# %sn

Jacobi's elliptic function

## Calling Sequence

    [y]=%sn(x,m)

## Arguments

x

  a point inside the fundamental rectangle defined by the elliptic integral; `x` is a vector of complex numbers

m

  parameter of the elliptic integral (`0<m<1`)

y

  result

## Description

Jacobi 's sn elliptic function with parameter `m`: the inverse of the elliptic integral for the parameter `m`.

The amplitude am is computed in fortran and the addition formulas for elliptic functions are applied

## Examples

    m=0.36;
    K=%k(m);
    P=4*K; //Real period
    real_val=0:(P/50):P;
    plot(real_val,real(%sn(real_val,m)))

m=0.36; K=%k(m); P=4*K; real_val=0:(P/50):P; plot(real_val,real(%sn(real_val,m)))

    clf();
    m=0.36;
    KK=%k(1-m);
    Ip=2*KK;
    ima_val1=0:(Ip/50):KK-0.001;
    ima_val2=(KK+0.05):(Ip/25):(Ip+KK);
    z1=%sn(%i*ima_val1,m);
    z2=%sn(%i*ima_val2,m);
    plot2d([ima_val1',ima_val2'],[imag(z1)',imag(z2)']);
    xgrid(3)

m=0.36; KK=%k(1-m); Ip=2*KK; ima_val1=0:(Ip/50):KK-0.001; ima_val2=(KK+0.05):(Ip/25):(Ip+KK); z1=%sn(%i*ima_val1,m); z2=%sn(%i*ima_val2,m); plot2d([ima_val1',ima_val2'],[imag(z1)',imag(z2)']); xgrid(3)

## See Also

- delip
- %k