p>
    </text>
  </region>
  <region id="83" left="27" top="1026" width="48" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="2">diff</e>
      </input>
    </math>
  </region>
  <region id="84" left="108" top="1035" width="143" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>erste Ableitung</p>
    </text>
    <text lang="eng">
      <p>first derivative</p>
    </text>
  </region>
  <region id="85" left="396" top="1035" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>diff(#;#)</p>
    </text>
    <text lang="eng">
      <p>diff(#,#)</p>
    </text>
  </region>
  <region id="86" left="27" top="1071" width="60" height="58" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="3">diff</e>
      </input>
    </math>
  </region>
  <region id="87" left="108" top="1080" width="127" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>nth derivative</p>
    </text>
  </region>
  <region id="88" left="396" top="1080" width="103" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>diff(#;#;#)</p>
    </text>
    <text lang="eng">
      <p>diff(#,#,#)</p>
    </text>
  </region>
  <region id="89" left="27" top="1134" width="34" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="2">el</e>
      </input>
    </math>
  </region>
  <region id="90" left="108" top="1143" width="176" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Elementindex (Adressindex)</p>
    </text>
    <text lang="eng">
      <p>element adress index</p>
    </text>
  </region>
  <region id="91" left="396" top="1143" width="70" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>el(#;#)</p>
    </text>
    <text lang="eng">
      <p>el(#,#)</p>
    </text>
  </region>
  <region id="92" left="27" top="1161" width="48" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="3">el</e>
      </input>
    </math>
  </region>
  <region id="93" left="108" top="1170" width="193" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Elementindex (Adressindex)</p>
    </text>
    <text lang="eng">
      <p>element adress indices</p>
    </text>
  </region>
  <region id="94" left="396" top="1170" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>el(#;#;#)</p>
    </text>
    <text lang="eng">
      <p>el(#,#,#)</p>
    </text>
  </region>
  <region id="95" left="27" top="1206" width="78" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="3">for</e>
      </input>
    </math>
  </region>
  <region id="96" left="108" top="1206" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>For-Schleife</p>
    </text>
    <text lang="eng">
      <p>for loop</p>
    </text>
  </region>
  <region id="97" left="396" top="1206" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>for(#;#;#)</p>
    </text>
    <text lang="eng">
      <p>for(#,#,#)</p>
    </text>
  </region>
  <region id="98" left="27" top="1242" width="94" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="4">for</e>
      </input>
    </math>
  </region>
  <region id="99" left="396" top="1242" width="111" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>for(#;#;#;#)</p>
    </text>
    <text lang="eng">
      <p>for(#,#,#,#)</p>
    </text>
  </region>
  <region id="100" left="27" top="1287" width="45" height="72" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="3">if</e>
      </input>
    </math>
  </region>
  <region id="101" left="108" top="1287" width="185" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Bedingte Anweisung</p>
    </text>
    <text lang="eng">
      <p>conditional statement</p>
    </text>
  </region>
  <region id="102" left="396" top="1287" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>if(#;#;#)</p>
    </text>
    <text lang="eng">
      <p>if(#,#,#)</p>
    </text>
  </region>
  <region id="103" left="27" top="1359" width="56" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="2">int</e>
      </input>
    </math>
  </region>
  <region id="104" left="108" top="1368" width="82" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Integral</p>
    </text>
    <text lang="eng">
      <p>integral </p>
    </text>
  </region>
  <region id="105" left="396" top="1368" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>int(#;#)</p>
    </text>
    <text lang="eng">
      <p>int(#,#)</p>
    </text>
  </region>
  <region id="106" left="27" top="1404" width="57" height="66" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="4">int</e>
      </input>
    </math>
  </region>
  <region id="107" left="108" top="1422" width="152" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Bestimmtes Integral</p>
    </text>
    <text lang="eng">
      <p>definite integral</p>
    </text>
  </region>
  <region id="108" left="396" top="1422" width="111" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>int(#;#;#;#)</p>
    </text>
    <text lang="eng">
      <p>int(#,#,#,#)</p>
    </text>
  </region>
  <region id="109" left="27" top="1467" width="56" height="37" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="3">lim</e>
      </input>
    </math>
  </region>
  <region id="110" left="108" top="1467" width="57" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Grenzwert</p>
    </text>
    <text lang="eng">
      <p>limit </p>
    </text>
  </region>
  <region id="111" left="396" top="1467" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>lim(#;#;#)</p>
    </text>
    <text lang="eng">
      <p>lim(#,#,#)</p>
    </text>
  </region>
  <region id="112" left="495" top="1467" width="210" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>funktioniert nur mit dem
Maxima-Plugin</p>
    </text>
  </region>
  <region id="113" left="27" top="1503" width="29" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
      </input>
    </math>
  </region>
  <region id="114" left="108" top="1503" width="135" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Anweisungsblock</p>
    </text>
    <text lang="eng">
      <p>statement block</p>
    </text>
  </region>
  <region id="115" left="396" top="1503" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>line()</p>
    </text>
  </region>
  <region id="116" left="27" top="1557" width="40" height="30" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="2">nthroot</e>
      </input>
    </math>
  </region>
  <region id="117" left="108" top="1557" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>n-te Wurzel</p>
    </text>
    <text lang="eng">
      <p>nth root</p>
    </text>
  </region>
  <region id="118" left="396" top="1557" width="111" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>nthroot(#;#)</p>
    </text>
    <text lang="eng">
      <p>nthroot(#,#)</p>
    </text>
  </region>
  <region id="119" left="27" top="1584" width="56" height="63" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="4">product</e>
      </input>
    </math>
  </region>
  <region id="120" left="108" top="1602" width="74" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Produkt</p>
    </text>
    <text lang="eng">
      <p>product </p>
    </text>
  </region>
  <region id="121" left="396" top="1602" width="144" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>product(#;#;#;#)</p>
    </text>
    <text lang="eng">
      <p>produkt(#,#,#,#)</p>
    </text>
  </region>
  <region id="122" left="27" top="1647" width="51" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="2">range</e>
      </input>
    </math>
  </region>
  <region id="123" left="108" top="1647" width="57" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Bereich</p>
    </text>
    <text lang="eng">
      <p>range </p>
    </text>
  </region>
  <region id="124" left="396" top="1647" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>range(#;#)</p>
    </text>
    <text lang="eng">
      <p>range(#,#)</p>
    </text>
  </region>
  <region id="125" left="27" top="1674" width="74" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="3">range</e>
      </input>
    </math>
  </region>
  <region id="126" left="108" top="1674" width="201" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Bereich mit Schrittweite</p>
    </text>
    <text lang="eng">
      <p>range with step control</p>
    </text>
  </region>
  <region id="127" left="396" top="1674" width="111" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>range(#;#;#)</p>
    </text>
    <text lang="eng">
      <p>range(#,#,#)</p>
    </text>
  </region>
  <region id="128" left="36" top="1710" width="34" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="1">sqrt</e>
      </input>
    </math>
  </region>
  <region id="129" left="108" top="1710" width="102" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Quadratwurzel</p>
    </text>
    <text lang="eng">
      <p>square root</p>
    </text>
  </region>
  <region id="130" left="396" top="1710" width="70" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>sqrt(#)</p>
    </text>
  </region>
  <region id="131" left="36" top="1746" width="40" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="1">sum</e>
      </input>
    </math>
  </region>
  <region id="132" left="108" top="1746" width="189" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Summe über alle Elemente
eines Feldes</p>
    </text>
    <text lang="eng">
      <p>sum over all elements 
of an array</p>
    </text>
  </region>
  <region id="133" left="396" top="1746" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>sum(#)</p>
    </text>
  </region>
  <region id="134" left="27" top="1782" width="56" height="63" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="4">sum</e>
      </input>
    </math>
  </region>
  <region id="135" left="108" top="1800" width="41" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Summe</p>
    </text>
    <text lang="eng">
      <p>sum </p>
    </text>
  </region>
  <region id="136" left="396" top="1800" width="111" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>sum(#;#;#;#)</p>
    </text>
    <text lang="eng">
      <p>sum(#,#,#,#)</p>
    </text>
  </region>
  <region id="137" left="27" top="1854" width="70" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="2">while</e>
      </input>
    </math>
  </region>
  <region id="138" left="108" top="1854" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>While-Schleife</p>
    </text>
    <text lang="eng">
      <p>while-loop</p>
    </text>
  </region>
  <region id="139" left="396" top="1854" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>while(#;#)</p>
    </text>
    <text lang="eng">
      <p>while(#,#)</p>
    </text>
  </region>
  <region id="140" left="18" top="1908" width="382" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p underline="true">Operatoren aus dem Plugin FunctionsExtensions</p>
    </text>
    <text lang="eng">
      <p underline="true">Operators from the FunctionsExtensions plugin</p>
    </text>
  </region>
  <region id="141" left="549" top="1908" width="169" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin FunctionsExtensions.sm">FunctionsExtensions</p>
    </text>
  </region>
  <region id="142" left="18" top="1944" width="692" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Die SMath-Programmierschnittstelle erlaubt die Definition eigener Operator-
Formatierungen, so geschehen im Plugin FunctionsExtensions von Davide Carpi.</p>
    </text>
    <text lang="eng">
      <p>The SMath API allows for definition of custom operators. This has been demonstrated
and used by Davide Carpi in his FunctionsExtensions plugin.</p>
    </text>
  </region>
  <region id="143" left="27" top="1998" width="62" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="3">ltlt</e>
      </input>
    </math>
  </region>
  <region id="144" left="108" top="1998" width="225" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Ternäre Operatoren zur Definition
von Gültigkeitsbereichen</p>
    </text>
    <text lang="eng">
      <p>ternary operators for 
specification of intervals</p>
    </text>
  </region>
  <region id="145" left="396" top="1998" width="103" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>ltlt(#,#,#)</p>
    </text>
  </region>
  <region id="146" left="27" top="2025" width="62" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="3">ltle</e>
      </input>
    </math>
  </region>
  <region id="147" left="396" top="2025" width="103" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>ltle(#,#,#)</p>
    </text>
  </region>
  <region id="148" left="27" top="2052" width="62" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="3">lelt</e>
      </input>
    </math>
  </region>
  <region id="149" left="108" top="2052" width="248" height="120" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Die Funktionsbezeichnungen setzen
sich aus den folgenden
Abkürzungen zusammen:

lt - less than
le - less than or equal to
gt - greater than
ge - greater than or equal to</p>
    </text>
    <text lang="eng">
      <p>The function are named by 
acronyms of the expressions

lt - less than
le - less than or equal to
gt - greater than
ge - greater than or equal to</p>
    </text>
  </region>
  <region id="150" left="396" top="2052" width="103" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>ltle(#,#,#)</p>
    </text>
  </region>
  <region id="151" left="27" top="2079" width="62" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="3">lele</e>
      </input>
    </math>
  </region>
  <region id="152" left="396" top="2079" width="103" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>lele(#,#,#)</p>
    </text>
  </region>
  <region id="153" left="27" top="2106" width="62" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="3">gtgt</e>
      </input>
    </math>
  </region>
  <region id="154" left="396" top="2106" width="103" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>gtgt(#,#,#)</p>
    </text>
  </region>
  <region id="155" left="27" top="2133" width="62" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="3">gtge</e>
      </input>
    </math>
  </region>
  <region id="156" left="396" top="2133" width="103" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>gtge(#,#,#)</p>
    </text>
  </region>
  <region id="157" left="27" top="2160" width="62" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="3">gegt</e>
      </input>
    </math>
  </region>
  <region id="158" left="396" top="2160" width="103" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>gegt(#,#,#)</p>
    </text>
  </region>
  <region id="159" left="27" top="2187" width="62" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="3">gege</e>
      </input>
    </math>
  </region>
  <region id="160" left="396" top="2187" width="103" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>gege(#,#,#)</p>
    </text>
  </region>
  <region id="161" left="27" top="2214" width="119" height="45" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="3">cases</e>
      </input>
    </math>
  </region>
  <region id="162" left="171" top="2214" width="176" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>stückweise definierte
Ausdrücke</p>
    </text>
    <text lang="eng">
      <p>piecewise continuous
expressions</p>
    </text>
  </region>
  <region id="163" left="396" top="2214" width="111" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>cases(#,#,#)</p>
    </text>
  </region>
  <region id="164" left="27" top="2268" width="30" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="1">Ceil</e>
      </input>
    </math>
  </region>
  <region id="165" left="108" top="2268" width="74" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>nächstgrößere Ganzzahl</p>
    </text>
    <text lang="eng">
      <p>ceiling </p>
    </text>
  </region>
  <region id="166" left="396" top="2268" width="70" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Ceil(#)</p>
    </text>
  </region>
  <region id="167" left="27" top="2295" width="30" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="1">Floor</e>
      </input>
    </math>
  </region>
  <region id="168" left="108" top="2295" width="57" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>nächstkleinere Ganzzahl</p>
    </text>
    <text lang="eng">
      <p>floor </p>
    </text>
  </region>
  <region id="169" left="396" top="2295" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Floor(#)</p>
    </text>
  </region>
  <region id="170" left="18" top="2340" width="645" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>The following operators have no effect, they are just for writing/documenting</p>
    </text>
  </region>
  <region id="171" left="27" top="2367" width="37" height="42" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="2">at</e>
      </input>
    </math>
  </region>
  <region id="172" left="108" top="2376" width="110" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>an der Stelle</p>
    </text>
    <text lang="eng">
      <p>evaluated at</p>
    </text>
  </region>
  <region id="173" left="396" top="2376" width="70" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>at(#,#)</p>
    </text>
  </region>
  <region id="174" left="504" top="2376" width="127" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>not functional</p>
    </text>
  </region>
  <region id="175" left="27" top="2412" width="37" height="42" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="3">at</e>
      </input>
    </math>
  </region>
  <region id="176" left="108" top="2412" width="257" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Ausdruck am oberen Wert minus 
Ausdruck am unteren Wert</p>
    </text>
    <text lang="eng">
      <p>evaluated at upper value minus
evaluated at lower value</p>
    </text>
  </region>
  <region id="177" left="396" top="2412" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>at(#,#,#)</p>
    </text>
  </region>
  <region id="178" left="504" top="2412" width="127" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>not functional</p>
    </text>
  </region>
  <region id="179" left="27" top="2457" width="38" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="1">grad</e>
      </input>
    </math>
  </region>
  <region id="180" left="108" top="2457" width="82" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Gradient</p>
    </text>
    <text lang="eng">
      <p>gradient </p>
    </text>
  </region>
  <region id="181" left="396" top="2457" width="70" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>grad(#)</p>
    </text>
  </region>
  <region id="182" left="504" top="2457" width="127" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>not functional</p>
    </text>
  </region>
  <region id="183" left="27" top="2484" width="58" height="38" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="2">grad</e>
      </input>
    </math>
  </region>
  <region id="184" left="108" top="2484" width="192" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Gradient an der Stelle...</p>
    </text>
    <text lang="eng">
      <p>gradient, evaluated at</p>
    </text>
  </region>
  <region id="185" left="396" top="2484" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>grad(#,#)</p>
    </text>
  </region>
  <region id="186" left="504" top="2484" width="127" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>not functional</p>
    </text>
  </region>
  <region id="187" left="27" top="2520" width="46" height="30" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="1">lapl</e>
      </input>
    </math>
  </region>
  <region id="188" left="108" top="2520" width="144" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Laplace-Operator</p>
    </text>
    <text lang="eng">
      <p>Laplace operator</p>
    </text>
  </region>
  <region id="189" left="396" top="2520" width="70" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>lapl(#)</p>
    </text>
  </region>
  <region id="190" left="504" top="2520" width="127" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>not functional</p>
    </text>
  </region>
  <region id="191" left="27" top="2556" width="63" height="38" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">#</e>
        <e type="operand">#</e>
        <e type="function" preserve="true" args="2">lapl</e>
      </input>
    </math>
  </region>
  <region id="192" left="108" top="2556" width="258" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Laplace operator, evaluated at</p>
    </text>
  </region>
  <region id="193" left="396" top="2556" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>lapl(#,#)</p>
    </text>
  </region>
  <region id="194" left="504" top="2556" width="127" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>not functional</p>
    </text>
  </region>
  <region id="195" left="18" top="2601" width="676" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Beachten Sie: Bei einigen Operatoren erkennt man die Grenzen der Argumente, wenn
weitere Operatoren folgen, bei anderen nicht.</p>
    </text>
    <text lang="eng">
      <p>Note that some formats indicate the extension of their arguments if combined with
other operators, some do not.</p>
    </text>
  </region>
  <region id="196" left="18" top="2655" width="459" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p underline="true">Funktionen und Operatoren in der internen Textdarstellung</p>
    </text>
    <text lang="eng">
      <p underline="true">Functions and operators in the internal representation </p>
    </text>
  </region>
  <region id="197" left="18" top="2691" width="649" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Die Unterscheidung von Funktionen und Operatoren erfolgt anhand der internen 
Darstellung, angezeigt durch die Funktion num2str() oder im xml-Code der .sm-Dateien.</p>
    </text>
    <text lang="eng">
      <p>The distinction is made based on the interal representation
as found by the function num2str() or in the xml file format of the .sm-files.</p>
    </text>
  </region>
  <region id="198" top="2736" color="#000000" bgColor="#ffffff">
    <area collapsed="true">
      <title lang="eng">
        <p>num2str() bug</p>
      </title>
    </area>
    <region id="199" left="18" top="2745" width="672" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>In einigen Fällen (Bugs) kann num2str() die Textdarstellung nicht liefern. Man
kann aber alternativ den Ausdruck aus der Zwischenablage in einen Textbereich
kopieren. Er wird dabei automatisch in die Textdarstellung umgewandelt.</p>
      </text>
      <text lang="eng">
        <p>In some cases (bugs), num2str() cannot find the internal text representation. In 
these cases still you can copy the expression to the clipboard and past it into
a text region.</p>
      </text>
    </region>
    <region id="200" left="243" top="2799" width="159" height="65" color="#000000" bgColor="#ffffff" fontSize="10">
      <math error="2">
        <input>
          <e type="operand">v</e>
          <e type="operand">i</e>
          <e type="operand">1</e>
          <e type="operand">n</e>
          <e type="function" preserve="true" args="4">sum</e>
          <e type="function" preserve="true" args="1">num2str</e>
        </input>
        <result action="symbolic">
          <e type="operand">#</e>
        </result>
      </math>
    </region>
    <region id="201" left="432" top="2799" width="298" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="ger">
        <p>Das ist ein Fehler. SMath sollte die
Textdarstellung anzeigen können,
auch wenn einige Variablen nicht 
definiert sind.</p>
      </text>
      <text lang="eng">
        <p>This is a bug. SMath should be able
to serialize the expression even if
the operands are not defined.</p>
      </text>
    </region>
    <region id="202" left="54" top="2817" width="143" height="36" color="#000000" bgColor="#ffffff" fontSize="10">
      <math error="68">
        <input>
          <e type="operand">v</e>
          <e type="function" preserve="true" args="1">sum</e>
          <e type="function" preserve="true" args="1">num2str</e>
        </input>
        <result action="symbolic">
          <e type="operand">#</e>
        </result>
      </math>
    </region>
    <region id="203" left="54" top="2871" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p>sum(v)</p>
      </text>
    </region>
    <region id="204" left="243" top="2871" width="111" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p>sum(v,i,1,n)</p>
      </text>
    </region>
    <region id="205" top="2898" color="#000000" bgColor="#ffffff">
      <area terminator="true" />
    </region>
  </region>
  <region id="206" left="36" top="2925" width="635" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>In der internen Darstellung sind Funktionen Namen mit Argumentlisten in Klammern.</p>
    </text>
    <text lang="eng">
      <p>Functions are internally represented by names with bracketed argument lists.</p>
    </text>
  </region>
  <region id="207" left="54" top="2961" width="267" height="68" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">f</e>
        <e type="operand">x</e>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="function" preserve="true" args="4">int</e>
        <e type="function" preserve="true" args="1">num2str</e>
      </input>
      <result action="numeric">
        <e type="operand" style="string">int(f,x,a,b)</e>
      </result>
    </math>
  </region>
  <region id="208" left="351" top="2979" width="218" height="28" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="function" preserve="true" args="1">num2str</e>
      </input>
      <result action="numeric">
        <e type="operand" style="string">sin(x)</e>
      </result>
    </math>
  </region>
  <region id="209" left="54" top="3033" width="250" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="operand">n</e>
        <e type="function" preserve="true" args="2">nthroot</e>
        <e type="function" preserve="true" args="1">num2str</e>
      </input>
      <result action="symbolic">
        <e type="operand" style="string">nthroot(x,n)</e>
      </result>
    </math>
  </region>
  <region id="210" left="36" top="3078" width="693" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Operatoren werden intern durch Symbole dargestellt. Diese stehen zwischen den 
Operanden (binärer Infix-Operator), links vom Operanden (Präfix-Operator) oder 
rechts vom Operanden (Postfix-Operator)</p>
    </text>
    <text lang="eng">
      <p>Operators are internally represented by symbols without brackets. Their arguments
stand between the arguments (binary infix operators, to the left (prefix operators)
or after the argument (postfix operator)</p>
    </text>
  </region>
  <region id="211" left="54" top="3150" width="155" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operator" args="1">!</e>
        <e type="function" preserve="true" args="1">num2str</e>
      </input>
      <result action="numeric">
        <e type="operand" style="string">a!</e>
      </result>
    </math>
  </region>
  <region id="212" left="225" top="3150" width="177" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operand">b</e>
        <e type="operator" args="2">≡</e>
        <e type="function" preserve="true" args="1">num2str</e>
      </input>
      <result action="numeric">
        <e type="operand" style="string">a≡b</e>
      </result>
    </math>
  </region>
  <region id="213" left="441" top="3150" width="157" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="operator" args="1">-</e>
        <e type="function" preserve="true" args="1">num2str</e>
      </input>
      <result action="numeric">
        <e type="operand" style="string">-2</e>
      </result>
    </math>
  </region>
  <region id="214" left="18" top="3195" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p underline="true">xml-Datei</p>
    </text>
    <text lang="eng">
      <p underline="true">xml-file</p>
    </text>
  </region>
  <region id="215" left="18" top="3231" width="730" height="104" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Die tatsächliche Struktur eines Ausdrucks findet man in der xml-Datei (.sm). Darin 
bestehen Ausdrücke aus Operatoren, Funktionen und Operanden, analog zur internen
Texdarstellung. Die Ausdrücke werden in umgekehrter polnischer Notation geschrieben.
Das ist die einzige eindeutige Ebene, hier macht es auch keinen Unterschied, ob eine 
Operation durch einen Operator oder eine Funktion dargestellt wird. Beide werden
identisch behandelt.</p>
    </text>
    <text lang="eng">
      <p>The internal structure of expressions is found in the SMath xml files (.sm). Here, 
expressions consist of operators, functions  and operands, corresponding to the internal
text representation. The expressions are written in reverse polish notation. This
is the only unique representation and here it does not matter if an operation is 
represented by a function or an operator. They have different names but are handled
identically.</p>
    </text>
  </region>
  <region id="216" left="18" top="3339" width="286" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Hier die xml-Darstellung von </p>
    </text>
    <text lang="eng">
      <p>This is the xml representation of </p>
    </text>
  </region>
  <region id="217" left="297" top="3339" width="78" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operator" args="2">+</e>
      </input>
    </math>
  </region>
  <region id="218" left="27" top="3366" width="437" height="82" color="#000000" bgColor="#ffffff">
    <picture>
      <raw format="png" encoding="base64"> </raw>
    </picture>
  </region>
  <region id="219" left="18" top="3465" width="103" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Mathematik.sm">Mathematik</p>
    </text>
    <text lang="eng">
      <p href="Mathematik.sm">Mathematics</p>
    </text>
  </region>
  <region id="220" left="18" top="3483" 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="221" left="18" top="3528" width="450" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p italic="true">$Author: mkraska $
$Date: 2013-12-01 23:13:16 +0100 (So, 01. Dez 2013) $ </p>
    </text>
  </region>
</regions>