Add derived elliptic functions

paulmasson · Jan 24, 2025 · a92e977 · a92e977
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diff --git a/build/math.js b/build/math.js
@@ -1319,6 +1319,25 @@ function am( x, m ) {
 
 }
 
+function ns( x, m ) { return inv( sn(x,m) ); }
+
+function nc( x, m ) { return inv( cn(x,m) ); }
+
+function nd( x, m ) { return inv( dn(x,m) ); }
+
+function sc( x, m ) { return div( sn(x,m), cn(x,m) ); }
+
+function cs( x, m ) { return div( cn(x,m), sn(x,m) ); }
+
+function sd( x, m ) { return div( sn(x,m), dn(x,m) ); }
+
+function ds( x, m ) { return div( dn(x,m), sn(x,m) ); }
+
+function cd( x, m ) { return div( cn(x,m), dn(x,m) ); }
+
+function dc( x, m ) { return div( dn(x,m), cn(x,m) ); }
+
+
 
 function weierstrassRoots( g2, g3 ) {
 

diff --git a/docs/functions.html b/docs/functions.html
@@ -225,6 +225,24 @@ <h1>Elliptic Functions</h1>
 
 <p><a href="functions/dn.html"><b>dn( <i>x</i>, <i>m</i> )</b></a> &mdash; Jacobi delta amplitude of a real or complex number with real or complex elliptic parameter&nbsp;<i>m</i></p>
 
+<p><b>ns( <i>x</i>, <i>m</i> )</b> &mdash; inverse of Jacobi elliptic sine of a real or complex number with real or complex elliptic parameter <i>m</i></p>
+
+<p><b>nc( <i>x</i>, <i>m</i> )</b> &mdash; inverse of Jacobi elliptic cosine of a real or complex number with real or complex elliptic parameter <i>m</i></p>
+
+<p><b>nd( <i>x</i>, <i>m</i> )</b> &mdash; inverse of Jacobi elliptic delta amplitude of a real or complex number with real or complex elliptic parameter <i>m</i></p>
+
+<p><b>sc( <i>x</i>, <i>m</i> )</b> &mdash; ratio of Jacobi elliptic sine and cosine of a real or complex number with real or complex elliptic parameter <i>m</i></p>
+
+<p><b>cs( <i>x</i>, <i>m</i> )</b> &mdash; ratio of Jacobi elliptic cosine and sine of a real or complex number with real or complex elliptic parameter <i>m</i></p>
+
+<p><b>sd( <i>x</i>, <i>m</i> )</b> &mdash; ratio of Jacobi elliptic sine and delta amplitude of a real or complex number with real or complex elliptic parameter <i>m</i></p>
+
+<p><b>ds( <i>x</i>, <i>m</i> )</b> &mdash; ratio of Jacobi elliptic delta amplitude and sine of a real or complex number with real or complex elliptic parameter <i>m</i></p>
+
+<p><b>cd( <i>x</i>, <i>m</i> )</b> &mdash; ratio of Jacobi elliptic cosine and delta amplitude of a real or complex number with real or complex elliptic parameter <i>m</i></p>
+
+<p><b>dc( <i>x</i>, <i>m</i> )</b> &mdash; ratio of Jacobi elliptic delta amplitude and cosine of a real or complex number with real or complex elliptic parameter <i>m</i></p>
+
 <p><b>weierstrassRoots( <i>g</i><sub>2</sub>, <i>g</i><sub>3</sub> )</b> &mdash; Weierstrass roots <i>e</i><sub>1</sub>, <i>e</i><sub>2</sub> and <i>e</i><sub>3</sub> for real or complex invariants. Returned as an array.</p>
 
 <p><b>weierstrassHalfPeriods( <i>g</i><sub>2</sub>, <i>g</i><sub>3</sub> )</b> &mdash; Weierstrass half periods <i>w</i><sub>1</sub> and <i>w</i><sub>2</sub> for real or complex invariants. Returned as an array. Consistent with evaluation of Weierstrass elliptic function in terms of Jacobi elliptic sine.</p>

diff --git a/src/functions/elliptic-functions.js b/src/functions/elliptic-functions.js
@@ -363,6 +363,25 @@ function am( x, m ) {
 
 }
 
+function ns( x, m ) { return inv( sn(x,m) ); }
+
+function nc( x, m ) { return inv( cn(x,m) ); }
+
+function nd( x, m ) { return inv( dn(x,m) ); }
+
+function sc( x, m ) { return div( sn(x,m), cn(x,m) ); }
+
+function cs( x, m ) { return div( cn(x,m), sn(x,m) ); }
+
+function sd( x, m ) { return div( sn(x,m), dn(x,m) ); }
+
+function ds( x, m ) { return div( dn(x,m), sn(x,m) ); }
+
+function cd( x, m ) { return div( cn(x,m), dn(x,m) ); }
+
+function dc( x, m ) { return div( dn(x,m), cn(x,m) ); }
+
+
 
 function weierstrassRoots( g2, g3 ) {