Trac #14996: Improve support for Jacobi elliptic functions

Currently, all evaluation (numeric and symbolic) of the Jacobi elliptic
functions is done through Maxima. No derivatives or arbitrary-precision
numeric evaluation are defined. Worse still, the Maxima numerical
evaluation is wrong for some of the inverse Jacobi functions; see
https://sourceforge.net/p/maxima/bugs/2615/.

URL: http://trac.sagemath.org/14996
Reported by: eviatarbach
Ticket author(s): Eviatar Bach
Reviewer(s): Ralf Stephan, Travis Scrimshaw

src/doc/en/reference/functions/index.rst

@@ -13,6 +13,7 @@ Functions
    sage/functions/orthogonal_polys
    sage/functions/other
    sage/functions/special
+   sage/functions/jacobi
    sage/functions/bessel
    sage/functions/exp_integral
    sage/functions/wigner

src/sage/functions/all.py

@@ -32,13 +32,20 @@
 from special import (hypergeometric_U,
                      spherical_bessel_J, spherical_bessel_Y,
                      spherical_hankel1, spherical_hankel2,
-                     spherical_harmonic, jacobi,
-                     inverse_jacobi,
+                     spherical_harmonic,
                      lngamma, error_fcn, elliptic_e,
                      elliptic_f, elliptic_ec, elliptic_eu,
                      elliptic_kc, elliptic_pi, elliptic_j,
                      airy_ai, airy_bi)
 
+from jacobi import (jacobi, inverse_jacobi, jacobi_nd, jacobi_ns, jacobi_nc,
+                    jacobi_dn, jacobi_ds, jacobi_dc, jacobi_sn, jacobi_sd,
+                    jacobi_sc, jacobi_cn, jacobi_cd, jacobi_cs, jacobi_am,
+                    inverse_jacobi_nd, inverse_jacobi_ns, inverse_jacobi_nc,
+                    inverse_jacobi_dn, inverse_jacobi_ds, inverse_jacobi_dc,
+                    inverse_jacobi_sn, inverse_jacobi_sd, inverse_jacobi_sc,
+                    inverse_jacobi_cn, inverse_jacobi_cd, inverse_jacobi_cs)
+
 from orthogonal_polys import (chebyshev_T,
                               chebyshev_U,
                               gen_laguerre,