Elliptic curves: Difference between revisions
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Use | Use | ||
:<math> y^2=x^3+ax+b \quad\ | :<math> y^2=x^3+ax+b \quad\Longrightarrow\quad y=\pm\sqrt{x^3+ax+b} </math> | ||
This approach is somewhat outdated. | This approach is somewhat outdated. | ||
<jsxgraph width="600" height="400" box="jxgbox1"> | <jsxgraph width="600" height="400" box="jxgbox1"> | ||
(function() { | |||
const board = JXG.JSXGraph.initBoard('jxgbox1', {boundingbox: [-15, 10, 15, -10], axis:true}); | |||
var b = | var b = board.create('slider',[[1,-3],[10,-3],[-10,2.10,10]],{name:'a'}); | ||
var a = | var a = board.create('slider',[[1,-4],[10,-4],[-10,-9.52,10]],{name:'b'}); | ||
var c1 = | var c1 = board.create('functiongraph', [function(x){ return Math.sqrt(x*x*x+a.Value()*x+b.Value()); }], | ||
{strokeWidth:3,strokeColor:'black'}); | {strokeWidth:3,strokeColor:'black'}); | ||
var c2 = | var c2 = board.create('functiongraph', [function(x){ return -Math.sqrt(x*x*x+a.Value()*x+b.Value()); }], | ||
{strokeWidth:3,strokeColor:'black'}); | {strokeWidth:3,strokeColor:'black'}); | ||
})(); | |||
</jsxgraph> | </jsxgraph> | ||
<source lang="javascript"> | <source lang="javascript"> | ||
brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-15, 10, 15, -10], axis:true}); | brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-15, 10, 15, -10], axis:true}); | ||
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'}); | ||
Revision as of 10:06, 8 July 2026
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]
Using `implicitcurve`
Using two function graphs
Use
- [math]\displaystyle{ y^2=x^3+ax+b \quad\Longrightarrow\quad y=\pm\sqrt{x^3+ax+b} }[/math]
This approach is somewhat outdated.
brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-15, 10, 15, -10], axis:true});
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'});
