Difference between revisions of "Elliptic curves"

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Any elliptic curve can be written as a plane algebraic curve defined by an equation of the form
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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>
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<html>
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<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
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<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
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<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
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<div id="jxgbox" class="jxgbox" style="width:600px; height:400px;"></div>
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<script language="JavaScript">
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brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 300, originY: 200, unitX: 20, unitY: 20});
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brd.suspendUpdate();
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brd.createElement('axis', [[0,0], [1,0]], {});
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brd.createElement('axis', [[0,0], [0,1]], {});
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//
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var b = brd.createElement('slider',[[-5,-2],[5,-2],[-5,1,5]],{name:'a'});
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var a = brd.createElement('slider',[[1,-4],[10,-4],[1,1,10]],{name:'b'});
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brd.createElement('curve', [function(x){ return x; }, function(x){ return Math.sqrt(x*x*x+a.Value()*x+b.Value(); }, 'x']);
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b.unsuspendUpdate();
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</script>
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</html>
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<source lang="html4strict">
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<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
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<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
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<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
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<div id="jxgbox" class="jxgbox" style="width:600px; height:400px;"></div>
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</source>
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<source lang="javascript">
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</source>
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[[Category:Examples]]

Revision as of 20:07, 30 January 2009

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]

<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>