Difference between revisions of "Elliptic curves"

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(New page: Any 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>)
 
 
(39 intermediate revisions by 2 users not shown)
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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>
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:<math>   y^2=x^3+ax+b\,. </math>
    y^2=x^3+ax+b\,
+
<jsxgraph width="600" height="400" box="jxgbox">
</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],[-10,2.10,10]],{name:'a'});
 +
var a = brd.create('slider',[[1,-4],[10,-4],[-10,-9.52,10]],{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();
 +
</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 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();
 +
</source>
 +
 
 +
===References===
 +
* [http://en.wikipedia.org/wiki/Elliptic_curves http://en.wikipedia.org/wiki/Elliptic_curves]
 +
 
 +
 
 +
[[Category:Examples]]
 +
[[Category:Curves]]

Latest revision as of 13:42, 28 February 2014

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]

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