Make elliptic_j function symbolic

[sagetrac-davidamadore]

Sage's elliptic_j function does not behave similarly to the other standard or special functions: it tries to numerically evaluate instead of building a symbolic expression:

sage: elliptic_j(I)
1728.00000000000
sage: elliptic_j(x)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
...
TypeError: Cannot evaluate symbolic expression to a numeric value.

This is very weird: it means, for example, that plot(real(elliptic_j(x+I)), (x,0,1)) will fail (instead, one must use plot(lambda t: real(elliptic_j(t+I)), (0,1)))

• http://mpmath.googlecode.com/svn/tags/0.15/doc/build/functions/elliptic.html#kleinj
• https://en.wikipedia.org/wiki/J-invariant

Component: symbolics

Keywords: special function, elliptic

Issue created by migration from https://trac.sagemath.org/ticket/15354

[rwst]

Changed keywords from special function to special function, elliptic

[rwst]

Description changed:

--- 
+++ 
@@ -6,41 +6,11 @@
 sage: elliptic_j(x)
 ---------------------------------------------------------------------------
 TypeError                                 Traceback (most recent call last)
-<ipython-input-5-b3ba173d2e63> in <module>()
-----> 1 elliptic_j(x)
-
-/usr/src/local/sage-5.12/local/lib/python2.7/site-packages/sage/functions/special.pyc in elliptic_j(z)
-    803       CC = ComplexField()
-    804       try:
---> 805          z = CC(z)
-    806       except ValueError:
-    807          raise ValueError, "elliptic_j only defined for complex arguments."
-
-/usr/src/local/sage-5.12/local/lib/python2.7/site-packages/sage/rings/complex_field.pyc in __call__(self, x, im)
-    345         if im is not None:
-    346             x = x, im
---> 347         return Parent.__call__(self, x)
-    348 
-    349     def _element_constructor_(self, x):
-
-/usr/src/local/sage-5.12/local/lib/python2.7/site-packages/sage/structure/parent.so in sage.structure.parent.Parent.__call__ (sage/structure/parent.c:8372)()
-
-/usr/src/local/sage-5.12/local/lib/python2.7/site-packages/sage/structure/coerce_maps.so in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (sage/structure/coerce_maps.c:3856)()
-
-/usr/src/local/sage-5.12/local/lib/python2.7/site-packages/sage/structure/coerce_maps.so in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (sage/structure/coerce_maps.c:3757)()
-
-/usr/src/local/sage-5.12/local/lib/python2.7/site-packages/sage/rings/complex_field.pyc in _element_constructor_(self, x)
-    375                 pass
-    376             try:
---> 377                 return x._complex_mpfr_field_( self )
-    378             except AttributeError:
-    379                 pass
-
-/usr/src/local/sage-5.12/local/lib/python2.7/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression._complex_mpfr_field_ (sage/symbolic/expression.cpp:7534)()
-
-/usr/src/local/sage-5.12/local/lib/python2.7/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression._eval_self (sage/symbolic/expression.cpp:6913)()
-
+...
 TypeError: Cannot evaluate symbolic expression to a numeric value.
 ```
 
 This is very weird: it means, for example, that plot(real(elliptic_j(x+I)), (x,0,1)) will fail (instead, one must use plot(lambda t: real(elliptic_j(t+I)), (0,1)))
+
+* http://mpmath.googlecode.com/svn/tags/0.15/doc/build/functions/elliptic.html#kleinj
+* https://en.wikipedia.org/wiki/J-invariant