<simulation>
  <header>
    <title lang="french">Polynômes osculateurs</title>
    <title lang="english">Osculating polynomials</title>
    <title lang="spanish">Polinomios osculadores</title>
    <author>Stéphane Mottelet, Guillaume Barbaud</author>
    <keywords lang="french">simulation,scilab,xml</keywords>
    <keywords lang="spanish">Simulación, Scilab, XML</keywords>
  </header>
  <notes>
    <p>Cette appliquette représente les polynômes osculateurs de la fonction sin(x). Un curseur
  permet de faire varier l'abcsisse du point de référence.
  </p>
  </notes>
  <notes lang="english">
    <p>This applet represents the osculating polynomials of the sin(x) function. A slider allows to change
  the abcsissa of the reference point.
  </p>
  </notes>
  <notes lang="spanish">
    <p>Este programita representa los polinomios osculadores de la función sin(x). Un cursor permite hacer variar la abscisa del punto de referencia.</p>
  </notes>
  <parameters><section>
      <title lang="french">Paramètres</title>
      <title lang="english">Parameters</title>
      <title lang="spanish">Parámetros</title>
      <scalar increment="0.01" label="a" max="6.28" min="0" period="10"><name lang="french">Abscisse du point</name><name lang="english">Abscissa of the point</name><name lang="spanish">Abscisa del punto</name><value>1</value></scalar>
    </section></parameters>
  <compute>
    <defdomain1d label="x">
      <name lang="french">Intervalle de représentation</name>
      <name lang="english">Representation interval</name>
      <name lang="spanish">Intervalo de representación</name>
      <interval steps="100">
        <initialvalue>0</initialvalue>
        <finalvalue>2*%pi</finalvalue>
      </interval>
    </defdomain1d>
    <defdomain1d label="xx">
      <name lang="french">Intervalle de représentation</name>
      <name lang="english">Representation interval</name>
      <name lang="spanish">Intervalo de representación</name>
      <interval steps="100">
        <initialvalue>0</initialvalue>
        <finalvalue>2*%pi</finalvalue>
      </interval>
    </defdomain1d>
  </compute>
  <graphs>
    <nonparametriccurve2d label="f">
      <name lang="french">Fonction sin(x)</name>
      <name lang="english">The sine function</name>
      <name lang="spanish">Función sin(x)</name>
      <refdomain1d ref="x" />
      <x2 label="y">
        <name lang="french">Ordonnée</name>
        <name lang="english">y</name>
        <name lang="spanish">Ordenada (y)</name>
        <value>sin(x)</value>
      </x2>
    </nonparametriccurve2d>
    <nonparametriccurve2d label="fprime">
      <name lang="french">Tangente de sin(x) en x=a</name>
      <name lang="english">Tangent of y=sin(x) at x=a</name>
      <name lang="spanish">Tangente de sin(x) en x=a</name>
      <refdomain1d ref="xx" />
      <x2 label="y1">
        <value>sin(a)+cos(a)*(xx-a)</value>
      </x2>
    </nonparametriccurve2d>
    <nonparametriccurve2d label="f2">
      <name lang="french">Approximation ordre 2</name>
      <name lang="english">2nd order approximation</name>
      <name lang="spanish">Aproximación orden 2</name>
      <refdomain1d ref="xx" />
      <x2 label="y2">
        <value>y1-sin(a)/2*(xx-a).^2</value>
      </x2>
    </nonparametriccurve2d>
    <nonparametriccurve2d label="f3">
      <name lang="french">Approximation ordre 3</name>
      <name lang="english">3rd order approximation</name>
      <name lang="spanish">Apromixación orden 3</name>
      <refdomain1d ref="xx" />
      <x2 label="y3">
        <value>y2-cos(a)/6*(xx-a).^3</value>
      </x2>
    </nonparametriccurve2d>
    <nonparametriccurve2d label="f4">
      <name lang="french">Approximation ordre 4</name>
      <name lang="english">4th order approximation</name>
      <name lang="spanish">Aproximación orden 4</name>
      <refdomain1d ref="xx" />
      <x2 label="y4">
        <value>y3+sin(a)/24*(xx-a).^4</value>
      </x2>
    </nonparametriccurve2d>
<nonparametriccurve2d label="f5">
      <name lang="french">degré 5</name>
      <name lang="english">degree 5</name>
      <name lang="spanish">Aproximación orden 5</name>
      <refdomain1d ref="xx" />
      <x2>
        <value>y4+cos(a)/120*(xx-a).^5</value>
      </x2>
    </nonparametriccurve2d>    
    <polyline label="barre">
      <vertex x1="a" x2="-1000" />
      <vertex x1="a" x2="sin(a)" />
    </polyline>
  </graphs>
  <display>
    <window editable="yes">
      <axis2d xmin="0" xmax="7" ymin="-1.5" ymax="1.5">
        <drawcurve2d ref="f" />
        <drawcurve2d ref="fprime" />
        <drawcurve2d ref="f2" />
        <drawcurve2d ref="f3" />
        <drawcurve2d ref="f4" />
        <drawcurve2d ref="f5" />
        <drawcurve2d ref="barre" />
      </axis2d>
    </window>
  </display>
</simulation>