<?xml version="1.0" encoding="utf-8" standalone="yes"?>
<?application progid="SMath Studio Desktop" version="0.96.4909.6802"?>
<regions>
  <settings>
    <identity>
      <id>be8ed228-7b9f-4d88-9521-f6039e697cd5</id>
      <revision>89</revision>
    </identity>
    <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="Nonlinear Solvers" version="1.0.9999.5" guid="618b7e96-330a-406a-b055-9e577672f0b8" />
      <assembly name="Math Region" version="0.96.4909.6802" guid="02f1ab51-215b-466e-a74d-5d8b1cf85e8d" />
      <assembly name="MaximaPlugin" version="1.0.5085.16396" guid="44011c1e-5d0d-4533-8e68-e32b5badce41" />
      <assembly name="Special Functions" version="1.10.4909.6779" guid="2814e667-4e12-48b1-8d51-194e480eabc5" />
    </dependences>
  </settings>
  <region id="0" left="18" top="18" width="209" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Plugin Nonlinear Solvers</p>
    </text>
    <text lang="eng">
      <p bold="true">Plugin Nonlinear Solvers</p>
    </text>
  </region>
  <region id="1" left="279" top="18" width="176" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Autor: Davide Carpi</p>
    </text>
    <text lang="eng">
      <p>Author: Davide Carpi</p>
    </text>
  </region>
  <region id="2" left="459" top="18" width="70" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin index.sm">Anwendungserweiterungen (Plugins)</p>
    </text>
    <text lang="eng">
      <p href="Plugin index.sm">Plugins</p>
    </text>
  </region>
  <region id="3" left="459" top="36" 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="72" width="635" height="88" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Leistungsfähige Funktionen zur Lösung nichtlinearer Gleichungssysteme. Besondere 
Merkmale sind:
- Die Gleichungen und unbekannten Variablen können dimensionsbehaftet (mit 
    Maßeinheiten) sein.
- Die Gleichungen können als Ausdrücke (deren Nullstellen bestimmt werden) oder als 
    boolsche Gleichungen angegeben werden.
- Die Lösung wird den unbekannten Variablen direkt zugewiesen.</p>
    </text>
    <text lang="eng">
      <p>Collection of powerful functions for solving nonlinear systems of equations.
Remarkable features are
- functions can handle units
- systems of equations can be given as expressions or as boolean equations
- embedded assignment of solution to unknown variables</p>
    </text>
  </region>
  <region id="5" left="18" top="198" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="findroot.sm">FindRoot()</p>
    </text>
  </region>
  <region id="6" left="243" top="198" width="218" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Standardlöser, benutzt intern verschiedene andere Funktionen</p>
    </text>
    <text lang="eng">
      <p>standard solving function</p>
    </text>
  </region>
  <region id="7" left="18" top="216" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Gradient.sm">Gradient()</p>
    </text>
  </region>
  <region id="8" left="243" top="216" width="78" 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="9" left="18" top="234" width="119" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Gradient.CD.sm">Gradient.CD()</p>
    </text>
  </region>
  <region id="10" left="243" top="234" width="296" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Gradient mit zentralem Differenzenquotienten</p>
    </text>
    <text lang="eng">
      <p>gradient using central differences </p>
    </text>
  </region>
  <region id="11" left="18" top="252" width="94" height="24" color="#c0c0c0" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Maximize.sm">Maximize()</p>
    </text>
  </region>
  <region id="12" left="243" top="252" width="217" height="24" color="#c0c0c0" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Maximum-Suche</p>
    </text>
    <text lang="eng">
      <p>Searches for local maxima</p>
    </text>
  </region>
  <region id="13" left="18" top="270" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Taylor.sm">Taylor()</p>
    </text>
  </region>
  <region id="14" left="243" top="270" width="200" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Taylor-Reihenentwicklung</p>
    </text>
    <text lang="eng">
      <p>Taylor series expansion</p>
    </text>
  </region>
  <region id="15" left="18" top="288" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Unknowns.sm">Unknowns()</p>
    </text>
  </region>
  <region id="16" left="243" top="288" width="445" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Unbekannte in einem Gleichungssystem identifizieren</p>
    </text>
    <text lang="eng">
      <p>identifies unknown variables in a system of equations</p>
    </text>
  </region>
  <region id="17" left="18" top="306" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Jacobian.sm">Jacobian()</p>
    </text>
  </region>
  <region id="18" left="243" top="306" width="118" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Jacobimatrix</p>
    </text>
    <text lang="eng">
      <p>Jacobi matrix</p>
    </text>
  </region>
  <region id="19" left="18" top="351" width="192" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Löser mit Intervallteilung</p>
    </text>
    <text lang="eng">
      <p bold="true">Bisection based solver</p>
    </text>
  </region>
  <region id="20" left="18" top="378" width="70" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="BDQRF.sm">BDQRF()</p>
    </text>
  </region>
  <region id="21" left="243" top="378" width="323" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Intervallteilung mit direkter quadratischer Interpolation</p>
    </text>
    <text lang="eng">
      <p>bisected direct quadratic regula falsi</p>
    </text>
  </region>
  <region id="22" left="18" top="396" width="103" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Bisection.sm">Bisection()</p>
    </text>
  </region>
  <region id="23" left="243" top="396" width="147" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Halbteilungsverfahren</p>
    </text>
    <text lang="eng">
      <p>bisection method </p>
    </text>
  </region>
  <region id="24" left="18" top="414" width="70" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Brent.sm">Brent()</p>
    </text>
  </region>
  <region id="25" left="243" top="414" width="332" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Intervallteilung mit inverser quadratischer Interpolation</p>
    </text>
    <text lang="eng">
      <p>bisected inverse quadratic regula falsi</p>
    </text>
  </region>
  <region id="26" left="18" top="432" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Ridder.sm">Ridder()</p>
    </text>
  </region>
  <region id="27" left="243" top="432" width="283" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Intervallteilung mit exponentieller Interpolation</p>
    </text>
    <text lang="eng">
      <p>bisected exponential regula falsi</p>
    </text>
  </region>
  <region id="28" left="18" top="468" width="193" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Gradientenbasierte Löser</p>
    </text>
    <text lang="eng">
      <p bold="true">Gradient based solvers</p>
    </text>
  </region>
  <region id="29" left="18" top="495" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Broyden.sm">Broyden()</p>
    </text>
  </region>
  <region id="30" left="243" top="495" width="249" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Quasi-Newtonverfahren nach Broyden</p>
    </text>
    <text lang="eng">
      <p>Broyden's quasi Newton method</p>
    </text>
  </region>
  <region id="31" left="18" top="513" width="136" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="NewtonRaphson.sm">NewtonRaphson()</p>
    </text>
  </region>
  <region id="32" left="243" top="513" width="184" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Newton-Raphson-Verfahren</p>
    </text>
    <text lang="eng">
      <p>Newton-Raphson method</p>
    </text>
  </region>
  <region id="33" left="18" top="531" width="160" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="NewtonRaphson.CD.sm">NewtonRaphson.CD()</p>
    </text>
  </region>
  <region id="34" left="270" top="531" width="210" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>mit zentralem Differenzenquotient</p>
    </text>
    <text lang="eng">
      <p>with central differences</p>
    </text>
  </region>
  <region id="35" left="18" top="549" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Secant.sm">Secant()</p>
    </text>
  </region>
  <region id="36" left="243" top="549" width="118" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Sekantenverfahren</p>
    </text>
    <text lang="eng">
      <p>Secant method</p>
    </text>
  </region>
  <region id="37" left="18" top="585" width="193" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Optimierer ohne Gradient</p>
    </text>
    <text lang="eng">
      <p bold="true">Non-Gradient Optimizer</p>
    </text>
  </region>
  <region id="38" left="18" top="612" width="218" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="GoldenSectionSearch.max.sm">GoldenSectionSearch.max()</p>
    </text>
  </region>
  <region id="39" left="243" top="612" width="283" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Goldener-Schnitt-Suchverfahren</p>
    </text>
    <text lang="eng">
      <p>golden section search for maximum</p>
    </text>
  </region>
  <region id="40" left="18" top="630" width="218" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="GoldenSectionSearch.min.sm">GoldenSectionSearch.min()</p>
    </text>
  </region>
  <region id="41" left="243" top="630" width="283" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Goldener-Schnitt-Suchverfahren</p>
    </text>
    <text lang="eng">
      <p>golden section search for minimum</p>
    </text>
  </region>
  <region id="42" left="18" top="648" width="111" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="NelderMead.sm">NelderMead()</p>
    </text>
  </region>
  <region id="43" left="243" top="648" width="144" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Simplexverfahren </p>
    </text>
    <text lang="eng">
      <p>Downhill Simplex</p>
    </text>
  </region>
  <region id="44" left="18" top="684" width="217" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Gradientbasierte Optimierer</p>
    </text>
    <text lang="eng">
      <p bold="true">Gradient based optimizers</p>
    </text>
  </region>
  <region id="45" left="18" top="711" width="119" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="GaussNewton.sm">GaussNewton()</p>
    </text>
  </region>
  <region id="46" left="243" top="711" width="167" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="GaussNewton Reference.sm">Gauss-Newton-Verfahren</p>
    </text>
    <text lang="eng">
      <p href="GaussNewton Reference.sm">Gauss Newton method</p>
    </text>
  </region>
  <region id="47" left="18" top="729" width="144" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="GaussNewton.CD.sm">GaussNewton.CD()</p>
    </text>
  </region>
  <region id="48" left="270" top="729" width="210" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>mit zentralem Differenzenquotient</p>
    </text>
    <text lang="eng">
      <p>with central differences</p>
    </text>
  </region>
  <region id="49" left="18" top="747" width="152" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="GaussNewton.GSS.sm">GaussNewton.GSS()</p>
    </text>
  </region>
  <region id="50" left="270" top="747" width="225" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>mit Goldener-Schnitt-Suche</p>
    </text>
    <text lang="eng">
      <p>with golden section search</p>
    </text>
  </region>
  <region id="51" left="18" top="765" width="177" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="GaussNewton.GSS;CD.sm">GaussNewton.GSS;CD()</p>
    </text>
  </region>
  <region id="52" left="270" top="765" width="423" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>mit Goldener-Schnitt-Suche und zentralem DQ</p>
    </text>
    <text lang="eng">
      <p>with golden section search and central differences</p>
    </text>
  </region>
  <region id="53" left="18" top="783" width="144" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="GradientAscent.sm">GradientAscent()</p>
    </text>
  </region>
  <region id="54" left="243" top="783" width="139" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Verfahren des Steilsten Anstiegs</p>
    </text>
    <text lang="eng">
      <p>Steepest ascent </p>
    </text>
  </region>
  <region id="55" left="18" top="801" width="177" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="GradientAscent.GSS.sm">GradientAscent.GSS()</p>
    </text>
  </region>
  <region id="56" left="270" top="801" width="234" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>mit Goldener-Schnitt-Suche</p>
    </text>
    <text lang="eng">
      <p>with golden section search)</p>
    </text>
  </region>
  <region id="57" left="18" top="819" width="152" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="GradientDescent.sm">GradientDescent()</p>
    </text>
  </region>
  <region id="58" left="243" top="819" width="144" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Verfahren des steilsten Abstiegs</p>
    </text>
    <text lang="eng">
      <p>Steepest descent</p>
    </text>
  </region>
  <region id="59" left="18" top="837" width="185" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="GradientDescent.GSS.sm">GradientDescent.GSS()</p>
    </text>
  </region>
  <region id="60" left="270" top="837" width="238" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>mit Goldener-Schnitt-Suche</p>
    </text>
    <text lang="eng">
      <p>with golden section search) </p>
    </text>
  </region>
  <region id="61" left="18" top="855" width="177" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="LevenbergMarquardt.sm">LevenbergMarquardt()</p>
    </text>
  </region>
  <region id="62" left="243" top="855" width="251" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Levenberg-Marquardt-Verfahren</p>
    </text>
  </region>
  <region id="63" left="18" top="873" width="202" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="LevenbergMarquardt.CD.sm">LevenbergMarquardt.CD()</p>
    </text>
  </region>
  <region id="64" left="270" top="873" width="210" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>mit zentralem Differenzenqotienten</p>
    </text>
    <text lang="eng">
      <p>with central differences</p>
    </text>
  </region>
  <region id="65" left="18" top="891" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="NCGM.sm">NCGM()</p>
    </text>
  </region>
  <region id="66" left="243" top="891" width="316" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Verfahren mit konjugierten Gradienten</p>
    </text>
  </region>
  <region id="67" left="18" top="909" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="NCGM.CD.sm">NCGM.CD()</p>
    </text>
  </region>
  <region id="68" left="270" top="909" width="210" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>mit zentralem Differenzenquotienten</p>
    </text>
    <text lang="eng">
      <p>with central differences</p>
    </text>
  </region>
  <region id="69" left="18" top="927" width="127" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="NewtonMethod.sm">NewtonMethod()</p>
    </text>
  </region>
  <region id="70" left="243" top="927" width="135" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Newton-Verfahren</p>
    </text>
    <text lang="eng">
      <p>Newton's method</p>
    </text>
  </region>
  <region id="71" left="18" top="945" width="152" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="NewtonMethod.CD.sm">NewtonMethod.CD()</p>
    </text>
  </region>
  <region id="72" left="270" top="945" width="218" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>mit zentralem Differenzenquotient</p>
    </text>
    <text lang="eng">
      <p>with central differences)</p>
    </text>
  </region>
  <region id="73" left="18" top="963" width="160" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="NewtonMethod.GSS.sm">NewtonMethod.GSS()</p>
    </text>
  </region>
  <region id="74" left="270" top="963" width="234" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>mit Goldener-Schnitt-Suche</p>
    </text>
    <text lang="eng">
      <p>with golden section search)</p>
    </text>
  </region>
  <region id="75" left="18" top="981" width="185" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="NewtonMethod.GSS;CD.sm">NewtonMethod.GSS;CD()</p>
    </text>
  </region>
  <region id="76" left="270" top="981" width="423" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>mit Goldener-Schnitt-Suche und zentralem DQ</p>
    </text>
    <text lang="eng">
      <p>with golden section search and central differences</p>
    </text>
  </region>
  <region id="77" left="18" top="1017" width="397" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>The golden section is a self similar bisection:</p>
    </text>
  </region>
  <region id="78" left="18" top="1044" width="255" height="43" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="operand">a</e>
        <e type="operator" args="2">+</e>
        <e type="operand">1</e>
        <e type="operand">a</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">a</e>
        <e type="operand">1</e>
        <e type="operator" args="2">≡</e>
        <e type="function" preserve="true" args="2">FindRoot</e>
      </input>
      <result action="numeric">
        <e type="operand">0.618</e>
      </result>
    </math>
  </region>
  <region id="79" left="279" top="1044" width="111" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">a</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
      </input>
      <result action="numeric">
        <e type="operand">0.618</e>
      </result>
    </math>
  </region>
  <region id="80" left="387" top="1044" width="90" height="41" 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>
      <result action="numeric">
        <e type="operand">0.618</e>
      </result>
    </math>
  </region>
  <region id="81" left="18" top="1089" width="414" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Das Beispiel zeigt die Anwendung der anderen Löser auf diese Gleichung.</p>
    </text>
    <text lang="eng">
      <p>See application of other solvers to this equation</p>
    </text>
  </region>
  <region id="82" left="621" top="1089" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin Nonlinear Solvers Example1.sm">Beispiel 1</p>
    </text>
    <text lang="eng">
      <p href="Plugin Nonlinear Solvers Example1.sm">Example 1</p>
    </text>
  </region>
  <region id="83" left="18" top="1125" width="447" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Beispiel 2: Scheitelpunkt einer quadratischen Parabel</p>
    </text>
  </region>
  <region id="84" left="621" top="1125" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin Nonlinear Solvers Example2.sm">Beispiel 2</p>
    </text>
    <text lang="eng">
      <p href="Plugin Nonlinear Solvers Example2.sm">Example 2</p>
    </text>
  </region>
  <region id="85" left="18" top="1179" width="380" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Zu optimierende oder lösende Ausdrücke (Funktionen)</p>
    </text>
    <text lang="eng">
      <p bold="true">Expressions or functions to solve or optimize</p>
    </text>
  </region>
  <region id="86" left="18" top="1215" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">f</e>
      </input>
    </math>
  </region>
  <region id="87" left="90" top="1215" width="535" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Ausdrücke die gelöst (Nullstellensuche) oder optimiert werden sollen. Die
darin enthaltenen Unbekannten werden mit Unknowns() ermittelt.</p>
    </text>
    <text lang="eng">
      <p>Expressions to solve (find roots) or to optimize. The  variables 
are determined using the function Unknown().</p>
    </text>
  </region>
  <region id="88" left="90" top="1260" width="481" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Die Ausdrücke und darin enthaltene Variablen können vektoriell sein</p>
    </text>
    <text lang="eng">
      <p>The expressions and the variables therein may be vectors.</p>
    </text>
  </region>
  <region id="89" left="90" top="1278" width="481" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Die Ausdrücke und darin enthaltene Variablen können einheitenbehaftet sein.</p>
    </text>
    <text lang="eng">
      <p>The expressions and the variables therein may have units.</p>
    </text>
  </region>
  <region id="90" left="90" top="1305" width="618" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Funktionen können in Gleichungsform gegeben werden. Diese werden intern in 
die Standardform  LHS-RHS (=0) gebracht. </p>
    </text>
    <text lang="eng">
      <p>Functions can be given as equations, these are transformed internally into
standard form LHS-RHS (=0)</p>
    </text>
  </region>
  <region id="91" left="99" top="1350" width="75" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">LHS</e>
        <e type="operand">RHS</e>
        <e type="operator" args="2">≡</e>
      </input>
    </math>
  </region>
  <region id="92" left="180" top="1350" width="28" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>-&gt;</p>
    </text>
  </region>
  <region id="93" left="225" top="1350" width="75" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">LHS</e>
        <e type="operand">RHS</e>
        <e type="operator" args="2">-</e>
      </input>
    </math>
  </region>
  <region id="94" left="90" top="1377" width="562" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Zielfunktion für mehrdimensionale Funktionen</p>
    </text>
    <text lang="eng">
      <p>Cost function for multidimensional functions (used in optimization)</p>
    </text>
  </region>
  <region id="95" left="90" top="1395" width="172" height="63" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">F</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="bracket">(</e>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">m</e>
        <e type="function" preserve="true" args="4">sum</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="96" left="18" top="1458" width="300" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Startwerte und Intervallgrenzen</p>
    </text>
    <text lang="eng">
      <p bold="true">Initial guesses and interval bounds</p>
    </text>
  </region>
  <region id="97" left="18" top="1485" width="29" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x.0</e>
      </input>
    </math>
  </region>
  <region id="98" left="90" top="1485" width="127" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Startwerte</p>
    </text>
    <text lang="eng">
      <p>Initial values</p>
    </text>
  </region>
  <region id="99" left="18" top="1512" width="29" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x.A</e>
      </input>
    </math>
  </region>
  <region id="100" left="45" top="1512" width="29" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x.B</e>
      </input>
    </math>
  </region>
  <region id="101" left="90" top="1512" width="283" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Intervalgrenzen für die Variablen</p>
    </text>
    <text lang="eng">
      <p>Interval bounds for the variables</p>
    </text>
  </region>
  <region id="102" left="90" top="1539" width="560" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Die Vektordimension und die Maßeinheiten dieser Werte  müssen zu den 
jeweiligen Variablen passen.</p>
    </text>
    <text lang="eng">
      <p>Vector dimension and units of these values must match the unknowns.</p>
    </text>
  </region>
  <region id="103" left="90" top="1566" width="585" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Die Reihenfolge der Variablen entspricht der Ausgabe von
Unknowns(f).</p>
    </text>
    <text lang="eng">
      <p>The sequence of the variables - as determined using Unknowns(f) - must
be observed.</p>
    </text>
  </region>
  <region id="104" left="90" top="1611" width="617" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Werden Startwerte oder Intervallgrenzen als Gleichung
Variablenname = Wert gegeben, so wird das Ergebnis auf diese Variablen 
direkt zugewiesen.</p>
    </text>
    <text lang="eng">
      <p>If these values are given as equations variable_name = value, then results
are mapped individually to the variables. </p>
    </text>
  </region>
  <region id="105" left="18" top="1656" width="98" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Toleranzen </p>
    </text>
  </region>
  <region id="106" left="18" top="1683" width="29" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">ε.f</e>
      </input>
    </math>
  </region>
  <region id="107" left="90" top="1683" width="369" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Toleranz auf den oder die Funktionswerte. </p>
    </text>
    <text lang="eng">
      <p>tolerance for the  expression or function(s)</p>
    </text>
  </region>
  <region id="108" left="18" top="1710" width="37" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">ε.Δx</e>
      </input>
    </math>
  </region>
  <region id="109" left="90" top="1710" width="374" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Toleranz auf die iterative Änderung der Variablenwerte.</p>
    </text>
    <text lang="eng">
      <p>tolerance for the unknowns iterative change.</p>
    </text>
  </region>
  <region id="110" left="90" top="1737" width="617" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Toleranzen können für jede Funktion (Ausdruck) und Variable separat
angegeben werden (als Vektor). Dann müssen sie einheitenäßig passen.</p>
    </text>
    <text lang="eng">
      <p>Tolerances may be specified for each function and variable separately (by
giving a vector). In this case the unit of a tolerance must match the unit
of the function or variable.</p>
    </text>
  </region>
  <region id="111" left="90" top="1791" width="581" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Bei Toleranzen können unabhängig von Einheit und Vektordimension auch 
Skalare verwendet werden. Diese werden auf die Euklidische Norm der 
einheitenfrei gemachten Werte angewendet.</p>
    </text>
    <text lang="eng">
      <p>Even in multi-function or multivariate problems the tolerances can be 
given as scalars. Then they are compared to f or x in base units.</p>
    </text>
  </region>
  <region id="112" left="18" top="1836" width="241" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Zahl der Iterationen</p>
    </text>
    <text lang="eng">
      <p bold="true">Maximum number of iterations</p>
    </text>
  </region>
  <region id="113" left="18" top="1863" width="45" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">n.max</e>
      </input>
    </math>
  </region>
  <region id="114" left="90" top="1863" width="649" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Nichtlineare Löser oder Optimierer sind iterative Verfahren, die unter
Umständen sehr viele Schleifendurchläufe benötigen oder die Abbruchtoleranzen
garnicht erreichen. Daher kann eine maximale Zahl der der Iterationen
vorgegeben werden.</p>
    </text>
    <text lang="eng">
      <p>Non-linear solver are iterative procedures, which may need high numbers of 
cycles or do not reach the stop tolerances at all. Therefore, a maximum number
of iterations can be specified.</p>
    </text>
  </region>
  <region id="115" left="18" top="1926" width="127" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Ausgabesteuerung </p>
    </text>
    <text lang="eng">
      <p bold="true">Output control</p>
    </text>
  </region>
  <region id="116" left="18" top="1953" width="569" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Jeder Löser oder Optimierer kennt drei optionale Schalter für die Ausgabesteuerung</p>
    </text>
    <text lang="eng">
      <p>Every solver or optimizer has tree optional flags for output control</p>
    </text>
  </region>
  <region id="117" left="18" top="1989" width="86" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">show.iters</e>
      </input>
    </math>
  </region>
  <region id="118" left="144" top="1989" width="347" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>benötigte Zahl der Iterationen ausgeben </p>
    </text>
    <text lang="eng">
      <p>show actually needed number of iterations</p>
    </text>
  </region>
  <region id="119" left="18" top="2016" width="103" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">show.summary</e>
      </input>
    </math>
  </region>
  <region id="120" left="144" top="2016" width="111" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Zusammenfassung ausgeben</p>
    </text>
    <text lang="eng">
      <p>show summary</p>
    </text>
  </region>
  <region id="121" left="18" top="2043" width="103" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">save.summary</e>
      </input>
    </math>
  </region>
  <region id="122" left="144" top="2043" width="561" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Zusammenfassung in eine Datei schreiben. Die Datei wird im aktuellen
Verzeichnis angelegt und hat einen Namen auf Basis des Zeitstempels.</p>
    </text>
    <text lang="eng">
      <p>write summary to file. The file is created in the current directory
and uniquely named using the time stamp. </p>
    </text>
  </region>
  <region id="123" left="18" top="2097" width="70" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin index.sm">Anwendungserweiterungen (Plugins)</p>
    </text>
    <text lang="eng">
      <p href="Plugin index.sm">Plugins</p>
    </text>
  </region>
  <region id="124" left="18" top="2115" 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="125" left="18" top="2151" width="450" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p italic="true">$Author: mkraska $
$Date: 2013-12-15 01:35:16 +0100 (So, 15. Dez 2013) $ </p>
    </text>
  </region>
</regions>