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<regions>
  <settings>
    <identity>
      <id>be8ed228-7b9f-4d88-9521-f6039e697cd5</id>
      <revision>54</revision>
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    <calculation>
      <precision>4</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <fractions>decimal</fractions>
    </calculation>
    <pageModel active="true" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
      <paper id="9" orientation="Portrait" width="827" height="1169" />
      <margins left="39" right="39" top="39" bottom="39" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
      <backgrounds />
    </pageModel>
    <dependences>
      <assembly name="SMath Studio Desktop" version="0.96.4909.6802" guid="a37cba83-b69c-4c71-9992-55ff666763bd" />
      <assembly name="Text Region" version="1.9.4909.6785" guid="485d28c5-349a-48b6-93be-12a35a1c1e39" />
      <assembly name="Math Region" version="0.96.4909.6802" guid="02f1ab51-215b-466e-a74d-5d8b1cf85e8d" />
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    </dependences>
  </settings>
  <region id="0" left="9" top="18" width="176" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Variablen in SMath Studio</p>
    </text>
    <text lang="eng">
      <p bold="true">Scoping of Variables</p>
    </text>
  </region>
  <region id="1" left="360" top="18" 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="2" left="9" top="54" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p bold="true">Concepts  </p>
    </text>
  </region>
  <region id="3" left="9" top="90" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Assignment</e>
      </input>
    </math>
  </region>
  <region id="4" left="108" top="90" width="586" height="104" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Creation of a reference by name to an expression using the assignment
operator ":=". Assignment can be
- on sheet level(as top level function of a math region)
- inside a function body (in the definition)
- inside a function call (as part of a parameter expression) 
- embedded (on dll-level, see FindRoot() from Nonlinear Solver plugin)</p>
    </text>
  </region>
  <region id="5" left="9" top="198" width="65" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Canvas </p>
    </text>
  </region>
  <region id="6" left="108" top="198" width="479" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>The canvas (or the sheet) is the outermost scoping level  
(top level namespace) in SMath</p>
    </text>
  </region>
  <region id="7" left="9" top="252" width="98" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Expression </p>
    </text>
  </region>
  <region id="8" left="108" top="252" width="626" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>A sequence of symbols which can be evaluated. Expressions are always formed
by functions with certain numbers of arguments.  </p>
    </text>
  </region>
  <region id="9" left="9" top="306" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Function  </p>
    </text>
  </region>
  <region id="10" left="108" top="306" width="622" height="72" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>named reference to an expression with dedicated channels for passing 
references to the expression. A function consists of an name, the argument 
list (set of names) and a body (the expression). The expression normally 
involves the names from the argument list.</p>
    </text>
  </region>
  <region id="11" left="9" top="396" width="78" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Global
variable</p>
    </text>
  </region>
  <region id="12" left="108" top="396" width="282" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>variable, assigned at sheet level</p>
    </text>
  </region>
  <region id="13" left="9" top="450" width="78" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>local 
variable</p>
    </text>
  </region>
  <region id="14" left="108" top="450" width="540" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>variable, assigned inside a function body or a function call and </p>
    </text>
  </region>
  <region id="15" left="9" top="495" width="90" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Procedure </p>
    </text>
  </region>
  <region id="16" left="108" top="495" width="589" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>special function, which can modify the value of passed arguments. This 
requires the top level function of the body to be line().</p>
    </text>
  </region>
  <region id="17" left="9" top="558" width="82" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Variable </p>
    </text>
  </region>
  <region id="18" left="108" top="558" width="601" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>named reference to an expression. The expression is assigned to the name
using the assignment operator := </p>
    </text>
  </region>
  <region id="19" left="9" top="684" width="397" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p bold="true">Factors that affect the behaviour of functions  </p>
    </text>
  </region>
  <region id="20" left="9" top="720" width="685" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Are the dummy argument names  in the function definitions globally defined or not? </p>
    </text>
  </region>
  <region id="21" left="9" top="756" width="554" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Optimization setting of the function definition (numeric/symbolic)</p>
    </text>
  </region>
  <region id="22" left="9" top="792" width="505" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Optimization setting of the function call (numeric/symbolic)</p>
    </text>
  </region>
  <region id="23" left="9" top="828" width="578" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Are any non-argument names in a function definition globally defined?</p>
    </text>
  </region>
  <region id="24" left="9" top="864" width="307" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Is the function body of type line()?</p>
    </text>
  </region>
  <region id="25" left="9" top="963" width="57" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Rules </p>
    </text>
  </region>
  <region id="26" left="9" top="999" width="562" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>All variables defined directly on the canvas, are global variables.</p>
    </text>
  </region>
  <region id="27" left="9" top="1035" width="335" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Global variables can only be changed on </p>
    </text>
  </region>
  <region id="28" left="9" top="1071" width="82" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Examples </p>
    </text>
  </region>
  <region id="29" left="36" top="1107" width="216" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Define a global variable:</p>
    </text>
  </region>
  <region id="30" left="261" top="1107" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operand">3</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="31" left="324" top="1107" width="53" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
      </input>
      <result action="numeric">
        <e type="operand">3</e>
      </result>
    </math>
  </region>
  <region id="32" left="450" top="1134" width="75" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">x</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="33" left="36" top="1143" width="356" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Define a global function with one argument</p>
    </text>
  </region>
  <region id="34" left="36" top="1179" width="365" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Evaluate that function, passing a constant:</p>
    </text>
  </region>
  <region id="35" left="450" top="1179" width="73" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="function" args="1">f</e>
      </input>
      <result action="numeric">
        <e type="operand">4</e>
      </result>
    </math>
  </region>
  <region id="36" left="234" top="1215" width="160" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>passing a variable</p>
    </text>
  </region>
  <region id="37" left="450" top="1215" width="73" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="function" args="1">f</e>
      </input>
      <result action="numeric">
        <e type="operand">9</e>
      </result>
    </math>
  </region>
  <region id="38" left="36" top="1251" width="578" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Function with output argument must be defined using the line operator</p>
    </text>
  </region>
  <region id="39" left="54" top="1278" width="130" height="35" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">g</e>
        <e type="operand">y</e>
        <e type="operand">x</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">:</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="40" left="207" top="1287" width="105" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">3</e>
        <e type="operand">b</e>
        <e type="function" args="2">g</e>
      </input>
      <result action="numeric">
        <e type="operand">27</e>
      </result>
    </math>
  </region>
  <region id="41" left="315" top="1287" width="310" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>b is undefined, output does not work </p>
    </text>
  </region>
  <region id="42" left="54" top="1323" width="131" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">g</e>
        <e type="operand">y</e>
        <e type="operand">x</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">:</e>
        <e type="operand">x</e>
        <e type="operand">4</e>
        <e type="operator" args="2">^</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="43" left="207" top="1323" width="105" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="operand">b</e>
        <e type="function" args="2">g</e>
      </input>
      <result action="numeric">
        <e type="operand">16</e>
      </result>
    </math>
  </region>
  <region id="44" left="315" top="1323" width="53" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">b</e>
      </input>
      <result action="numeric">
        <e type="operand">8</e>
      </result>
    </math>
  </region>
  <region id="45" left="54" top="1395" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="46" left="54" top="1422" width="131" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">g</e>
        <e type="operand">y</e>
        <e type="operand">x</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">:</e>
        <e type="operand">x</e>
        <e type="operand">4</e>
        <e type="operator" args="2">^</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="47" left="207" top="1422" width="105" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="operand">b</e>
        <e type="function" args="2">g</e>
      </input>
      <result action="numeric">
        <e type="operand">16</e>
      </result>
    </math>
  </region>
  <region id="48" left="315" top="1422" width="53" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">b</e>
      </input>
      <result action="numeric">
        <e type="operand">8</e>
      </result>
    </math>
  </region>
  <region id="49" left="54" top="1494" width="108" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="function" args="2">h</e>
        <e type="operand">x</e>
        <e type="operand">y</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="50" left="198" top="1494" width="97" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="operand">3</e>
        <e type="function" args="2">h</e>
      </input>
      <result action="symbolic">
        <e type="operand">6</e>
      </result>
    </math>
  </region>
  <region id="51" left="54" top="1539" width="126" height="32" color="#000000" bgColor="#ffffff" fontSize="10" showInputData="False">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="operand">z</e>
        <e type="function" args="2">h.1</e>
        <e type="operand">x</e>
        <e type="operand">z</e>
        <e type="operator" args="2">+</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="52" left="198" top="1539" width="127" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="operand">3</e>
        <e type="function" args="2">h.1</e>
      </input>
      <result action="symbolic">
        <e type="operand">3</e>
        <e type="operand">y</e>
        <e type="operator" args="2">+</e>
      </result>
    </math>
  </region>
  <region id="53" left="18" top="1584" width="488" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p bold="true">Modifiying arguments inside a function (output parameters)</p>
    </text>
  </region>
  <region id="54" left="18" top="1620" width="646" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>A function can modify passed arguments, if the top level function of the body 
expression is line(), i.e. if the function body is a statement block. </p>
    </text>
  </region>
  <region id="55" left="45" top="1665" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operand">1</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="56" left="45" top="1692" width="147" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">t</e>
        <e type="operand">v</e>
        <e type="function" args="2">fo</e>
        <e type="operand">t</e>
        <e type="operand">v</e>
        <e type="operand">t</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="57" left="243" top="1692" width="105" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operand">4</e>
        <e type="function" args="2">fo</e>
      </input>
      <result action="numeric">
        <e type="operand">5</e>
      </result>
    </math>
  </region>
  <region id="58" left="405" top="1692" width="53" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
      </result>
    </math>
  </region>
  <region id="59" left="45" top="1728" width="164" height="75" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">t</e>
        <e type="operand">v</e>
        <e type="function" args="2">fo</e>
        <e type="operand">1</e>
        <e type="operand">t</e>
        <e type="operand">v</e>
        <e type="operand">t</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">line</e>
        <e type="operand">0</e>
        <e type="function" preserve="true" args="3">if</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="60" left="243" top="1728" width="105" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operand">4</e>
        <e type="function" args="2">fo</e>
      </input>
      <result action="numeric">
        <e type="operand">9</e>
      </result>
    </math>
  </region>
  <region id="61" left="405" top="1728" width="53" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
      </result>
    </math>
  </region>
  <region id="62" left="477" top="1728" width="225" height="72" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>It is not sufficient, that
parameter re-assignment 
occures within a statement
block</p>
    </text>
  </region>
  <region id="63" left="45" top="1809" width="155" height="73" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">t</e>
        <e type="operand">v</e>
        <e type="function" args="2">fo</e>
        <e type="operand">1</e>
        <e type="operand">t</e>
        <e type="operand">v</e>
        <e type="operand">t</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
        <e type="operand">0</e>
        <e type="function" preserve="true" args="3">if</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="64" left="243" top="1809" width="105" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operand">4</e>
        <e type="function" args="2">fo</e>
      </input>
      <result action="numeric">
        <e type="operand">5</e>
      </result>
    </math>
  </region>
  <region id="65" left="405" top="1809" width="53" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
      </result>
    </math>
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    <math>
      <input>
        <e type="operand">t</e>
        <e type="operand">v</e>
        <e type="function" args="2">fo</e>
        <e type="operand">t</e>
        <e type="operand">v</e>
        <e type="operand">t</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="67" left="243" top="1881" width="105" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operand">4</e>
        <e type="function" args="2">fo</e>
      </input>
      <result action="numeric">
        <e type="operand">5</e>
      </result>
    </math>
  </region>
  <region id="68" left="405" top="1881" width="53" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
      </input>
      <result action="numeric">
        <e type="operand">5</e>
      </result>
    </math>
  </region>
  <region id="69" left="18" top="1980" width="340" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Global variables in function definitions</p>
    </text>
  </region>
  <region id="70" left="18" top="2034" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operand">2</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="71" left="81" top="2034" width="93" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">a</e>
        <e type="operand">x</e>
        <e type="operator" args="2">+</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="72" left="234" top="2034" width="73" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="function" args="1">f</e>
      </input>
      <result action="symbolic">
        <e type="operand">3</e>
      </result>
    </math>
  </region>
  <region id="73" left="18" top="2070" width="51" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operand">10</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="74" left="234" top="2070" width="81" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="function" args="1">f</e>
      </input>
      <result action="symbolic">
        <e type="operand">11</e>
      </result>
    </math>
  </region>
  <region id="75" left="18" top="2106" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">2</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="76" left="81" top="2106" width="133" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">out</e>
        <e type="operand">a</e>
        <e type="operand">x</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="77" left="234" top="2106" width="73" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="function" args="1">f</e>
      </input>
      <result action="numeric">
        <e type="operand">3</e>
      </result>
    </math>
  </region>
  <region id="78" left="333" top="2106" width="381" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Global variables in the function body are not
evaluated at definition time, regardless of 
optimization setting</p>
    </text>
  </region>
  <region id="79" left="90" top="2124" width="132" height="34" color="#000000" bgColor="#ffffff">
    <picture>
      <raw format="png" encoding="base64"> </raw>
    </picture>
  </region>
  <region id="80" left="18" top="2142" width="51" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">10</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="81" left="234" top="2142" width="81" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="function" args="1">f</e>
      </input>
      <result action="numeric">
        <e type="operand">11</e>
      </result>
    </math>
  </region>
  <region id="82" left="18" top="2196" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">2</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="83" left="81" top="2196" width="84" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <description active="true" position="Top" lang="ger">
        <p>Numeric optimization</p>
      </description>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">a</e>
        <e type="operand">x</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="84" left="324" top="2196" width="73" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="function" args="1">f</e>
      </input>
      <result action="numeric">
        <e type="operand">3</e>
      </result>
    </math>
  </region>
  <region id="85" left="405" top="2196" width="348" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Global variables in the function body are</p>
    </text>
  </region>
  <region id="86" left="162" top="2223" width="88" height="35" color="#000000" bgColor="#ffffff">
    <picture>
      <raw format="png" encoding="base64"> </raw>
    </picture>
  </region>
  <region id="87" left="18" top="2232" width="51" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">10</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="88" left="324" top="2232" width="81" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="function" args="1">f</e>
      </input>
      <result action="numeric">
        <e type="operand">11</e>
      </result>
    </math>
  </region>
  <region id="89" left="18" top="2277" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">2</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="90" left="81" top="2277" width="84" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <description active="true" position="Top" lang="ger">
        <p>Symbolic optimization</p>
      </description>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">a</e>
        <e type="operand">x</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="91" left="324" top="2277" width="73" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="function" args="1">f</e>
      </input>
      <result action="numeric">
        <e type="operand">3</e>
      </result>
    </math>
  </region>
  <region id="92" left="162" top="2304" width="88" height="34" color="#000000" bgColor="#ffffff">
    <picture>
      <raw format="png" encoding="base64"> </raw>
    </picture>
  </region>
  <region id="93" left="18" top="2313" width="51" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">a</e>
        <e type="operand">10</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="94" left="324" top="2313" width="73" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="function" args="1">f</e>
      </input>
      <result action="numeric">
        <e type="operand">3</e>
      </result>
    </math>
  </region>
  <region id="95" left="9" top="2376" width="267" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Section Math ODE.sm">Gewöhnliche Differenzialgleichungen</p>
    </text>
    <text lang="eng">
      <p href="Section Math ODE.sm">Ordinary Differential Equations</p>
    </text>
  </region>
  <region id="96" left="9" top="2394" 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="97" left="9" top="2412" 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="98" left="9" top="2439" width="188" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p italic="true">M. Kraska, 2013-08-06 </p>
    </text>
  </region>
</regions>