17505: unevaluated symbolic product

Author: rwst

src/sage/calculus/calculus.py

@@ -2024,7 +2024,10 @@ def symbolic_expression_from_maxima_string(x, equals_sub=False, maxima=maxima):
     formal_functions = maxima_tick.findall(s)
     if len(formal_functions) > 0:
         for X in formal_functions:
-            syms[X[1:]] = function_factory(X[1:])
+            try:
+                syms[X[1:]] = _syms[X[1:]]
+            except KeyError:
+                syms[X[1:]] = function_factory(X[1:])
         # You might think there is a potential very subtle bug if 'foo
         # is in a string literal -- but string literals should *never*
         # ever be part of a symbolic expression.

src/sage/functions/other.py

@@ -2608,3 +2608,33 @@ def __init__(self):
                                conversions=dict(maxima='sum'))
 
 symbolic_sum = Function_sum()
+
+
+class Function_prod(BuiltinFunction):
+    """
+    Placeholder symbolic product function that is only accessible internally.
+
+    EXAMPLES::
+
+        sage: from sage.functions.other import symbolic_product as sprod
+        sage: sprod(x, x, 1, 10)
+        product(x, x, 1, 10)
+    """
+    def __init__(self):
+        """
+        EXAMPLES::
+
+            sage: from sage.functions.other import symbolic_product as sprod
+            sage: _ = var('n')
+            sage: r = maxima(sprod(sin(x), x, 1, n)).sage(); r
+            product(sin(x), x, 1, n)
+            sage: isinstance(r.operator(), sage.functions.other.Function_prod)
+            True
+            sage: maxima(sprod(x, x, 1, 5))
+            120
+        """
+        BuiltinFunction.__init__(self, "product", nargs=4,
+                               conversions=dict(maxima='product',
+                                   sympy='Product'))
+
+symbolic_product = Function_prod()