Difference between revisions of "Elliptic curves"

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:<math>    y^2=x^3+ax+b\,. </math>
 
:<math>    y^2=x^3+ax+b\,. </math>
 
<html>
 
<html>
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
+
<jsxgraph width="600" height="400" box="box0">
<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">
 
 
JXG.Options.axis.strokeColor = '#cccccc';
 
JXG.Options.axis.strokeColor = '#cccccc';
 
brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 300, originY: 200, unitX: 20, unitY: 20, axis:true});
 
brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 300, originY: 200, unitX: 20, unitY: 20, axis:true});
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                       {strokeWidth:3,strokeColor:'black'});
 
                       {strokeWidth:3,strokeColor:'black'});
 
brd.unsuspendUpdate();
 
brd.unsuspendUpdate();
</script>
+
</jsxgraph>  
</html>
 
  
<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/jsxgraphcore.js"></script>
 
<div id="jxgbox" class="jxgbox" style="width:600px; height:400px;"></div>
 
</source>
 
 
<source lang="javascript">
 
<source lang="javascript">
 +
JXG.Options.axis.strokeColor = '#cccccc';
 
JXG.Options.axis.strokeColor = '#cccccc';
 
JXG.Options.axis.strokeColor = '#cccccc';
 
brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 300, originY: 200, unitX: 20, unitY: 20, axis:true});
 
brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 300, originY: 200, unitX: 20, unitY: 20, axis:true});

Revision as of 13:03, 25 March 2011

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]

<html>

JXG.Options.axis.strokeColor = '#cccccc';
JXG.Options.axis.strokeColor = '#cccccc';
brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 300, originY: 200, unitX: 20, unitY: 20, 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