Difference between revisions of "Elliptic curves"

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</source>
 
</source>
 
<source lang="javascript">
 
<source lang="javascript">
 +
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',[[1,-3],[10,-3],[-10,1,10]],{name:'a'});
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brd.createElement('text',[12,-3,'(a)']);
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var a = brd.createElement('slider',[[1,-4],[10,-4],[-10,-8,10]],{name:'b'});
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brd.createElement('text',[12,-4,'(b)']);
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var c1 = brd.createElement('curve', ['x', function(x){ return Math.sqrt(x*x*x+a.Value()*x+b.Value()); }, 'x'], {strokeWidth:3,strokeColor:'black'});
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var c2 = brd.createElement('curve', ['x', function(x){ return -Math.sqrt(x*x*x+a.Value()*x+b.Value()); }, 'x'], {strokeWidth:3,strokeColor:'black'});
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brd.unsuspendUpdate();
 
</source>
 
</source>
  
 
[[Category:Examples]]
 
[[Category:Examples]]

Revision as of 19:23, 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>
brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 300, originY: 200, unitX: 20, unitY: 20});
brd.suspendUpdate();
brd.createElement('axis', [[0,0], [1,0]], {});
brd.createElement('axis', [[0,0], [0,1]], {});
//
var b = brd.createElement('slider',[[1,-3],[10,-3],[-10,1,10]],{name:'a'});
brd.createElement('text',[12,-3,'(a)']);
var a = brd.createElement('slider',[[1,-4],[10,-4],[-10,-8,10]],{name:'b'});
brd.createElement('text',[12,-4,'(b)']);

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

brd.unsuspendUpdate();