Add lemniscate function pages

paulmasson · Jan 25, 2025 · 841cf42 · 841cf42
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diff --git a/docs/functions/lemniscateCos.html b/docs/functions/lemniscateCos.html
@@ -0,0 +1,169 @@
+<!DOCTYPE html>
+<html>
+<head>
+<title>lemniscateCos &mdash; Math</title>
+<link rel="stylesheet" type="text/css" href="../style.css">
+</head>
+
+<body>
+
+<script src="../../build/math.js"></script>
+<script src="../../../mathcell/build/mathcell.js"></script>
+
+<script src="https://cdn.jsdelivr.net/gh/mathjax/[email protected]/MathJax.js?config=TeX-AMS_HTML"></script>
+
+<p class="function"> lemniscateCos( <i>z</i> ) </p>
+
+<p>The lemniscate cosine of <i>z</i> in Math. A special case of the Jacobi delta amplitude function:</p>
+
+\[ \operatorname{cl}( z ) = \operatorname{dn}( z | 2 ) \]
+
+<p>Real part on the real axis:</p>
+
+<div class="mathcell" style="height: 4in">
+<script>
+
+var parent = document.currentScript.parentNode;
+
+var id = generateId();
+parent.id = id;
+
+MathCell( id, [] );
+
+parent.update = function( id ) {
+
+  var p = plot( x => lemniscateCos( complex(x) ).re, [-5,5] );
+
+  var config = { type: 'svg' };
+
+  evaluate( id, [ p ], config );
+
+}
+
+parent.update( id );
+
+</script>
+</div>
+
+<p>Imaginary part on the real axis is zero.</p>
+
+<p>Real part on the imaginary axis:</p>
+
+<div class="mathcell" style="height: 4in">
+<script>
+
+var parent = document.currentScript.parentNode;
+
+var id = generateId();
+parent.id = id;
+
+MathCell( id, [] );
+
+parent.update = function( id ) {
+
+  var p = plot( x => lemniscateCos( complex(0,x) ).re, [-5,5] );
+
+  var config = { type: 'svg', yMin: -5, yMax: 5 };
+
+  evaluate( id, [ p ], config );
+
+}
+
+parent.update( id );
+
+</script>
+</div>
+
+<p>Imaginary part on the imaginary axis is zero.</p>
+
+<p>Real part on the complex plane:</p>
+
+<div class="mathcell" style="width: 6in; height: 6in">
+<script>
+
+var parent = document.currentScript.parentNode;
+
+var id = generateId();
+parent.id = id;
+
+MathCell( id, [] );
+
+parent.update = function( id ) {
+
+  var p = parametric( (x,y) => [ x, y, lemniscateCos( complex(x,y) ) ], [-5,5,150], [-5,5,150],
+                      { complexFunction: 're', colormap: 'complexArgument' } );
+
+  var config = { type: 'threejs', zMin: -5, zMax: 5 };
+
+  evaluate( id, [ p ], config );
+
+}
+
+parent.update( id );
+
+</script>
+</div>
+
+<p>Imaginary part on the complex plane:</p>
+
+<div class="mathcell" style="width: 6in; height: 6in">
+<script>
+
+var parent = document.currentScript.parentNode;
+
+var id = generateId();
+parent.id = id;
+
+MathCell( id, [] );
+
+parent.update = function( id ) {
+
+  var p = parametric( (x,y) => [ x, y, lemniscateCos( complex(x,y) ) ], [-5,5,150], [-5,5,150],
+                      { complexFunction: 'im', colormap: 'complexArgument' } );
+
+  var config = { type: 'threejs', zMin: -5, zMax: 5 };
+
+  evaluate( id, [ p ], config );
+
+}
+
+parent.update( id );
+
+</script>
+</div>
+
+<p>Absolute value on the complex plane:</p>
+
+<div class="mathcell" style="width: 6in; height: 6in">
+<script>
+
+var parent = document.currentScript.parentNode;
+
+var id = generateId();
+parent.id = id;
+
+MathCell( id, [] );
+
+parent.update = function( id ) {
+
+  var p = parametric( (x,y) => [ x, y, lemniscateCos( complex(x,y) ) ], [-5,5,150], [-5,5,150],
+                      { complexFunction: 'abs', colormap: 'complexArgument' } );
+
+  var config = { type: 'threejs', zMax: 5 };
+
+  evaluate( id, [ p ], config );
+
+}
+
+parent.update( id );
+
+</script>
+</div>
+
+<p>Related functions: &nbsp; <a href="dn.html">dn</a>
+                      &nbsp; <a href="lemniscateSin.html">lemniscateSin</a></p>
+
+<p>Function category: <a href="../functions.html#elliptic">elliptic functions</a></p>
+
+</body>
+</html>
diff --git a/docs/functions/lemniscateSin.html b/docs/functions/lemniscateSin.html
@@ -0,0 +1,169 @@
+<!DOCTYPE html>
+<html>
+<head>
+<title>lemniscateSin &mdash; Math</title>
+<link rel="stylesheet" type="text/css" href="../style.css">
+</head>
+
+<body>
+
+<script src="../../build/math.js"></script>
+<script src="../../../mathcell/build/mathcell.js"></script>
+
+<script src="https://cdn.jsdelivr.net/gh/mathjax/[email protected]/MathJax.js?config=TeX-AMS_HTML"></script>
+
+<p class="function"> lemniscateSin( <i>z</i> ) </p>
+
+<p>The lemniscate sine of <i>z</i> in Math. A special case of the Jacobi elliptic sine:</p>
+
+\[ \operatorname{sl}( z ) = \operatorname{sn}( z | -1 ) \]
+
+<p>Real part on the real axis:</p>
+
+<div class="mathcell" style="height: 4in">
+<script>
+
+var parent = document.currentScript.parentNode;
+
+var id = generateId();
+parent.id = id;
+
+MathCell( id, [] );
+
+parent.update = function( id ) {
+
+  var p = plot( x => lemniscateSin( complex(x) ).re, [-5,5] );
+
+  var config = { type: 'svg' };
+
+  evaluate( id, [ p ], config );
+
+}
+
+parent.update( id );
+
+</script>
+</div>
+
+<p>Imaginary part on the real axis is zero.</p>
+
+<p>Real part on the imaginary axis is zero.</p>
+
+<p>Imaginary part on the imaginary axis:</p>
+
+<div class="mathcell" style="height: 4in">
+<script>
+
+var parent = document.currentScript.parentNode;
+
+var id = generateId();
+parent.id = id;
+
+MathCell( id, [] );
+
+parent.update = function( id ) {
+
+  var p = plot( x => lemniscateSin( complex(0,x) ).im, [-5,5] );
+
+  var config = { type: 'svg' };
+
+  evaluate( id, [ p ], config );
+
+}
+
+parent.update( id );
+
+</script>
+</div>
+
+<p>Real part on the complex plane:</p>
+
+<div class="mathcell" style="width: 6in; height: 6in">
+<script>
+
+var parent = document.currentScript.parentNode;
+
+var id = generateId();
+parent.id = id;
+
+MathCell( id, [] );
+
+parent.update = function( id ) {
+
+  var p = parametric( (x,y) => [ x, y, lemniscateSin( complex(x,y) ) ], [-5,5,150], [-5,5,150],
+                      { complexFunction: 're', colormap: 'complexArgument' } );
+
+  var config = { type: 'threejs', zMin: -5, zMax: 5 };
+
+  evaluate( id, [ p ], config );
+
+}
+
+parent.update( id );
+
+</script>
+</div>
+
+<p>Imaginary part on the complex plane:</p>
+
+<div class="mathcell" style="width: 6in; height: 6in">
+<script>
+
+var parent = document.currentScript.parentNode;
+
+var id = generateId();
+parent.id = id;
+
+MathCell( id, [] );
+
+parent.update = function( id ) {
+
+  var p = parametric( (x,y) => [ x, y, lemniscateSin( complex(x,y) ) ], [-5,5,150], [-5,5,150],
+                      { complexFunction: 'im', colormap: 'complexArgument' } );
+
+  var config = { type: 'threejs', zMin: -5, zMax: 5 };
+
+  evaluate( id, [ p ], config );
+
+}
+
+parent.update( id );
+
+</script>
+</div>
+
+<p>Absolute value on the complex plane:</p>
+
+<div class="mathcell" style="width: 6in; height: 6in">
+<script>
+
+var parent = document.currentScript.parentNode;
+
+var id = generateId();
+parent.id = id;
+
+MathCell( id, [] );
+
+parent.update = function( id ) {
+
+  var p = parametric( (x,y) => [ x, y, lemniscateSin( complex(x,y) ) ], [-5,5,150], [-5,5,150],
+                      { complexFunction: 'abs', colormap: 'complexArgument' } );
+
+  var config = { type: 'threejs', zMax: 5 };
+
+  evaluate( id, [ p ], config );
+
+}
+
+parent.update( id );
+
+</script>
+</div>
+
+<p>Related functions: &nbsp; <a href="sn.html">sn</a>
+                      &nbsp; <a href="lemniscateCos.html">lemniscateCos</a></p>
+
+<p>Function category: <a href="../functions.html#elliptic">elliptic functions</a></p>
+
+</body>
+</html>