Adding pytests for from_sympy / to_sympy. (#828)

This PR adds some basic tests to check the consistency in the behavior
of `from_sympy`. When I was writing the tests, I found some issues in
the behavior of these functions, and also some failures in the
modularity. So, this PR

* moves `mathics_to_sympy` and `sympy_to_mathics` dicts from
`mathics.builtin` to `mathics.core.convert.sympy`. This allows for
avoiding some local imports.
* `to_numeric_sympy_args` was moved from
`mathics.core.convert.expression` to `mathics.core.convert.sympy`, which
again helps to reduce local imports.
* moves the implementation of `Expression.to_sympy` and
`Symbol.to_sympy` to `mathics.core.convert.sympy`.
* Constant expressions like `MATHICS_*INFINITY` and numbers
`MATHICS_COMPLEX_I` were included in `mathics.core.expression` to avoid
local duplication.
* Improves the implementation of `Symbol.to_sympy` by using a dictionary
to translate some predefined symbols in SymPy, like `pi`, `E`,
`GoldenRatio` or `I`.
* adds pytests for `from_sympy` and `to_sympy`.

In the code, it is also a proposal for a rewriting of `from_sympy` using
dictionaries, which could help to get a clearer code.

mathics/builtin/__init__.py

@@ -50,6 +50,8 @@
 
 
 def add_builtins(new_builtins):
+    from mathics.core.convert.sympy import mathics_to_sympy, sympy_to_mathics
+
     for var_name, builtin in new_builtins:
         name = builtin.get_name()
         if hasattr(builtin, "python_equivalent"):
@@ -255,8 +257,6 @@ def name_is_builtin_symbol(module, name: str) -> Optional[type]:
                 _builtins_list.append((instance.get_name(), instance))
                 builtins_by_module[module.__name__].append(instance)
 
-mathics_to_sympy = {}  # here we have: name -> sympy object
-sympy_to_mathics = {}
 
 new_builtins = _builtins_list
 

mathics/builtin/arithmetic.py

@@ -18,6 +18,7 @@
     IterationFunction,
     Predefined,
     SympyFunction,
+    SympyObject,
     Test,
 )
 from mathics.builtin.inference import evaluate_predicate, get_assumptions_list
@@ -788,7 +789,7 @@ def eval_Element_alternatives(
         return Element(Expression(elems.head, *unknown), domain)
 
 
-class I_(Predefined):
+class I_(Predefined, SympyObject):
     """
     <url>:Imaginary unit:https://en.wikipedia.org/wiki/Imaginary_unit</url> \
     (<url>:WMA:https://reference.wolfram.com/language/ref/I.html</url>)
@@ -805,9 +806,17 @@ class I_(Predefined):
     """
 
     name = "I"
+    sympy_name = "I"
+    sympy_obj = sympy.I
     summary_text = "imaginary unit"
     python_equivalent = 1j
 
+    def is_constant(self) -> bool:
+        return True
+
+    def to_sympy(self, symb, **kwargs):
+        return self.sympy_obj
+
     def evaluate(self, evaluation: Evaluation):
         return Complex(Integer0, Integer1)
 

mathics/builtin/base.py

@@ -19,10 +19,10 @@
     String,
 )
 from mathics.core.attributes import A_HOLD_ALL, A_NO_ATTRIBUTES, A_PROTECTED
-from mathics.core.convert.expression import to_expression, to_numeric_sympy_args
+from mathics.core.convert.expression import to_expression
 from mathics.core.convert.op import ascii_operator_to_symbol
 from mathics.core.convert.python import from_bool
-from mathics.core.convert.sympy import from_sympy
+from mathics.core.convert.sympy import from_sympy, to_numeric_sympy_args
 from mathics.core.definitions import Definition
 from mathics.core.evaluation import Evaluation
 from mathics.core.exceptions import MessageException

mathics/builtin/specialfns/elliptic.py

@@ -15,8 +15,7 @@
 from mathics.builtin.base import SympyFunction
 from mathics.core.atoms import Integer
 from mathics.core.attributes import A_LISTABLE, A_NUMERIC_FUNCTION, A_PROTECTED
-from mathics.core.convert.expression import to_numeric_sympy_args
-from mathics.core.convert.sympy import from_sympy
+from mathics.core.convert.sympy import from_sympy, to_numeric_sympy_args
 from mathics.eval.numerify import numerify
 
 

mathics/core/convert/expression.py

@@ -99,23 +99,6 @@ def to_numeric_args(mathics_args: Type[BaseElement], evaluation) -> list:
     )
 
 
-def to_numeric_sympy_args(mathics_args: Type[BaseElement], evaluation) -> list:
-    """
-    Convert Mathics arguments, such as the arguments in an evaluation
-    method a Python list that is sutiable for feeding as arguments
-    into SymPy.
-
-    We make use of fast conversions for literals.
-    """
-    if mathics_args.is_literal:
-        sympy_args = [mathics_args.value]
-    else:
-        args = numerify(mathics_args, evaluation).get_sequence()
-        sympy_args = [a.to_sympy() for a in args]
-
-    return sympy_args
-
-
 expression_constructor_map = {
     SymbolList: lambda head, *args, **kwargs: ListExpression(*args, **kwargs)
 }