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>
<jsxgraph width="600" height="400" box="box0">
<jsxgraph width="600" height="400" box="jxgbox">
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', {boundingbox: [-15, 10, 15, -10], axis:true});
brd.suspendUpdate();
brd.suspendUpdate();
var b = brd.create('slider',[[1,-3],[10,-3],[-10,0,10]],{name:'a'});
var b = brd.create('slider',[[1,-3],[10,-3],[-10,2.10,10]],{name:'a'});
var a = brd.create('slider',[[1,-4],[10,-4],[-10,0,10]],{name:'b'});
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()); }],
var c1 = brd.create('functiongraph', [function(x){ return Math.sqrt(x*x*x+a.Value()*x+b.Value()); }],
Line 17: Line 17:
<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', {boundingbox: [-15, 10, 15, -10], axis:true});
brd = JXG.JSXGraph.initBoard('jxgbox', {originX: 300, originY: 200, unitX: 20, unitY: 20, axis:true});
brd.suspendUpdate();
brd.suspendUpdate();
var b = brd.create('slider',[[1,-3],[10,-3],[-10,0,10]],{name:'a'});
var b = brd.create('slider',[[1,-3],[10,-3],[-10,0,10]],{name:'a'});

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