Rational functions: Difference between revisions

From JSXGraph Wiki
No edit summary
No edit summary
 
(4 intermediate revisions by 2 users not shown)
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/prototype.js"></script>
<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 56: 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 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);