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> | ||
== Using `implicitcurve` == | |||
<jsxgraph width="600" height="400" box="jxgbox"> | <jsxgraph width="600" height="400" box="jxgbox"> | ||
JXG.Options.axis.strokeColor = '#cccccc'; | JXG.Options.axis.strokeColor = '#cccccc'; | ||
brd = JXG.JSXGraph.initBoard(' | const board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-15, 10, 15, -10], axis:true}); | ||
var b = board.create('slider',[[1,-3],[10,-3],[-10,2.10,10]],{name:'a'}); | |||
var a = board.create('slider',[[1,-4],[10,-4],[-10,-9.52,10]],{name:'b'}); | |||
var c1 = board.create('implicitcurve', [(x, y) => Math.sqrt(x*x*x+a.Value()*x+b.Value())], | |||
{strokeWidth:3,strokeColor:'black'}); | |||
</jsxgraph> | |||
== Using two function graphs == | |||
Use | |||
:<math> y^2=x^3+ax+b \quad\Longrigrtarrow\quad y=\pm\sqrt{x^3+ax+b} </math> | |||
This approach is somewhat outdated. | |||
<jsxgraph width="600" height="400" box="jxgbox1"> | |||
brd = JXG.JSXGraph.initBoard('jxgbox1', {boundingbox: [-15, 10, 15, -10], axis:true}); | |||
brd.suspendUpdate(); | brd.suspendUpdate(); | ||
var b = brd.create('slider',[[1,-3],[10,-3],[-10,2.10,10]],{name:'a'}); | var b = brd.create('slider',[[1,-3],[10,-3],[-10,2.10,10]],{name:'a'}); | ||
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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', {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'}); | ||
var a = brd.create('slider',[[1,-4],[10,-4],[-10,0,10]],{name:'b'}); | var a = brd.create('slider',[[1,-4],[10,-4],[-10,0,10]],{name:'b'}); | ||
| Line 26: | Line 44: | ||
var c2 = brd.create('functiongraph', [function(x){ return -Math.sqrt(x*x*x+a.Value()*x+b.Value()); }], | var c2 = brd.create('functiongraph', [function(x){ return -Math.sqrt(x*x*x+a.Value()*x+b.Value()); }], | ||
{strokeWidth:3,strokeColor:'black'}); | {strokeWidth:3,strokeColor:'black'}); | ||
</source> | </source> | ||
Revision as of 10:02, 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\Longrigrtarrow\quad y=\pm\sqrt{x^3+ax+b} }[/math]
This approach is somewhat outdated.
JXG.Options.axis.strokeColor = '#cccccc';
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'});
