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      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
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  <region id="0" left="18" top="18" width="172" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Eigene Maßeinheiten </p>
    </text>
    <text lang="eng">
      <p bold="true">Custom units</p>
    </text>
  </region>
  <region id="1" left="378" top="18" width="61" 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="378" top="36" width="152" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Programmbedienung.sm">Programmbedienung</p>
    </text>
    <text lang="eng">
      <p href="Programmbedienung.sm">Program Operation</p>
    </text>
  </region>
  <region id="3" left="378" top="54" width="111" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Chapter Units.sm">Maßeinheiten</p>
    </text>
    <text lang="eng">
      <p href="Chapter Units.sm">Units of Measurement</p>
    </text>
  </region>
  <region id="4" left="18" top="90" width="349" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Maßenheiten als Parameter in Berechnungen</p>
    </text>
    <text lang="eng">
      <p bold="true">Units as parameters in numeric calculations</p>
    </text>
  </region>
  <region id="5" left="18" top="126" width="673" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Wenn numerische Verfahren den Umgang mit Maßeinheiten beherrschen, dann kann man 
numerische Berechnungen mit Maßeinheiten parametrieren.</p>
    </text>
    <text lang="eng">
      <p>If a numeric procedure can handle units, then you can parametrize such calculations
using units.</p>
    </text>
  </region>
  <region id="6" left="18" top="180" width="685" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Im gegebenen Beispiel soll die Auflagerkraft bei A als Funktion der Parameter
l und q0 gegeben. Dafür ist normalerweise ein symbolischer Löser erforderlich, wie
ihn z.B. Maple oder Maxima  bieten.</p>
    </text>
    <text lang="eng">
      <p>In the given example the support reaction at A has to be expressed in terms of the
parameters l and q0. This normally is done using symbolic solvers, as they are
available in Maple and Maxima.</p>
    </text>
  </region>
  <region id="7" left="450" top="234" width="286" height="144" color="#000000" bgColor="#ffffff">
    <picture>
      <raw format="png" encoding="base64"> </raw>
    </picture>
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  <region id="8" left="18" top="243" width="465" height="46" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">F.B</e>
        <e type="operand">l</e>
        <e type="operator" args="2">*</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operand">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand">l</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">F.B</e>
        <e type="function" preserve="true" args="2">solve</e>
        <e type="function" preserve="true" args="1">maple</e>
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      <result action="symbolic">
        <e type="operand" style="string">Der Stapel ist leer.</e>
      </result>
    </math>
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  <region id="9" left="18" top="306" width="297" height="50" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">F.B</e>
        <e type="operand">l</e>
        <e type="operator" args="2">*</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operand">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand">l</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">F.B</e>
        <e type="function" preserve="true" args="2">Solve</e>
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        <e type="operand">F.B</e>
        <e type="operand">l</e>
        <e type="operand">q.0</e>
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        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">≡</e>
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    </math>
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  <region id="10" left="18" top="360" width="115" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">F.B</e>
        <e type="function" preserve="true" args="1">Clear</e>
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      <result action="numeric">
        <e type="operand">1</e>
      </result>
    </math>
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  <region id="11" left="18" top="396" width="365" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Kennzeichnet man die Parameter als 
Maßeinheiten, dann kann auch der 
numerische Löser FindRoot() benutzt werden.</p>
    </text>
    <text lang="eng">
      <p>If you mark the parameters as units,
then you can use the numeric solver
FindRoot()</p>
    </text>
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  <region id="12" left="27" top="459" width="174" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">eq</e>
        <e type="operand">F.B</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
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        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operand" preserve="false" style="unit">q.0</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
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  <region id="13" left="216" top="459" width="42" height="35" color="#000000" bgColor="#ffffff">
    <picture>
      <raw format="png" encoding="base64"> </raw>
    </picture>
  </region>
  <region id="14" left="270" top="468" width="111" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>eq:(F.B*'l.0</p>
    </text>
  </region>
  <region id="15" left="378" top="468" width="61" height="24" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Strg++</p>
    </text>
    <text lang="eng">
      <p>Ctrl+=</p>
    </text>
  </region>
  <region id="16" left="441" top="468" width="37" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>1/2</p>
    </text>
  </region>
  <region id="17" left="477" top="468" width="53" height="24" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p> Leer </p>
    </text>
    <text lang="eng">
      <p>Space</p>
    </text>
  </region>
  <region id="18" left="531" top="468" width="103" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>'q.0*'l.0^2</p>
    </text>
  </region>
  <region id="19" left="27" top="504" width="290" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">eq</e>
        <e type="operand">F.B</e>
        <e type="operand" preserve="false" style="unit">q.o</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">≡</e>
        <e type="function" preserve="true" args="2">FindRoot</e>
      </input>
      <result action="numeric">
        <e type="operand">0.5</e>
        <e type="operand" preserve="false" style="unit">q.o</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">l.0</e>
        <e type="operator" args="2">*</e>
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    </math>
  </region>
  <region id="20" left="18" top="540" width="381" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Eigene Maßeinheiten im Rechenblatt definieren</p>
    </text>
    <text lang="eng">
      <p bold="true">Defining custom units within the SMath sheet</p>
    </text>
  </region>
  <region id="21" left="18" top="576" width="439" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Man kann im Rechenblatt eigene Einheiten definieren:</p>
    </text>
    <text lang="eng">
      <p>You can define own units in the sheet:</p>
    </text>
  </region>
  <region id="22" left="18" top="612" width="70" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand" preserve="false" style="unit">Bier</e>
        <e type="operand">1</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="23" left="108" top="612" width="134" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand" preserve="false" style="unit">Sixpack</e>
        <e type="operand">6</e>
        <e type="operand" preserve="false" style="unit">Bier</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="24" left="261" top="612" width="133" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand" preserve="false" style="unit">Kasten</e>
        <e type="operand">20</e>
        <e type="operand" preserve="false" style="unit">Bier</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="25" left="18" top="648" width="627" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Diese können in mathematischen Ausdrücken vorkommen und als Ergebniseinheit
verwendet werden.</p>
    </text>
    <text lang="eng">
      <p>These can be used in mathematical expressions and as result units.</p>
    </text>
  </region>
  <region id="26" left="27" top="684" width="201" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="operand" preserve="false" style="unit">Kasten</e>
        <e type="operator" args="2">*</e>
        <e type="operand">3</e>
        <e type="operand" preserve="false" style="unit">Sixpack</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
      </input>
      <result action="numeric">
        <e type="operand">58</e>
      </result>
    </math>
  </region>
  <region id="27" left="333" top="684" width="291" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>&lt;- Ergebniseinheit nicht angegeben</p>
    </text>
    <text lang="eng">
      <p>&lt;- result unit not specified</p>
    </text>
  </region>
  <region id="28" left="27" top="711" width="228" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="operand" preserve="false" style="unit">Kasten</e>
        <e type="operator" args="2">*</e>
        <e type="operand">3</e>
        <e type="operand" preserve="false" style="unit">Sixpack</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
      </input>
      <contract>
        <e type="operand" preserve="false" style="unit">Bier</e>
      </contract>
      <result action="numeric">
        <e type="operand">58</e>
      </result>
    </math>
  </region>
  <region id="29" left="27" top="738" width="286" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="operand" preserve="false" style="unit">Kasten</e>
        <e type="operator" args="2">*</e>
        <e type="operand">3</e>
        <e type="operand" preserve="false" style="unit">Sixpack</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
      </input>
      <contract>
        <e type="operand" preserve="false" style="unit">Sixpack</e>
      </contract>
      <result action="numeric">
        <e type="operand">9.6667</e>
      </result>
    </math>
  </region>
  <region id="30" left="27" top="765" width="253" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">2</e>
        <e type="operand" preserve="false" style="unit">Kasten</e>
        <e type="operator" args="2">*</e>
        <e type="operand">3</e>
        <e type="operand" preserve="false" style="unit">Sixpack</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
      </input>
      <contract>
        <e type="operand" preserve="false" style="unit">Kasten</e>
      </contract>
      <result action="numeric">
        <e type="operand">2.9</e>
      </result>
    </math>
  </region>
  <region id="31" left="18" top="810" width="61" 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="32" left="18" top="828" width="152" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Programmbedienung.sm">Programmbedienung</p>
    </text>
    <text lang="eng">
      <p href="Programmbedienung.sm">Program Operation</p>
    </text>
  </region>
  <region id="33" left="18" top="846" width="111" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Chapter Units.sm">Maßeinheiten</p>
    </text>
    <text lang="eng">
      <p href="Chapter Units.sm">Units of Measurement</p>
    </text>
  </region>
  <region id="34" left="18" top="882" width="450" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p italic="true">$Author: mkraska $
$Date: 2014-01-03 00:31:00 +0100 (Fr, 03. Jan 2014) $ </p>
    </text>
  </region>
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