Rational functions: Difference between revisions

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Polynomial <math>f</math>:
<html><form><input type="button" value="Add point" onClick="addPoint1()"></form>
</html>
<jsxgraph width="600" height="200" box="box1">
var board = JXG.JSXGraph.initBoard('box1', {boundingbox: [-10, 4, 10, -4], axis:true});
var p = [];
var q = [];
p[0] = board.create('point', [-1,2], {size:4});
p[1] = board.create('point', [3,-1], {size:4});
var f = JXG.Math.Numerics.lagrangePolynomial(p);
var graph = board.create('functiongraph', [f,-10, 10]);
function addPoint1() {
  p.push(board.create('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{size:4}));
  board.update();
}
</jsxgraph>
Polynomial <math>g</math>:
<html>
<html>
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
<div style="float:left"><form><input type="button" value="Add point" onClick="addPoint1()"></form>
<div id="box1" class="jxgbox" style="width:300px; height:400px;"></div></div>
<form><input type="button" value="Add point" onClick="addPoint2()"></form>
<form><input type="button" value="Add point" onClick="addPoint2()"></form>
<div><div id="box2" class="jxgbox" style="width:300px; height:400px;"></div></div>
</html>
<script language="JavaScript">
<jsxgraph width="600" height="200" box="box2">
        board = JXG.JSXGraph.initBoard('box1', {originX: 150, originY: 200, unitX: 30, unitY: 25});
var board2 = JXG.JSXGraph.initBoard('box2', {boundingbox: [-10, 4, 10, -4], axis:true});
        // Axes
q[0] = board2.create('point', [-1,2], {size:4});
        b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
q[1] = board2.create('point', [3,-1], {size:4});
        b1axisy = board.createElement('axis', [[0,0], [0,1]], {});
var f2 = JXG.Math.Numerics.lagrangePolynomial(q);
var graph2 = board2.create('functiongraph', [f2, -10, 10]);


        var p = [];
function addPoint2() {
        p[0] = board.createElement('point', [-1,2], {style:6});
  q.push(board2.create('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{size:4}));
        p[1] = board.createElement('point', [3,-1], {style:6});
  board2.update();
        var polynomial = function(x) {
}
                var i;
</jsxgraph>
                var y = 0.0;
Rational function <math>\frac{f}{g}</math>:  
                var xc = [];
                for (i=0;i<p.length;i++) {
                  xc[i] = p[i].X();
                }
                for (i=0;i<p.length;i++) {
                  var t = p[i].Y();
                  for (var k=0;k<p.length;k++) {
                    if (k!=i) {
                      t *= (x-xc[k])/(xc[i]-xc[k]);
                    }
                  }
                  y += t;
                }
                return y;
            };
        graph = board.createElement('curve', ['x', polynomial, 'x', -10, 10], {curveType:'graph'});


        function addPoint1() {
<jsxgraph width="600" height="400" box="box3">
          p.push(board.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
var board3 = JXG.JSXGraph.initBoard('box3', {boundingbox: [-10, 8, 10, -8], axis:true});
          board.update();
var graph3 = board3.create('functiongraph', [function(x){return f(x)/f2(x);}, -10, 10], {strokeColor:'#ff0000'});
        }
board.addChild(board3);
board2.addChild(board3);
</jsxgraph>
         
=== References ===
* [http://en.wikipedia.org/wiki/Rational_function http://en.wikipedia.org/wiki/Rational_function]
 
=== The underlying JavaScript source code ===
 
<source lang="javascript">
var board = JXG.JSXGraph.initBoard('box1', {boundingbox: [-10, 4, 10, -4], axis:true});
var p = [];
var q = [];
p[0] = board.create('point', [-1,2], {size:4});
p[1] = board.create('point', [3,-1], {size:4});
var f = JXG.Math.Numerics.lagrangePolynomial(p);
var graph = board.create('functiongraph', [f,-10, 10]);
 
function addPoint1() {
  p.push(board.create('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{size:4}));
  board.update();
}
 
var board2 = JXG.JSXGraph.initBoard('box2', {boundingbox: [-10, 4, 10, -4], axis:true});
q[0] = board2.create('point', [-1,2], {size:4});
q[1] = board2.create('point', [3,-1], {size:4});
var f2 = JXG.Math.Numerics.lagrangePolynomial(q);
var graph2 = board2.create('functiongraph', [f2, -10, 10]);
 
function addPoint2() {
  q.push(board2.create('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{size:4}));
  board2.update();
}
 
var board3 = JXG.JSXGraph.initBoard('box3', {boundingbox: [-10, 8, 10, -8], axis:true});
var graph3 = board3.create('functiongraph', [function(x){return f(x)/f2(x);}, -10, 10], {strokeColor:'#ff0000'});
 
board.addChild(board3);
board2.addChild(board3);
            
            
</script>
</source>
</html>
 
[[Category:Examples]]
[[Category:Calculus]]

Latest revision as of 15:47, 20 February 2013

Polynomial [math]\displaystyle{ f }[/math]:

Polynomial [math]\displaystyle{ g }[/math]:

Rational function [math]\displaystyle{ \frac{f}{g} }[/math]:

References

The underlying JavaScript source code

var board = JXG.JSXGraph.initBoard('box1', {boundingbox: [-10, 4, 10, -4], axis:true});
var p = [];
var q = [];
p[0] = board.create('point', [-1,2], {size:4});
p[1] = board.create('point', [3,-1], {size:4});
var f = JXG.Math.Numerics.lagrangePolynomial(p);
var graph = board.create('functiongraph', [f,-10, 10]);

function addPoint1() {
   p.push(board.create('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{size:4}));
   board.update();
}

var board2 = JXG.JSXGraph.initBoard('box2', {boundingbox: [-10, 4, 10, -4], axis:true});
q[0] = board2.create('point', [-1,2], {size:4});
q[1] = board2.create('point', [3,-1], {size:4});
var f2 = JXG.Math.Numerics.lagrangePolynomial(q);
var graph2 = board2.create('functiongraph', [f2, -10, 10]);

function addPoint2() {
   q.push(board2.create('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{size:4}));
   board2.update();
}

var board3 = JXG.JSXGraph.initBoard('box3', {boundingbox: [-10, 8, 10, -8], axis:true});
var graph3 = board3.create('functiongraph', [function(x){return f(x)/f2(x);}, -10, 10], {strokeColor:'#ff0000'});

board.addChild(board3);
board2.addChild(board3);
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