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Add inverseWeierstrassP function page
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| <!DOCTYPE html> | ||
| <html> | ||
| <head> | ||
| <title>inverseWeierstrassP — Math</title> | ||
| <link rel="stylesheet" type="text/css" href="../style.css"> | ||
| </head> | ||
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| <body> | ||
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| <script src="../../build/math.js"></script> | ||
| <script src="../../../mathcell/build/mathcell.js"></script> | ||
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| <script src="https://cdn.jsdelivr.net/gh/mathjax/[email protected]/MathJax.js?config=TeX-AMS_HTML"></script> | ||
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| <p class="function"> inverseWeierstrassP( <i>z</i>, <i>g</i><sub>2</sub>, <i>g</i><sub>3</sub> ) </p> | ||
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| <p>The inverse of the Weierstrass elliptic function ℘ of <i>z</i> and invariants <i>g</i><sub>2</sub> and <i>g</i><sub>3</sub> in Math. Defined as the direct integral</p> | ||
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| \[ \wp^{-1}(z) = \int_{ z }^\infty \frac{ dt }{ \sqrt{ 4t^3 - g_2 t - g_3 } } \] | ||
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| <p>Real part on the real axis:</p> | ||
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| <div class="mathcell" style="height: 5in"> | ||
| <script> | ||
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| var parent = document.currentScript.parentNode; | ||
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| var id = generateId(); | ||
| parent.id = id; | ||
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| MathCell( id, [ { type: 'slider', min: -10, max: 10, default: 0, | ||
| name: 'g2', label: '<i>g</i><sub>2</sub>' }, | ||
| { type: 'slider', min: -10, max: 10, default: 0, | ||
| name: 'g3', label: '<i>g</i><sub>3</sub>' } ] ); | ||
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| parent.update = function( id ) { | ||
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| var g2 = getVariable( id, 'g2' ); | ||
| var g3 = getVariable( id, 'g3' ); | ||
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| var p1 = plot( x => inverseWeierstrassP( complex(x), g2, g3 ).re, [-5,-.01] ); | ||
| var p2 = plot( x => inverseWeierstrassP( complex(x), g2, g3 ).re, [.01,5] ); | ||
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| var config = { type: 'svg', includeOrigin: true }; | ||
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| evaluate( id, [ p1, p2 ], config ); | ||
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| } | ||
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| parent.update( id ); | ||
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| </script> | ||
| </div> | ||
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| <p>Imaginary part on the real axis:</p> | ||
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| <div class="mathcell" style="height: 5in"> | ||
| <script> | ||
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| var parent = document.currentScript.parentNode; | ||
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| var id = generateId(); | ||
| parent.id = id; | ||
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| MathCell( id, [ { type: 'slider', min: -10, max: 10, default: 0, | ||
| name: 'g2', label: '<i>g</i><sub>2</sub>' }, | ||
| { type: 'slider', min: -10, max: 10, default: 0, | ||
| name: 'g3', label: '<i>g</i><sub>3</sub>' } ] ); | ||
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| parent.update = function( id ) { | ||
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| var g2 = getVariable( id, 'g2' ); | ||
| var g3 = getVariable( id, 'g3' ); | ||
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| var p1 = plot( x => inverseWeierstrassP( complex(x), g2, g3 ).im, [-5,-.01] ); | ||
| var p2 = plot( x => inverseWeierstrassP( complex(x), g2, g3 ).im, [.01,5] ); | ||
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| var config = { type: 'svg' }; | ||
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| evaluate( id, [ p1, p2 ], config ); | ||
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| } | ||
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| parent.update( id ); | ||
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| </script> | ||
| </div> | ||
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| <p>Real part on the imaginary axis:</p> | ||
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| <div class="mathcell" style="height: 5in"> | ||
| <script> | ||
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| var parent = document.currentScript.parentNode; | ||
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| var id = generateId(); | ||
| parent.id = id; | ||
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| MathCell( id, [ { type: 'slider', min: -10, max: 10, default: 0, | ||
| name: 'g2', label: '<i>g</i><sub>2</sub>' }, | ||
| { type: 'slider', min: -10, max: 10, default: 0, | ||
| name: 'g3', label: '<i>g</i><sub>3</sub>' } ] ); | ||
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| parent.update = function( id ) { | ||
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| var g2 = getVariable( id, 'g2' ); | ||
| var g3 = getVariable( id, 'g3' ); | ||
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| var p = plot( x => inverseWeierstrassP( complex(0,x), g2, g3 ).re, [-5,5] ); | ||
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| var config = { type: 'svg', includeOrigin: true }; | ||
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| evaluate( id, [ p ], config ); | ||
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| } | ||
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| parent.update( id ); | ||
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| </script> | ||
| </div> | ||
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| <p>Imaginary part on the imaginary axis:</p> | ||
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| <div class="mathcell" style="height: 5in"> | ||
| <script> | ||
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| var parent = document.currentScript.parentNode; | ||
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| var id = generateId(); | ||
| parent.id = id; | ||
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| MathCell( id, [ { type: 'slider', min: -10, max: 10, default: 0, | ||
| name: 'g2', label: '<i>g</i><sub>2</sub>' }, | ||
| { type: 'slider', min: -10, max: 10, default: 0, | ||
| name: 'g3', label: '<i>g</i><sub>3</sub>' } ] ); | ||
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| parent.update = function( id ) { | ||
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| var g2 = getVariable( id, 'g2' ); | ||
| var g3 = getVariable( id, 'g3' ); | ||
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| var p1 = plot( x => inverseWeierstrassP( complex(0,x), g2, g3 ).im, [-5,-.01] ); | ||
| var p2 = plot( x => inverseWeierstrassP( complex(0,x), g2, g3 ).im, [.01,5] ); | ||
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| var config = { type: 'svg' }; | ||
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| evaluate( id, [ p1, p2 ], config ); | ||
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| } | ||
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| parent.update( id ); | ||
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| </script> | ||
| </div> | ||
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| <p>Real part on the complex plane:</p> | ||
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| <div class="mathcell" style="width: 6in; height: 6.5in"> | ||
| <script> | ||
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| var parent = document.currentScript.parentNode; | ||
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| var id = generateId(); | ||
| parent.id = id; | ||
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| MathCell( id, [ { type: 'slider', min: -5, max: 5, default: 0, | ||
| name: 'g2', label: '<i>g</i><sub>2</sub>' }, | ||
| { type: 'slider', min: -5, max: 5, default: 0, | ||
| name: 'g3', label: '<i>g</i><sub>3</sub>' } ] ); | ||
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| parent.update = function( id ) { | ||
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| var g2 = getVariable( id, 'g2' ); | ||
| var g3 = getVariable( id, 'g3' ); | ||
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| // pole at origin degraded - to be fixed | ||
| var p = parametric( (x,y) => [ x, y, inverseWeierstrassP( complex(x,y), g2, g3 ) ], | ||
| [-5,5,101], [-5,5,101], | ||
| { complexFunction: 're', colormap: 'complexArgument', maxFaceSlope: 5 } ); | ||
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| var config = { type: 'threejs' }; | ||
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| evaluate( id, [ p ], config ); | ||
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| } | ||
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| parent.update( id ); | ||
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| </script> | ||
| </div> | ||
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| <p>Imaginary part on the complex plane:</p> | ||
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| <div class="mathcell" style="width: 6in; height: 6.5in"> | ||
| <script> | ||
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| var parent = document.currentScript.parentNode; | ||
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| var id = generateId(); | ||
| parent.id = id; | ||
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| MathCell( id, [ { type: 'slider', min: -5, max: 5, default: 0, | ||
| name: 'g2', label: '<i>g</i><sub>2</sub>' }, | ||
| { type: 'slider', min: -5, max: 5, default: 0, | ||
| name: 'g3', label: '<i>g</i><sub>3</sub>' } ] ); | ||
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| parent.update = function( id ) { | ||
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| var g2 = getVariable( id, 'g2' ); | ||
| var g3 = getVariable( id, 'g3' ); | ||
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| // pole at origin degraded - to be fixed | ||
| var p = parametric( (x,y) => [ x, y, inverseWeierstrassP( complex(x,y), g2, g3 ) ], | ||
| [-5,5,101], [-5,5,101], | ||
| { complexFunction: 'im', colormap: 'complexArgument', maxFaceSlope: 5 } ); | ||
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| var config = { type: 'threejs' }; | ||
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| evaluate( id, [ p ], config ); | ||
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| } | ||
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| parent.update( id ); | ||
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| </script> | ||
| </div> | ||
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| <p>Absolute value on the complex plane:</p> | ||
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| <div class="mathcell" style="width: 6in; height: 6.5in"> | ||
| <script> | ||
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| var parent = document.currentScript.parentNode; | ||
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| var id = generateId(); | ||
| parent.id = id; | ||
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| MathCell( id, [ { type: 'slider', min: -5, max: 5, default: 0, | ||
| name: 'g2', label: '<i>g</i><sub>2</sub>' }, | ||
| { type: 'slider', min: -5, max: 5, default: 0, | ||
| name: 'g3', label: '<i>g</i><sub>3</sub>' } ] ); | ||
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| parent.update = function( id ) { | ||
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| var g2 = getVariable( id, 'g2' ); | ||
| var g3 = getVariable( id, 'g3' ); | ||
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| // pole at origin degraded - to be fixed | ||
| var p = parametric( (x,y) => [ x, y, inverseWeierstrassP( complex(x,y), g2, g3 ) ], | ||
| [-5,5,101], [-5,5,101], | ||
| { complexFunction: 'abs', colormap: 'complexArgument', maxFaceSlope: 5 } ); | ||
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| var config = { type: 'threejs' }; | ||
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| evaluate( id, [ p ], config ); | ||
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| } | ||
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| parent.update( id ); | ||
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| </script> | ||
| </div> | ||
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| <p>Related functions: <a href="weierstrassP.html">weierstrassP</a> | ||
| <a href="weierstrassPPrime.html">weierstrassPPrime</a></p> | ||
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| <p>Function category: <a href="../functions.html#elliptic">elliptic functions</a></p> | ||
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| </body> | ||
| </html> |