Elliptic curves: Difference between revisions

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An elliptic curve can be written as a plane algebraic curve defined by an equation of the form
An elliptic curve can be written as a plane algebraic curve defined by an equation of the form
:<math>    y^2=x^3+ax+b\,. </math>
:<math>    y^2=x^3+ax+b\,. </math>
<html>
<jsxgraph width="600" height="400" box="jxgbox">
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
JXG.Options.axis.strokeColor = '#cccccc';
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-15, 10, 15, -10], axis:true});
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
<div id="jxgbox" class="jxgbox" style="width:600px; height:400px;"></div>
<script language="JavaScript">
brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 300, originY: 200, unitX: 20, unitY: 20});
brd.suspendUpdate();
brd.suspendUpdate();
brd.createElement('axis', [[0,0], [1,0]], {});
var b = brd.create('slider',[[1,-3],[10,-3],[-10,2.10,10]],{name:'a'});
brd.createElement('axis', [[0,0], [0,1]], {});
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brd.createElement('text',[12,-3,'a']);
var a = brd.createElement('slider',[[1,-4],[10,-4],[-10,1,10]],{name:'b'});
brd.createElement('text',[12,-4,'b']);


var c1 = brd.createElement('curve', [function(x){ return x; }, function(x){ return Math.sqrt(x*x*x+a.Value()*x+b.Value()); }, 'x'], {strokeWidth:3,strokeColor:'black'});
var c1 = brd.create('functiongraph', [function(x){ return Math.sqrt(x*x*x+a.Value()*x+b.Value()); }],
var c2 = brd.createElement('curve', [function(x){ return x; }, function(x){ return -Math.sqrt(x*x*x+a.Value()*x+b.Value()); }, 'x'], {strokeWidth:3,strokeColor:'black'});
                      {strokeWidth:3,strokeColor:'black'});
var c2 = brd.create('functiongraph', [function(x){ return -Math.sqrt(x*x*x+a.Value()*x+b.Value()); }],  
                      {strokeWidth:3,strokeColor:'black'});
brd.unsuspendUpdate();
</jsxgraph>


<source lang="javascript">
JXG.Options.axis.strokeColor = '#cccccc';
brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-15, 10, 15, -10], axis:true});
brd.suspendUpdate();
var b = brd.create('slider',[[1,-3],[10,-3],[-10,0,10]],{name:'a'});
var a = brd.create('slider',[[1,-4],[10,-4],[-10,0,10]],{name:'b'});


var g1 = brd.createElement('glider',[0,1,c1]);
var c1 = brd.create('functiongraph', [function(x){ return Math.sqrt(x*x*x+a.Value()*x+b.Value()); }],
var g2 = brd.createElement('glider',[0,-1,c2]);
                      {strokeWidth:3,strokeColor:'black'});
var c2 = brd.create('functiongraph', [function(x){ return -Math.sqrt(x*x*x+a.Value()*x+b.Value()); }],  
                      {strokeWidth:3,strokeColor:'black'});
brd.unsuspendUpdate();
</source>


brd.unsuspendUpdate();
===References===
</script>
* [http://en.wikipedia.org/wiki/Elliptic_curves http://en.wikipedia.org/wiki/Elliptic_curves]
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<source lang="html4strict">
<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 id="jxgbox" class="jxgbox" style="width:600px; height:400px;"></div>
</source>
<source lang="javascript">
</source>


[[Category:Examples]]
[[Category:Examples]]
[[Category:Curves]]

Latest revision as of 11:42, 28 February 2014

An elliptic curve can be written as a plane algebraic curve defined by an equation of the form

[math]\displaystyle{ y^2=x^3+ax+b\,. }[/math]

JXG.Options.axis.strokeColor = '#cccccc';
brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-15, 10, 15, -10], axis:true});
brd.suspendUpdate();
var b = brd.create('slider',[[1,-3],[10,-3],[-10,0,10]],{name:'a'});
var a = brd.create('slider',[[1,-4],[10,-4],[-10,0,10]],{name:'b'});

var c1 = brd.create('functiongraph', [function(x){ return Math.sqrt(x*x*x+a.Value()*x+b.Value()); }],
                       {strokeWidth:3,strokeColor:'black'});
var c2 = brd.create('functiongraph', [function(x){ return -Math.sqrt(x*x*x+a.Value()*x+b.Value()); }], 
                       {strokeWidth:3,strokeColor:'black'});
brd.unsuspendUpdate();

References