Merge branch 'public/22802_sympy_abstract_function' of git://trac.sag…

…emath.org/sage into public/22802_sympy_abstract_function

build/pkgs/sympy/package-version.txt

@@ -1 +1 @@
-1.0.p2
+1.0.p3

build/pkgs/sympy/patches/02_undeffun_sage.patch

@@ -0,0 +1,59 @@
+diff --git a/sympy/core/function.py b/sympy/core/function.py
+index 4c4ce9c..63c52da 100644
+--- a/sympy/core/function.py
++++ b/sympy/core/function.py
+@@ -746,8 +746,21 @@ def _eval_as_leading_term(self, x):
+     def _sage_(self):
+         import sage.all as sage
+         fname = self.func.__name__
+-        func = getattr(sage, fname)
++        func = getattr(sage, fname,None)
+         args = [arg._sage_() for arg in self.args]
++
++        # In the case the function is not known in sage:
++        if func is None:
++            import sympy
++            if getattr(sympy, fname,None) is None:
++                # abstract function
++                return sage.function(fname)(*args)
++
++            else:
++                # the function defined in sympy is not known in sage
++                # this exception is catched in sage
++                raise AttributeError
++
+         return func(*args)
+
+
+diff --git a/sympy/external/tests/test_sage.py b/sympy/external/tests/test_sage.py
+index bc404b6..ed41d42 100644
+--- a/sympy/external/tests/test_sage.py
++++ b/sympy/external/tests/test_sage.py
+@@ -222,6 +222,19 @@ def test_undefined_function():
+     assert bool(sf(sx) == f(x)._sage_())
+     #assert bool(f == sympy.sympify(sf))
+
++def test_abstract_function():
++    from sage.symbolic.expression import Expression
++    x,y = sympy.symbols('x y')
++    f = sympy.Function('f')
++    expr =  f(x,y)
++    sexpr = expr._sage_()
++    assert isinstance(sexpr,Expression), "converted expression %r is not sage expression" % sexpr
++    # This test has to be uncommented in the future: it depends on the sage ticket #22802 (https://trac.sagemath.org/ticket/22802)
++    # invexpr = sexpr._sympy_()
++    # assert invexpr == expr, "inverse coversion %r is not correct " % invexpr
++
++
++
+ # This string contains Sage doctests, that execute all the functions above.
+ # When you add a new function, please add it here as well.
+ """
+@@ -244,6 +257,7 @@ def test_undefined_function():
+     sage: test_issue_4023()
+     sage: test_integral()
+     sage: test_undefined_function()
++    sage  test_abstract_function()
+
+ Sage has no symbolic Lucas function at the moment::
+

src/sage/symbolic/expression_conversions.py

@@ -603,15 +603,15 @@ def derivative(self, ex, operator):
             subs = ["%s = %s"%(t._maxima_init_(),a._maxima_init_()) for t,a in zip(temp_args,args)]
             outstr = "at(diff(%s, %s), [%s])"%(f._maxima_init_(),
                 ", ".join(params),
-                ", ".join(subs))            
+                ", ".join(subs))
         else:
             f = operator.function()(*args)
             params = operator.parameter_set()
             params = ["%s, %s"%(args[i]._maxima_init_(), params.count(i)) for i in set(params)]
             outstr = "diff(%s, %s)"%(f._maxima_init_(),
                                         ", ".join(params))
         return outstr
-    
+
     def arithmetic(self, ex, operator):
         """
         EXAMPLES::
@@ -674,7 +674,7 @@ class SympyConverter(Converter):
         sage: sympy.sympify(x) # indirect doctest
         x
 
-    TESTS:
+    TESTS::
 
     Make sure we can convert I (:trac:`6424`)::
 
@@ -764,7 +764,61 @@ def composition(self, ex, operator):
         if f_sympy:
             return f_sympy(*sympy.sympify(g, evaluate=False))
         else:
-            raise NotImplementedError("SymPy function '%s' doesn't exist" % f)
+            from sage.symbolic.function_factory import SymbolicFunction
+            if isinstance(ex.operator(), SymbolicFunction):
+                return sympy.Function(str(f))(*g, evaluate=False)
+
+
+    def derivative(self, ex, operator):
+        """
+        Convert the derivative in sympy
+        INPUT:
+
+        - ``ex`` -- a symbolic expression
+
+        - ``operator`` -- operator
+
+        TESTS::
+            sage: import sympy
+
+            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 aa in range(len(_args)):
+            gg = order.count(aa)
+            if gg > 0 :
+                sympy_arg.append(_args[aa])
+                sympy_arg.append(gg)
+
+        return f_sympy.diff(*sympy_arg)
+
+
 
 sympy = SympyConverter()
 
@@ -1769,7 +1823,7 @@ def arithmetic(self, ex, operator):
         if operator == add_vararg:
             operator = _operator.add
         elif operator == mul_vararg:
-            operator = _operator.mul         
+            operator = _operator.mul
         return reduce(operator, map(self, operands))
 
     def composition(self, ex, operator):
@@ -2026,4 +2080,3 @@ def composition(self, ex, operator):
             return operator(*map(self, ex.operands()), hold=True)
         else:
             return operator(*map(self, ex.operands()))
-

src/sage/symbolic/function.pyx

@@ -619,9 +619,7 @@ cdef class Function(SageObject):
             sage: g._sympy_init_()
             'gg'
             sage: g(x)._sympy_()
-            Traceback (most recent call last):
-            ...
-            NotImplementedError: SymPy function 'gg' doesn't exist
+            gg(x)
         """
         return self._conversions.get('sympy', self._name)
 

src/sage/tests/french_book/recequadiff.py

@@ -378,9 +378,10 @@
   sage: from sympy import Function, Symbol
   sage: u = Function('u'); n = Symbol('n', integer=True)
 
-Sage example in ./recequadiff.tex, line 1208::
+Sage example in ./recequadiff.tex, line 1208 (WARNING: the order of factors is
+inverted, see :trac:`23496` )::
 
-  sage: f = u(n+2)-(3/2)*u(n+1)+(1/2)*u(n)
+  sage: f = u(n+2)-u(n+1)*(3/2)+u(n)*(1/2)
 
 Sage example in ./recequadiff.tex, line 1214::
 
@@ -396,4 +397,3 @@
   2**n*C0 + 2**(n + 2)*(C0 + n/2)
 
 """
-