<simulation>
  <header>
    <title lang="french">Interpolation de Lagrange</title>
    <title lang="english">Lagrange Interpolation</title>
    <title lang="spanish">Interpolación de Lagrange</title>
    <author>Stéphane Mottelet, Guillaume Barbaud</author>
    <keywords lang="french">simulation,scilab,xml</keywords>
    <keywords lang="spanish">Simulación, Scilab, XML</keywords>
  </header>
  <notes lang="french">
    <p>Cet appliquette représente le polynome de Lagrange passant par trois points distincts (c'est une parabole). Déplacez les points avec la souris.</p>
  </notes>
  <notes lang="english">
    <p>This applet represents the Lagrange Polynomial passing through 3 distinct points (this is a parabola). Move the points with the mouse.</p>
  </notes>
  <notes lang="spanish">
    <p>Este programita representa un polinomio de Lagrange que pasa por tres puntos distintos (Es una parábola). Desplace los puntos con el ratón..</p>
  </notes>
  <parameters><section>
      <title lang="french">Points à interpoler</title>
      <title lang="english">Points to interpolate</title>
      <title lang="spanish">Puntos a interpolar</title>
      <point label="p1" state="disabled"><name lang="french">Point numéro 1</name><name lang="english">Point number 1</name><name lang="spanish">Punto número 1</name><x1 label="x1">
          <value>1</value>
        </x1><x2 label="y1">
          <value>2</value>
        </x2><constraints label="constr">
          <inequality>-x1</inequality>
          <inequality>x1-x2</inequality>
          <inequality>x2-x3</inequality>
          <inequality>x3-5</inequality>
          <inequality>y1*(y1-4)</inequality>
          <inequality>y2*(y2-4)</inequality>
          <inequality>y3*(y3-4)</inequality>
        </constraints></point>
      <point label="p2" state="disabled"><name lang="french">Point numéro 2</name><name lang="english">Point number 2</name><name lang="spanish">Punto número 2</name><x1 label="x2">
          <value>2</value>
        </x1><x2 label="y2">
          <value>3</value>
        </x2><refconstraints ref="constr" /></point>
      <point label="p3" state="disabled"><name lang="english">Point number 3</name><name lang="french">Point numéro 3</name><name lang="spanish">Punto número 3</name><x1 label="x3">
          <value>3</value>
        </x1><x2 label="y3">
          <value>3</value>
        </x2><refconstraints ref="constr" /></point>
    </section></parameters>
  <compute />
  <graphs>
    <nonparametriccurve2d label="parabole">
      <name lang="french">Polynome d''interpolation</name>
      <name lang="english">Interpolating Polynomial</name>
      <name lang="spanish">Polinomio de interpolación</name>
      <defdomain1d label="x">
        <name lang="french">Abscisse</name>
        <name lang="english">Abscissa</name>
        <name lang="spanish">Abscisa</name>
        <interval steps="500">
          <initialvalue>-5</initialvalue>
          <finalvalue>10</finalvalue>
        </interval>
      </defdomain1d>
      <x2>
        <name lang="french">ordonnee</name>
        <name lang="english">ordinate</name>
        <name lang="spanish">Ordenada</name>
        <value>y1*(x-x2).*(x-x3)/(x1-x2)/(x1-x3)+y2*(x-x1).*(x-x3)/(x2-x1)/(x2-x3)+y3*(x-x2).*(x-x1)/(x3-x2)/(x3-x1)</value>
      </x2>
    </nonparametriccurve2d>
  </graphs>
  <display>
    <window>
      <title lang="french">Polynome d'interpolation</title>
      <title lang="english">Interpolating Polynomial</title>
      <title lang="spanish">Polinomio de interpolación</title>
      <axis2d iso="yes" xmax="5" xmin="0" ymax="4" ymin="0">
        <drawcurve2d ref="parabole" thickness="2" />
        <drawpoints ref="p1 p2 p3" />
      </axis2d>
    </window>
  </display>
</simulation>