Merge pull request #1204 from mathics/SymbolList

Singletonize Symbols frequently used in Head

Author: rocky

mathics/builtin/arithmetic.py

@@ -31,15 +31,16 @@
     Real,
     String,
     Symbol,
+    SymbolComplexInfinity,
+    SymbolDirectedInfinity,
     SymbolFalse,
+    SymbolInfinity,
+    SymbolN,
     SymbolNull,
+    SymbolSequence,
     SymbolTrue,
-    SymbolList,
-    SymbolInfinity,
-    SymbolDirectedInfinity,
-    SymbolComplexInfinity,
-    from_python,
     from_mpmath,
+    from_python,
 )
 from mathics.core.numbers import min_prec, dps, SpecialValueError
 
@@ -122,7 +123,7 @@ def apply(self, z, evaluation):
             prec = min_prec(*args)
             d = dps(prec)
             args = [
-                Expression("N", arg, Integer(d)).evaluate(evaluation) for arg in args
+                Expression(SymbolN, arg, Integer(d)).evaluate(evaluation) for arg in args
             ]
             with mpmath.workprec(prec):
                 mpmath_args = [x.to_mpmath() for x in args]
@@ -947,7 +948,7 @@ def apply_check(self, x, y, evaluation):
             if isinstance(y, Number):
                 y_err = y
             else:
-                y_err = Expression("N", y).evaluate(evaluation)
+                y_err = Expression(SymbolN, y).evaluate(evaluation)
             if isinstance(y_err, Number):
                 py_y = y_err.round_to_float(permit_complex=True).real
                 if py_y > 0:
@@ -963,7 +964,7 @@ def apply_check(self, x, y, evaluation):
             factor = self.apply(Expression("Sequence", x.imag, y), evaluation)
             return Expression("Times", factor, Expression("Power", Integer(-1), yhalf))
 
-        result = self.apply(Expression("Sequence", x, y), evaluation)
+        result = self.apply(Expression(SymbolSequence, x, y), evaluation)
         if result is None or result != SymbolNull:
             return result
 
@@ -1418,7 +1419,7 @@ def apply(self, expr, evaluation):
             result = _iszero(exprexp)
         if result is None:
             # Can't get exact answer, so try approximate equal
-            numeric_val = Expression("N", expr).evaluate(evaluation)
+            numeric_val = Expression(SymbolN, expr).evaluate(evaluation)
             if numeric_val and hasattr(numeric_val, "is_approx_zero"):
                 result = numeric_val.is_approx_zero
             elif (

mathics/builtin/calculus.py

@@ -6,7 +6,7 @@
 from mathics.version import __version__  # noqa used in loading to check consistency.
 
 from mathics.builtin.base import Builtin, PostfixOperator, SympyFunction
-from mathics.core.expression import Expression, Integer, Number, SymbolTrue, SymbolFalse
+from mathics.core.expression import Expression, Integer, Number, SymbolTrue, SymbolFalse, SymbolList, SymbolN, SymbolRule
 from mathics.core.convert import sympy_symbol_prefix, SympyExpression, from_sympy
 from mathics.core.rules import Pattern
 from mathics.core.numbers import dps
@@ -190,7 +190,7 @@ def summand(leaf, index):
     def apply_wrong(self, expr, x, other, evaluation):
         "D[expr_, {x_, other___}]"
 
-        arg = Expression("List", x, *other.get_sequence())
+        arg = Expression(SymbolList, x, *other.get_sequence())
         evaluation.message("D", "dvar", arg)
         return Expression("D", expr, arg)
 
@@ -743,7 +743,7 @@ def apply(self, eqs, vars, evaluation):
             if eq == SymbolTrue:
                 pass
             elif eq == SymbolFalse:
-                return Expression("List")
+                return Expression(SymbolList)
             elif not eq.has_form("Equal", 2):
                 return evaluation.message("Solve", "eqf", eqs_original)
             else:
@@ -816,9 +816,9 @@ def transform_solution(sol):
             if not isinstance(result, list):
                 result = [result]
             if isinstance(result, list) and len(result) == 1 and result[0] is True:
-                return Expression("List", Expression("List"))
+                return Expression(SymbolList, Expression(SymbolList))
             if result == [None]:
-                return Expression("List")
+                return Expression(SymbolList)
             results = []
             for sol in result:
                 results.extend(transform_solution(sol))
@@ -842,7 +842,7 @@ def transform_solution(sol):
                     Expression(
                         "List",
                         *(
-                            Expression("Rule", var, from_sympy(sol[var_sympy]))
+                            Expression(SymbolRule, var, from_sympy(sol[var_sympy]))
                             for var, var_sympy in zip(vars, vars_sympy)
                             if var_sympy in sol
                         )
@@ -1098,7 +1098,7 @@ class FindRoot(Builtin):
     def apply(self, f, x, x0, evaluation):
         "FindRoot[f_, {x_, x0_}]"
 
-        x0 = Expression("N", x0).evaluate(evaluation)
+        x0 = Expression(SymbolN, x0).evaluate(evaluation)
         if not isinstance(x0, Number):
             evaluation.message("FindRoot", "snum", x0)
             return
@@ -1134,11 +1134,11 @@ def sub(evaluation):
                 return
             if x1 == x0:
                 break
-            x0 = Expression("N", x1).evaluate(
+            x0 = Expression(SymbolN, x1).evaluate(
                 evaluation
             )  # N required due to bug in sympy arithmetic
             count += 1
         else:
             evaluation.message("FindRoot", "maxiter")
 
-        return Expression("List", Expression("Rule", x, x0))
+        return Expression(SymbolList, Expression(SymbolRule, x, x0))

mathics/builtin/files.py

@@ -42,6 +42,7 @@
     SymbolFalse,
     SymbolNull,
     SymbolTrue,
+    SymbolList,
     from_mpmath,
     from_python,
     valid_context_name,
@@ -396,7 +397,7 @@ class Path(Predefined):
     name = "$Path"
 
     def evaluate(self, evaluation):
-        return Expression("List", *[String(p) for p in PATH_VAR])
+        return Expression(SymbolList, *[String(p) for p in PATH_VAR])
 
 
 class OperatingSystem(Predefined):

mathics/builtin/graphics.py

@@ -26,6 +26,9 @@
     Real,
     String,
     Symbol,
+    SymbolList,
+    SymbolN,
+    SymbolMakeBoxes,
     strip_context,
     system_symbols,
     system_symbols_dict,
@@ -290,7 +293,7 @@ def _CMC_distance(lab1, lab2, l, c):
 
 
 def _extract_graphics(graphics, format, evaluation):
-    graphics_box = Expression("MakeBoxes", graphics).evaluate(evaluation)
+    graphics_box = Expression(SymbolMakeBoxes, graphics).evaluate(evaluation)
     builtin = GraphicsBox(expression=False)
     elements, calc_dimensions = builtin._prepare_elements(
         graphics_box.leaves, {"evaluation": evaluation}, neg_y=True
@@ -398,7 +401,7 @@ def apply(self, graphics, evaluation, options):
 
         for option in options:
             if option not in ("System`ImageSize",):
-                options[option] = Expression("N", options[option]).evaluate(evaluation)
+                options[option] = Expression(SymbolN, options[option]).evaluate(evaluation)
 
         # The below could probably be done with graphics.filter..
         new_leaves = []
@@ -475,7 +478,7 @@ def convert(content):
             head = content.get_head_name()
 
             if head == "System`List":
-                return Expression("List", *[convert(item) for item in content.leaves])
+                return Expression(SymbolList, *[convert(item) for item in content.leaves])
             elif head == "System`Style":
                 return Expression(
                     "StyleBox", *[convert(item) for item in content.leaves]
@@ -492,12 +495,12 @@ def convert(content):
                 ):
                     if head == "System`Inset":
                         n_leaves = [content.leaves[0]] + [
-                            Expression("N", leaf).evaluate(evaluation)
+                            Expression(SymbolN, leaf).evaluate(evaluation)
                             for leaf in content.leaves[1:]
                         ]
                     else:
                         n_leaves = (
-                            Expression("N", leaf).evaluate(evaluation)
+                            Expression(SymbolN, leaf).evaluate(evaluation)
                             for leaf in content.leaves
                         )
                 else:
@@ -507,7 +510,7 @@ def convert(content):
 
         for option in options:
             if option not in ("System`ImageSize",):
-                options[option] = Expression("N", options[option]).evaluate(evaluation)
+                options[option] = Expression(SymbolN, options[option]).evaluate(evaluation)
         from mathics.builtin.graphics3d import Graphics3DBox, Graphics3D
 
         if type(self) is Graphics:
@@ -986,9 +989,9 @@ def distance(a, b):
                             *[distance(a, b) for a, b in zip(c1.leaves, c2.leaves)]
                         )
                 else:
-                    return Expression("List", *[distance(c, c2) for c in c1.leaves])
+                    return Expression(SymbolList, *[distance(c, c2) for c in c1.leaves])
             elif c2.get_head_name() == "System`List":
-                return Expression("List", *[distance(c1, c) for c in c2.leaves])
+                return Expression(SymbolList, *[distance(c1, c) for c in c2.leaves])
             else:
                 return distance(c1, c2)
         except ColorError:
@@ -1436,7 +1439,7 @@ def do_init(self, graphics, points):
             leaves = points.leaves
             self.multi_parts = True
         else:
-            leaves = [Expression("List", *points.leaves)]
+            leaves = [Expression(SymbolList, *points.leaves)]
             self.multi_parts = False
         lines = []
         for leaf in leaves:
@@ -1492,7 +1495,7 @@ def init(self, graphics, style, item=None):
             points = item.leaves[0]
             if points.has_form("List", None) and len(points.leaves) != 0:
                 if all(not leaf.has_form("List", None) for leaf in points.leaves):
-                    points = Expression("List", points)
+                    points = Expression(SymbolList, points)
             self.do_init(graphics, points)
         else:
             raise BoxConstructError
@@ -1890,7 +1893,7 @@ def process_option(self, name, value):
             self.vertex_colors = [[black] * len(line) for line in self.lines]
             colors = value.leaves
             if not self.multi_parts:
-                colors = [Expression("List", *colors)]
+                colors = [Expression(SymbolList, *colors)]
             for line_index, line in enumerate(self.lines):
                 if line_index >= len(colors):
                     break
@@ -2046,7 +2049,7 @@ def vertices():
                     )
 
             new_item = Expression(
-                "RegularPolygonBox", Expression("List", *list(vertices()))
+                "RegularPolygonBox", Expression(SymbolList, *list(vertices()))
             )
         else:
             raise BoxConstructError
@@ -3525,7 +3528,7 @@ def apply(self, colors, u, evaluation):
             if not colors:
                 raise ColorError
         except ColorError:
-            evaluation.message("Blend", "arg", Expression("List", colors_orig))
+            evaluation.message("Blend", "arg", Expression(SymbolList, colors_orig))
             return
 
         if u.has_form("List", None):
@@ -3546,7 +3549,7 @@ def apply(self, colors, u, evaluation):
             use_list = False
         if values is None:
             return evaluation.message(
-                "Blend", "argl", u, Expression("List", colors_orig)
+                "Blend", "argl", u, Expression(SymbolList, colors_orig)
             )
 
         if use_list: