Trac #22802: Symbolic to SymPy convertion for generic function

Implement generic function coversion from Symbolic to SymPy

{{{
sage: a = function('A')(x,y)

sage: type(A)
<class 'sage.symbolic.function_factory.NewSymbolicFunction'>

sage: type(a)
<type 'sage.symbolic.expression.Expression'>

sage: a._sympy_()
------------------------------------------------------------------------
---
NotImplementedError                       Traceback (most recent call
last)
<ipython-input-101-eeb95aeda6e6> in <module>()
----> 1 a._sympy_()

}}}

URL: https://trac.sagemath.org/22802
Reported by: mmancini
Ticket author(s): Marco Mancini
Reviewer(s): Travis Scrimshaw

src/sage/symbolic/expression_conversions.py

@@ -764,10 +764,53 @@ def composition(self, ex, operator):
         if f_sympy:
             return f_sympy(*sympy.sympify(g, evaluate=False))
         else:
-            from sage.symbolic.function_factory import SymbolicFunction
-            if isinstance(ex.operator(), SymbolicFunction):
-                return sympy.Function(str(f))(*g, evaluate=False)
-            raise NotImplementedError("SymPy function '%s' doesn't exist" % f)
+            return sympy.Function(str(f))(*g, evaluate=False)
+
+    def derivative(self, ex, operator):
+        """
+        Convert the derivative of ``self`` in sympy.
+
+        INPUT:
+
+        - ``ex`` -- a symbolic expression
+
+        - ``operator`` -- operator
+
+        TESTS::
+
+            sage: var('x','y')
+            (x, y)
+
+            sage: f_sage = function('f_sage')(x, y)
+            sage: f_sympy = f_sage._sympy_()
+
+            sage: df_sage = f_sage.diff(x, 2, y, 1); df_sage
+            diff(f_sage(x, y), x, x, y)
+            sage: df_sympy = df_sage._sympy_(); df_sympy
+            Derivative(f_sage(x, y), x, x, y)
+            sage: df_sympy == f_sympy.diff(x, 2, y, 1)
+            True
+        """
+        import sympy
+
+        # retrive derivated function
+        f = operator.function()
+        f_sympy = self.composition(ex, f)
+
+        # retrive order
+        order = operator._parameter_set
+        # arguments
+        _args = ex.arguments()
+
+        sympy_arg = []
+        for i, a in enumerate(_args):
+            gg = order.count(i)
+            if gg > 0:
+                sympy_arg.append(a)
+                sympy_arg.append(gg)
+
+        return f_sympy.diff(*sympy_arg)
+
 
 sympy = SympyConverter()