Underscore instead of grave tilde in sympy names as context separators (#1536)

This continues #1535, by changing the way in which symbol names are
translated to sympy.

Author: mmatera

mathics/builtin/numbers/calculus.py

@@ -57,6 +57,7 @@
     SymbolPower,
     SymbolTimes,
     SymbolTrue,
+    sympy_name,
 )
 from mathics.core.systemsymbols import (
     SymbolAnd,
@@ -528,7 +529,7 @@ def to_sympy(self, expr, **kwargs):
             return
 
         func = exprs[1].elements[0]
-        sym_func = sympy.Function(str(SYMPY_SYMBOL_PREFIX + func.__str__()))(*sym_args)
+        sym_func = sympy.Function(sympy_name(func))(*sym_args)
 
         counts = [element.get_int_value() for element in exprs[2].elements]
         if None in counts:

mathics/core/convert/sympy.py

@@ -113,6 +113,16 @@
 }
 
 
+def sympy_decode_mathics_symbol_name(name: str):
+    """
+    Remove the Prefix for Mathics symbols
+    and restore the context separator character.
+    """
+    if name.startswith(SYMPY_SYMBOL_PREFIX):
+        return name[len(SYMPY_SYMBOL_PREFIX) :].replace("_", "`")
+    return name
+
+
 def is_Cn_expr(name: str) -> bool:
     """Check if name is of the form {prefix}Cnnn"""
     if name.startswith(SYMPY_SYMBOL_PREFIX) or name.startswith(SYMPY_SLOT_PREFIX):
@@ -236,7 +246,6 @@ def expression_to_sympy(expr: Expression, **kwargs):
     """
     Convert `expr` to its sympy form.
     """
-
     if len(expr.elements) > 0:
         head_name = expr.get_head_name()
         if head_name.startswith("Global`"):
@@ -250,6 +259,7 @@ def expression_to_sympy(expr: Expression, **kwargs):
 
     lookup_name = expr.get_lookup_name()
     builtin = mathics_to_sympy.get(lookup_name)
+
     if builtin is not None:
         sympy_expr = builtin.to_sympy(expr, **kwargs)
         if sympy_expr is not None:
@@ -348,7 +358,6 @@ def old_from_sympy(expr) -> BaseElement:
     """
     converts a SymPy object to a Mathics3 element.
     """
-
     if isinstance(expr, (tuple, list)):
         return to_mathics_list(*expr, elements_conversion_fn=from_sympy)
     if isinstance(expr, int):
@@ -373,16 +382,15 @@ def old_from_sympy(expr) -> BaseElement:
             name = str(expr)
             if isinstance(expr, sympy.Dummy):
                 name = name[1:]
-                if "`" not in name:
+                if "_" not in name:
                     name = f"sympy`dummy`Dummy${expr.dummy_index}"  # type: ignore[attr-defined]
                 else:
-                    name = name[len(SYMPY_SYMBOL_PREFIX) :]
+                    name = sympy_decode_mathics_symbol_name(name)
                 # Probably, this should be the value attribute
                 return Symbol(name)
             if is_Cn_expr(name):
                 return Expression(SymbolC, Integer(int(name[1:])))
-            if name.startswith(SYMPY_SYMBOL_PREFIX):
-                name = name[len(SYMPY_SYMBOL_PREFIX) :]
+            name = sympy_decode_mathics_symbol_name(name)
             if name.startswith(SYMPY_SLOT_PREFIX):
                 index = int(name[len(SYMPY_SLOT_PREFIX) :])
                 return Expression(SymbolSlot, Integer(index))
@@ -421,7 +429,8 @@ def old_from_sympy(expr) -> BaseElement:
         if isinstance(expr, sympy.core.numbers.NaN):
             return SymbolIndeterminate
         if isinstance(expr, sympy.core.function.FunctionClass):
-            return Symbol(str(expr))
+            name = str(expr).replace("_", "`")
+            return Symbol(name)
         if expr is sympy.true:
             return SymbolTrue
         if expr is sympy.false:
@@ -547,8 +556,7 @@ def old_from_sympy(expr) -> BaseElement:
                     Expression(Symbol("C"), Integer(int(name[1:]))),
                     *[from_sympy(arg) for arg in expr.args],
                 )
-            if name.startswith(SYMPY_SYMBOL_PREFIX):
-                name = name[len(SYMPY_SYMBOL_PREFIX) :]
+            name = sympy_decode_mathics_symbol_name(name)
         args = [from_sympy(arg) for arg in expr.args]
         builtin = sympy_to_mathics.get(name)
         if builtin is not None:

mathics/core/symbols.py

@@ -126,7 +126,7 @@ def sympy_strip_context(name) -> str:
     produce invalid code. In a next round, we would like
     to use another character for split contexts in sympy variables.
     """
-    return strip_context(name)
+    return name.split("_")[-1]
 
 
 # system_symbols_dict({'SomeSymbol': ...}) -> {Symbol('System`SomeSymbol'): ...}
@@ -342,6 +342,7 @@ class Symbol(Atom, NumericOperators, EvalMixin):
 
     name: str
     hash: int
+    sympy_dummy: Any
     _short_name: str
 
     # Dictionary of Symbols defined so far.
@@ -354,7 +355,7 @@ class Symbol(Atom, NumericOperators, EvalMixin):
 
     # __new__ instead of __init__ is used here because we want
     # to return the same object for a given "name" value.
-    def __new__(cls, name: str):
+    def __new__(cls, name: str, sympy_dummy=None):
         """
         Allocate an object ensuring that for a given ``name`` and ``cls`` we get back the same object,
         id(object) is the same and its object.__hash__() is the same.
@@ -384,6 +385,18 @@ def __new__(cls, name: str):
             # For example, this can happen with String constants.
 
             self.hash = hash((cls, name))
+
+            # TODO: revise how we convert sympy.Dummy
+            # symbols.
+            #
+            # In some cases, SymPy returns a sympy.Dummy
+            # object. It is converted to Mathics as a
+            # Symbol. However, we probably should have
+            # a different class for this kind of symbols.
+            # Also, sympy_dummy should be stored as the
+            # value attribute.
+            self.sympy_dummy = sympy_dummy
+
             self._short_name = strip_context(name)
 
         return self
@@ -392,7 +405,7 @@ def __eq__(self, other) -> bool:
         return self is other
 
     def __getnewargs__(self):
-        return (self.name,)
+        return (self.name, self.sympy_dummy)
 
     def __hash__(self) -> int:
         """
@@ -690,12 +703,6 @@ def __new__(cls, name, value):
             self.hash = hash((cls, name))
         return self
 
-    def __getnewargs__(self):
-        return (
-            self.name,
-            self._value,
-        )
-
     @property
     def is_literal(self) -> bool:
         """
@@ -754,7 +761,7 @@ def symbol_set(*symbols: Symbol) -> FrozenSet[Symbol]:
 
 def sympy_name(mathics_symbol: Symbol):
     """Convert a mathics symbol name into a sympy symbol name"""
-    return SYMPY_SYMBOL_PREFIX + mathics_symbol.name
+    return SYMPY_SYMBOL_PREFIX + mathics_symbol.name.replace("`", "_")
 
 
 # Symbols used in this module.

mathics/eval/drawing/plot_compile.py

@@ -18,8 +18,8 @@
 import scipy
 import sympy
 
-from mathics.core.convert.sympy import SympyExpression
-from mathics.core.symbols import strip_context
+from mathics.core.convert.sympy import SympyExpression, mathics_to_sympy
+from mathics.core.symbols import sympy_strip_context
 from mathics.core.util import print_expression_tree, print_sympy_tree
 
 
@@ -69,7 +69,8 @@ def plot_compile(evaluation, expr, names, debug=0):
 
     # Strip symbols in sympy expression of context.
     subs = {
-        sym: sympy.Symbol(strip_context(str(sym))) for sym in sympy_expr.free_symbols
+        sym: sympy.Symbol(sympy_strip_context(str(sym)))
+        for sym in sympy_expr.free_symbols
     }
     sympy_expr = sympy_expr.subs(subs)
 

test/core/test_sympy_python_convert.py

@@ -25,6 +25,7 @@
     SYMPY_SYMBOL_PREFIX,
     Symbol,
     SymbolPlus,
+    sympy_name,
 )
 from mathics.core.systemsymbols import (
     SymbolD,
@@ -36,6 +37,12 @@
     SymbolSlot,
 )
 
+Symbol_f = Symbol("Global`f")
+Symbol_x = Symbol("Global`x")
+Symbol_y = Symbol("Global`y")
+Symbol_z = Symbol("Global`z")
+Symbol_Mathics_User_x = Symbol("Mathics`User`x")
+
 
 class SympyConvert(unittest.TestCase):
     def compare_to_sympy(self, mathics_expr, sympy_expr, **kwargs):
@@ -49,11 +56,17 @@ def compare(self, mathics_expr, sympy_expr, **kwargs):
         self.compare_to_mathics(mathics_expr, sympy_expr)
 
     def testSymbol(self):
-        self.compare(Symbol("Global`x"), sympy.Symbol(f"{SYMPY_SYMBOL_PREFIX}Global`x"))
+        self.compare(Symbol_x, sympy.Symbol(sympy_name(Symbol_x)))
         self.compare(
-            Symbol("_Mathics_User_x"),
-            sympy.Symbol(f"{SYMPY_SYMBOL_PREFIX}System`_Mathics_User_x"),
+            Symbol_Mathics_User_x,
+            sympy.Symbol(sympy_name(Symbol_Mathics_User_x)),
         )
+        # Sympy symbols without prefix are mapped to symbols in
+        # System` context:
+        self.compare_to_mathics(Symbol("x"), sympy.Symbol("x"))
+        # Notice that a sympy Symbol named "x" is converted
+        # to the Mathics symbol "System`x", and then, when converted
+        # back to sympy, goes to sympy.Symbol("_uSystem_x").
 
     def testReal(self):
         self.compare(Real("1.0"), sympy.Float("1.0"))
@@ -87,25 +100,25 @@ def testString(self):
 
     def testAdd(self):
         self.compare(
-            Expression(SymbolPlus, Integer1, Symbol("Global`x")),
-            sympy.Add(sympy.Integer(1), sympy.Symbol(f"{SYMPY_SYMBOL_PREFIX}Global`x")),
+            Expression(SymbolPlus, Integer1, Symbol_x),
+            sympy.Add(sympy.Integer(1), sympy.Symbol(sympy_name(Symbol_x))),
         )
 
     def testIntegrate(self):
         self.compare(
-            Expression(SymbolIntegrate, Symbol("Global`x"), Symbol("Global`y")),
+            Expression(SymbolIntegrate, Symbol_x, Symbol_y),
             sympy.Integral(
-                sympy.Symbol(f"{SYMPY_SYMBOL_PREFIX}Global`x"),
-                sympy.Symbol(f"{SYMPY_SYMBOL_PREFIX}Global`y"),
+                sympy.Symbol(sympy_name(Symbol_x)),
+                sympy.Symbol(sympy_name(Symbol_y)),
             ),
         )
 
     def testDerivative(self):
         self.compare(
-            Expression(SymbolD, Symbol("Global`x"), Symbol("Global`y")),
+            Expression(SymbolD, Symbol_x, Symbol_y),
             sympy.Derivative(
-                sympy.Symbol(f"{SYMPY_SYMBOL_PREFIX}Global`x"),
-                sympy.Symbol(f"{SYMPY_SYMBOL_PREFIX}Global`y"),
+                sympy.Symbol(sympy_name(Symbol_x)),
+                sympy.Symbol(sympy_name(Symbol_y)),
             ),
         )
 
@@ -114,47 +127,43 @@ def testDerivative2(self):
 
         head = Expression(
             Expression(SymbolDerivative, Integer1, Integer0),
-            Symbol("Global`f"),
+            Symbol_f,
         )
-        expr = Expression(head, Symbol("Global`x"), Symbol("Global`y"))
+        expr = Expression(head, Symbol_x, Symbol_y)
 
-        sfxy = sympy.Function(str(f"{SYMPY_SYMBOL_PREFIX}Global`f"))(
-            sympy.Symbol(f"{SYMPY_SYMBOL_PREFIX}Global`x"),
-            sympy.Symbol(f"{SYMPY_SYMBOL_PREFIX}Global`y"),
-        )
-        sym_expr = sympy.Derivative(
-            sfxy, sympy.Symbol(f"{SYMPY_SYMBOL_PREFIX}Global`x")
+        sfxy = sympy.Function(sympy_name(Symbol_f))(
+            sympy.Symbol(sympy_name(Symbol_x)),
+            sympy.Symbol(sympy_name(Symbol_y)),
         )
+        sym_expr = sympy.Derivative(sfxy, sympy.Symbol(sympy_name(Symbol_x)))
 
         self.compare_to_sympy(expr, sym_expr, **kwargs)
         # compare_to_mathics fails because Derivative becomes D (which then evaluates to Derivative)
 
     def testConvertedFunctions(self):
         kwargs = {"converted_functions": set(["Global`f"])}
 
-        marg1 = Expression(Symbol("Global`f"), Symbol("Global`x"))
-        sarg1 = sympy.Function(str(f"{SYMPY_SYMBOL_PREFIX}Global`f"))(
-            sympy.Symbol(f"{SYMPY_SYMBOL_PREFIX}Global`x")
-        )
+        marg1 = Expression(Symbol_f, Symbol_x)
+        sarg1 = sympy.Function(sympy_name(Symbol_f))(sympy.Symbol(sympy_name(Symbol_x)))
         self.compare(marg1, sarg1, **kwargs)
 
-        marg2 = Expression(Symbol("Global`f"), Symbol("Global`x"), Symbol("Global`y"))
-        sarg2 = sympy.Function(str(f"{SYMPY_SYMBOL_PREFIX}Global`f"))(
-            sympy.Symbol(f"{SYMPY_SYMBOL_PREFIX}Global`x"),
-            sympy.Symbol(f"{SYMPY_SYMBOL_PREFIX}Global`y"),
+        marg2 = Expression(Symbol_f, Symbol_x, Symbol_y)
+        sarg2 = sympy.Function(sympy_name(Symbol_f))(
+            sympy.Symbol(sympy_name(Symbol_x)),
+            sympy.Symbol(sympy_name(Symbol_y)),
         )
         self.compare(marg2, sarg2, **kwargs)
 
         self.compare(
-            Expression(SymbolD, marg2, Symbol("Global`x")),
-            sympy.Derivative(sarg2, sympy.Symbol(f"{SYMPY_SYMBOL_PREFIX}Global`x")),
+            Expression(SymbolD, marg2, Symbol_x),
+            sympy.Derivative(sarg2, sympy.Symbol(sympy_name(Symbol_x))),
             **kwargs,
         )
 
     def testExpression(self):
         self.compare(
-            Expression(SymbolSin, Symbol("Global`x")),
-            sympy.sin(sympy.Symbol(f"{SYMPY_SYMBOL_PREFIX}Global`x")),
+            Expression(SymbolSin, Symbol_x),
+            sympy.sin(sympy.Symbol(sympy_name(Symbol_x))),
         )
 
     def testConstant(self):
@@ -163,14 +172,14 @@ def testConstant(self):
 
     def testGamma(self):
         self.compare(
-            Expression(SymbolGamma, Symbol("Global`z")),
-            sympy.gamma(sympy.Symbol(f"{SYMPY_SYMBOL_PREFIX}Global`z")),
+            Expression(SymbolGamma, Symbol_z),
+            sympy.gamma(sympy.Symbol(sympy_name(Symbol_z))),
         )
         self.compare(
-            Expression(SymbolGamma, Symbol("Global`z"), Symbol("Global`x")),
+            Expression(SymbolGamma, Symbol_z, Symbol_x),
             sympy.uppergamma(
-                sympy.Symbol(f"{SYMPY_SYMBOL_PREFIX}Global`z"),
-                sympy.Symbol(f"{SYMPY_SYMBOL_PREFIX}Global`x"),
+                sympy.Symbol(sympy_name(Symbol_z)),
+                sympy.Symbol(sympy_name(Symbol_x)),
             ),
         )