Difference between revisions of "Rational functions"

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Line 1: Line 1:
<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/jsxgraphcore.js"></script>
 
</html>
 
 
Polynomial <math>f</math>:  
 
Polynomial <math>f</math>:  
 
<html><form><input type="button" value="Add point" onClick="addPoint1()"></form>
 
<html><form><input type="button" value="Add point" onClick="addPoint1()"></form>
<div id="box1" class="jxgbox" style="width:600px; height:200px;"></div>
 
 
</html>
 
</html>
Polynomial <math>g</math>:
+
<jsxgraph width="600" height="200" box="box1">
<html>
+
var board = JXG.JSXGraph.initBoard('box1', {boundingbox: [-10, 4, 10, -4], axis:true});
<form><input type="button" value="Add point" onClick="addPoint2()"></form>
 
<div id="box2" class="jxgbox" style="width:600px; height:200px;"></div>
 
</html>
 
Rational function <math>\frac{f}{g}</math>:
 
<html>
 
<div id="box3" class="jxgbox" style="width:600px; height:400px;"></div>
 
<script language="JavaScript">
 
board = JXG.JSXGraph.initBoard('box1', {originX: 300, originY: 100, unitX: 30, unitY: 25, axis:true});
 
 
var p = [];
 
var p = [];
 
var q = [];
 
var q = [];
p[0] = board.createElement('point', [-1,2], {style:6});
+
p[0] = board.create('point', [-1,2], {size:4});
p[1] = board.createElement('point', [3,-1], {style:6});
+
p[1] = board.create('point', [3,-1], {size:4});
var f = board.lagrangePolynomial(p);
+
var f = JXG.Math.Numerics.lagrangePolynomial(p);
graph = board.createElement('functiongraph', [f,-10, 10]);
+
var graph = board.create('functiongraph', [f,-10, 10]);
  
 
function addPoint1() {
 
function addPoint1() {
   p.push(board.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
+
   p.push(board.create('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{size:4}));
 
   board.update();
 
   board.update();
 
}
 
}
  
board2 = JXG.JSXGraph.initBoard('box2', {originX: 300, originY: 100, unitX: 30, unitY: 25, axis:true});
+
</jsxgraph>
q[0] = board2.createElement('point', [-1,2], {style:6});
+
Polynomial <math>g</math>:
q[1] = board2.createElement('point', [3,-1], {style:6});
+
<html>
var f2 = board2.lagrangePolynomial(q);
+
<form><input type="button" value="Add point" onClick="addPoint2()"></form>
graph2 = board2.createElement('functiongraph', [f2, -10, 10]);
+
</html>
 +
<jsxgraph width="600" height="200" box="box2">
 +
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() {
 
function addPoint2() {
   q.push(board2.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
+
   q.push(board2.create('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{size:4}));
 
   board2.update();
 
   board2.update();
 
}
 
}
 +
</jsxgraph>
 +
Rational function <math>\frac{f}{g}</math>:
  
board3 = JXG.JSXGraph.initBoard('box3', {originX: 300, originY: 200, unitX: 30, unitY: 25, axis:true});
+
<jsxgraph width="600" height="400" box="box3">
graph3 = board3.createElement('functiongraph', [function(x){return f(x)/f2(x);}, -10, 10], {strokeColor:'#ff0000'});
+
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);
 
board.addChild(board3);
 
board2.addChild(board3);
 
board2.addChild(board3);
         
+
</jsxgraph>
</script>
+
         
</html>
 
 
 
 
=== References ===
 
=== References ===
 
* [http://en.wikipedia.org/wiki/Rational_function http://en.wikipedia.org/wiki/Rational_function]
 
* [http://en.wikipedia.org/wiki/Rational_function http://en.wikipedia.org/wiki/Rational_function]
Line 55: Line 48:
  
 
<source lang="javascript">
 
<source lang="javascript">
board = JXG.JSXGraph.initBoard('box1', {originX: 300, originY: 100, unitX: 30, unitY: 25, axis:true});
+
var board = JXG.JSXGraph.initBoard('box1', {boundingbox: [-10, 4, 10, -4], axis:true});
 
var p = [];
 
var p = [];
 
var q = [];
 
var q = [];
p[0] = board.createElement('point', [-1,2], {style:6});
+
p[0] = board.create('point', [-1,2], {size:4});
p[1] = board.createElement('point', [3,-1], {style:6});
+
p[1] = board.create('point', [3,-1], {size:4});
var f = board.lagrangePolynomial(p);
+
var f = JXG.Math.Numerics.lagrangePolynomial(p);
graph = board.createElement('functiongraph', [f,-10, 10]);
+
var graph = board.create('functiongraph', [f,-10, 10]);
  
 
function addPoint1() {
 
function addPoint1() {
   p.push(board.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
+
   p.push(board.create('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{size:4}));
 
   board.update();
 
   board.update();
 
}
 
}
  
board2 = JXG.JSXGraph.initBoard('box2', {originX: 300, originY: 100, unitX: 30, unitY: 25, axis:true});
+
var board2 = JXG.JSXGraph.initBoard('box2', {boundingbox: [-10, 4, 10, -4], axis:true});
q[0] = board2.createElement('point', [-1,2], {style:6});
+
q[0] = board2.create('point', [-1,2], {size:4});
q[1] = board2.createElement('point', [3,-1], {style:6});
+
q[1] = board2.create('point', [3,-1], {size:4});
var f2 = board2.lagrangePolynomial(q);
+
var f2 = JXG.Math.Numerics.lagrangePolynomial(q);
graph2 = board2.createElement('functiongraph', [f2, -10, 10]);
+
var graph2 = board2.create('functiongraph', [f2, -10, 10]);
  
 
function addPoint2() {
 
function addPoint2() {
   q.push(board2.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
+
   q.push(board2.create('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{size:4}));
 
   board2.update();
 
   board2.update();
 
}
 
}
  
board3 = JXG.JSXGraph.initBoard('box3', {originX: 300, originY: 200, unitX: 30, unitY: 25, axis:true});
+
var board3 = JXG.JSXGraph.initBoard('box3', {boundingbox: [-10, 8, 10, -8], axis:true});
graph3 = board3.createElement('functiongraph', [function(x){return f(x)/f2(x);}, -10, 10], {strokeColor:'#ff0000'});
+
var graph3 = board3.create('functiongraph', [function(x){return f(x)/f2(x);}, -10, 10], {strokeColor:'#ff0000'});
  
 
board.addChild(board3);
 
board.addChild(board3);
 
board2.addChild(board3);
 
board2.addChild(board3);
 +
         
 
</source>
 
</source>
  
 
[[Category:Examples]]
 
[[Category:Examples]]
 
[[Category:Calculus]]
 
[[Category:Calculus]]

Latest revision as of 17:47, 20 February 2013

Polynomial [math]f[/math]:

Polynomial [math]g[/math]:

Rational function [math]\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);