Fix SymPy errors when using reserved symbols in differentiate2c

The user should now make sure to pass all of the symbols to the function
as SymPy objects.

python/nmodl/ode.py

@@ -252,6 +252,51 @@ def make_symbol(var, /):
     return sp.Symbol(var, real=True) if isinstance(var, str) else var
 
 
+def rename_to_sympy(var, /):
+    """
+    Symbol-aware renaming of reserved or built-in symbols.
+
+    Notes
+    -----
+    For renaming variables in complex expressions, see
+    :ref:``regex_rename_to_sympy``.
+    """
+    var = make_symbol(var)
+
+    if var.name in forbidden_var:
+        new_name = f"_sympy_{var.name}"
+
+        # there is no "Pythonic" way of doing this since the SymPy API does not
+        # allow changing names of symbols, or actually copying objects properly
+        if isinstance(var, sp.Symbol):
+            assumptions = var.assumptions0
+            return sp.Symbol(new_name, **assumptions)
+
+        elif isinstance(var, sp.IndexedBase):
+            return sp.IndexedBase(new_name, shape=var.shape)
+
+        elif isinstance(var, sp.FunctionClass):
+            return sp.Function(new_name)
+
+    return var
+
+
+def regex_rename_to_sympy(expression, /):
+    """
+    Rename expression containing reserved or built-in symbols using a regex.
+
+    Notes
+    -----
+    For renaming single variables, see :ref:``rename_to_sympy``.
+    """
+
+    for var in forbidden_var:
+        pattern = re.compile(rf"\b{var}\b")
+        expression = re.sub(pattern, f"_sympy_{var}", expression)
+
+    return expression
+
+
 def solve_lin_system(
     eq_strings,
     vars,
@@ -622,18 +667,23 @@ def differentiate2c(
     if stepsize <= 0:
         raise ValueError("arg `stepsize` must be > 0")
     prev_expressions = prev_expressions or []
-    # every symbol (a.k.a variable) that SymPy
-    # is going to manipulate needs to be declared
-    # explicitly
-    x = make_symbol(dependent_var)
-    vars = set(vars)
-    vars.discard(dependent_var)
+
+    # we keep the original symbol around as well so we can rename it back
+    x_original = make_symbol(dependent_var)
+    sympy_vars_original = {
+        **{str(var): make_symbol(var) for var in vars},
+        str(x_original): x_original,
+    }
+
     # declare all other supplied variables
-    sympy_vars = {str(var): make_symbol(var) for var in vars}
-    sympy_vars[dependent_var] = x
+    x = rename_to_sympy(dependent_var)
+    sympy_vars = {
+        **{str(rename_to_sympy(var)): rename_to_sympy(var) for var in vars},
+        str(x): x,
+    }
 
     # parse string into SymPy equation
-    expr = sp.sympify(expression, locals=sympy_vars)
+    expr = sp.sympify(regex_rename_to_sympy(expression), locals=sympy_vars)
 
     # parse previous expressions in the order that they came in
     # substitute any x-dependent vars in rhs with their rhs expressions,
@@ -672,6 +722,16 @@ def differentiate2c(
             .evalf()
         )
 
+    # once we have the derivative, it's safe to put back the original variables
+    reverse_map = {
+        old_var: new_var
+        for old_var, new_var in zip(
+            sympy_vars.values(),
+            sympy_vars_original.values(),
+        )
+    }
+    diff = diff.subs(reverse_map)
+
     # the codegen method does not like undefined function calls, so we extract
     # them here
     custom_fcts = {str(f.func): str(f.func) for f in diff.atoms(sp.Function)}