Adjust builtins_precedence and doc parenthesize

We should be using Symbols insead of string where possible.
builtins_precedence is really used in eval/makeboxes so it is defined
there.

It is just initialized in `mathics.buitins`.

Author: rocky

mathics/builtin/__init__.py

@@ -36,6 +36,8 @@
     mathics_to_python,
 )
 from mathics.core.pattern import pattern_objects
+from mathics.core.symbols import Symbol
+from mathics.eval.makeboxes import builtins_precedence
 from mathics.settings import ENABLE_FILES_MODULE
 from mathics.version import __version__  # noqa used in loading to check consistency.
 
@@ -60,7 +62,7 @@ def add_builtins(new_builtins):
                 # print("XXX1", sympy_name)
                 sympy_to_mathics[sympy_name] = builtin
         if isinstance(builtin, Operator):
-            builtins_precedence[name] = builtin.precedence
+            builtins_precedence[Symbol(name)] = builtin.precedence
         if isinstance(builtin, PatternObject):
             pattern_objects[name] = builtin.__class__
     _builtins.update(dict(new_builtins))
@@ -236,8 +238,6 @@ def name_is_builtin_symbol(module, name: str) -> Optional[type]:
 mathics_to_sympy = {}  # here we have: name -> sympy object
 sympy_to_mathics = {}
 
-builtins_precedence = {}
-
 new_builtins = _builtins_list
 
 # FIXME: some magic is going on here..

mathics/eval/makeboxes.py

@@ -7,7 +7,7 @@
 
 
 import typing
-from typing import Any
+from typing import Any, Dict, Type
 
 from mathics.core.atoms import Complex, Integer, Rational, Real, String, SymbolI
 from mathics.core.convert.expression import to_expression_with_specialization
@@ -42,6 +42,8 @@
     SymbolStandardForm,
 )
 
+builtins_precedence: Dict[Symbol, int] = {}
+
 element_formatters = {}
 
 
@@ -290,9 +292,17 @@ def do_format_expression(
     return expr
 
 
-def parenthesize(precedence, element, element_boxes, when_equal):
-    from mathics.builtin import builtins_precedence
+def parenthesize(
+    precedence: int, element: Type[BaseElement], element_boxes, when_equal: bool
+) -> Type[Expression]:
+    """
+    "Determines if ``element_boxes`` needs to be surrounded with parenthesis.
+    This is done based on ``precedence`` and the computed preceence of
+    ``element``.  The adjusted ListExpression is returned.
 
+    If when_equal is True, parentheses will be added if the two
+    precedence values are equal.
+    """
     while element.has_form("HoldForm", 1):
         element = element.elements[0]
 
@@ -304,7 +314,7 @@ def parenthesize(precedence, element, element_boxes, when_equal):
     elif isinstance(element, (Integer, Real)) and element.value < 0:
         element_prec = precedence
     else:
-        element_prec = builtins_precedence.get(element.get_head_name())
+        element_prec = builtins_precedence.get(element.get_head())
     if precedence is not None and element_prec is not None:
         if precedence > element_prec or (precedence == element_prec and when_equal):
             return Expression(