1 <?xml version="1.0" encoding="UTF-8"?>
3     <refnamediv>
4         <refname>%sn</refname>
5         <refpurpose>Jacobi's elliptic function <emphasis role="bold">(obsolete)</emphasis></refpurpose>
6     </refnamediv>
7     <refsynopsisdiv>
8         <title>Syntax</title>
9         <synopsis>y = %sn(x, m)</synopsis>
10     </refsynopsisdiv>
11     <refsection>
12         <title>Arguments</title>
13         <variablelist>
14             <varlistentry>
15                 <term>x</term>
16                 <listitem>
17                     <para>
18                         a point inside the fundamental rectangle  defined by the elliptic integral; <literal>x</literal> is a vector of complex numbers
19                     </para>
20                 </listitem>
21             </varlistentry>
22             <varlistentry>
23                 <term>m</term>
24                 <listitem>
25                     <para>
26                         parameter of the elliptic integral (<literal>0&lt;m&lt;1</literal>)
27                     </para>
28                 </listitem>
29             </varlistentry>
30             <varlistentry>
31                 <term>y</term>
32                 <listitem>
33                     <para>result</para>
34                 </listitem>
35             </varlistentry>
36         </variablelist>
37     </refsection>
38     <refsection>
39         <title>Description</title>
40         <warning>
41             <para>
42                 %sn() is obsolete and will be removed from Scilab 6.1.x. Please use ellipj() instead.
43             </para>
44         </warning>
45         <para>
46             Jacobi 's sn elliptic function with parameter <literal>m</literal>: the inverse
47             of the elliptic integral for the parameter <literal>m</literal>.
48         </para>
49         <para>
50             The amplitude am is computed in fortran and
51             the addition formulas for elliptic functions are applied
52         </para>
53     </refsection>
54     <refsection>
55         <title>Examples</title>
56         <programlisting role="example"><![CDATA[
57 m=0.36;
58 K=%k(m);
59 P=4*K; //Real period
60 real_val=0:(P/50):P;
61 plot(real_val,real(%sn(real_val,m)))
62  ]]></programlisting>
63         <scilab:image>
64             m=0.36;
65             K=%k(m);
66             P=4*K;
67             real_val=0:(P/50):P;
68             plot(real_val,real(%sn(real_val,m)))
69         </scilab:image>
70         <programlisting role="example"><![CDATA[
71 clf();
72 m=0.36;
73 KK=%k(1-m);
74 Ip=2*KK;
75 ima_val1=0:(Ip/50):KK-0.001;
76 ima_val2=(KK+0.05):(Ip/25):(Ip+KK);
77 z1=%sn(%i*ima_val1,m);
78 z2=%sn(%i*ima_val2,m);
79 plot2d([ima_val1',ima_val2'],[imag(z1)',imag(z2)']);
80 xgrid(3)
81  ]]></programlisting>
82         <scilab:image>
83             m=0.36;
84             KK=%k(1-m);
85             Ip=2*KK;
86             ima_val1=0:(Ip/50):KK-0.001;
87             ima_val2=(KK+0.05):(Ip/25):(Ip+KK);
88             z1=%sn(%i*ima_val1,m);
89             z2=%sn(%i*ima_val2,m);
90             plot2d([ima_val1',ima_val2'],[imag(z1)',imag(z2)']);
91             xgrid(3)
92         </scilab:image>
93     </refsection>
94     <refsection role="see also">
95         <title>See also</title>
96         <simplelist type="inline">
97             <member>
99             </member>
100             <member>
102             </member>
103             <member>
105             </member>
106         </simplelist>
107     </refsection>
108     <refsection role="history">
109         <title>History</title>
110         <revhistory>
111             <revision>
112                 <revnumber>6.1.0</revnumber>
113                 <revdescription>
114                     %sn() is declared obsolete. ellipj() must be used instead.
115                 </revdescription>
116             </revision>
117         </revhistory>
118     </refsection>
119 </refentry>