Ticket #8568: trac_8568-diff-conv-and-erf-deriv.patch

sage/functions/other.py

@@ -79 +79 @@
             raise NotImplementedError, "erf not implemented for precision higher than 53"
         return parent(1 - pari(float(x)).erfc())
         
+    def _derivative_(self, x, diff_param=None):
+        """
+        Derivative of erf function
+
+        EXAMPLES::
+
+            sage: erf(x).diff(x)
+            2*e^(-x^2)/sqrt(pi)
+
+        TESTS::
+
+        Check if #8568 is fixed::
+
+            sage: var('c,x')
+            (c, x)
+            sage: derivative(erf(c*x),x)
+            2*c*e^(-c^2*x^2)/sqrt(pi)
+            sage: erf(c*x).diff(x)._maxima_init_()
+            '((%pi)^(-1/2))*(c)*(exp(((c)^(2))*((x)^(2))*(-1)))*(2)'
+        """
+        return 2*exp(-x**2)/sqrt(pi)
+
+
 erf = Function_erf()
 
 class Function_abs(GinacFunction):

sage/symbolic/expression_conversions.py

@@ -463 +463 @@
         """
         EXAMPLES::
 
-            sage: import operator
             sage: from sage.symbolic.expression_conversions import InterfaceInit
             sage: m = InterfaceInit(maxima)
-            sage: a = function('f', x).diff(x); a
+            sage: f = function('f')
+            sage: a = f(x).diff(x); a
             D[0](f)(x)
             sage: print m.derivative(a, a.operator())
             diff('f(x), x, 1)
-            sage: b = function('f', x).diff(x).diff(x)
+            sage: b = f(x).diff(x, x)
             sage: print m.derivative(b, b.operator())
             diff('f(x), x, 2)
+
+        We can only convert to Maxima derivatives if the corresponding operand
+        of the function is a variable::
+
+            sage: y = var('y')
+            sage: t = f(x*y).diff(x)
+            sage: m.derivative(t, t.operator())
+            Traceback (most recent call last):
+            ...
+            NotImplementedError: arguments must be distinct variables
         """        
         #This code should probably be moved into the interface
         #object in a nice way.
         from sage.symbolic.ring import is_SymbolicVariable
         if self.name_init != "_maxima_init_":
             raise NotImplementedError
-        args = ex.args()
+        args = ex.operands()
         if (not all(is_SymbolicVariable(v) for v in args) or
             len(args) != len(set(args))):
             raise NotImplementedError, "arguments must be distinct variables"