pycalphad doesn't depend on sympy anymore, only on symengine. I'm still reading so I'll see if I can advise on how to eliminate the dependency.

Does this logic still work if we actually have an ideal gas phase in the Database? What if it's a GAS phase with interaction parameters, pressure dependence, etc.? This is one of the cases that needs a test.

Certainly works with an ideal gas in. Frankly I don't yet understand other gas models well enough yet, I should probably read up on the options in both the TDB and DAT formats before deciding how to handle.

In my experience with other TDB -> DAT converters, they often break on pressure-dependent terms. This might be a tricky spot.

@bocklund Please check this during your review

I think you can replace this function with Model.symbol_replace and eliminate the sympy dependency:

# Maximum number of levels deep we check for symbols that are functions of
# other symbols
_MAX_PARAM_NESTING = 32
def symbol_replace(obj, symbols):
    """
    Substitute values of symbols into 'obj'.
    Parameters
    ----------
    obj : SymEngine object
    symbols : dict mapping symengine.Symbol to SymEngine object
    Returns
    -------
    SymEngine object
    """
    try:
        # Need to do more substitutions to catch symbols that are functions
        # of other symbols
        for iteration in range(_MAX_PARAM_NESTING):
            obj = obj.xreplace(symbols)
            undefs = [x for x in obj.free_symbols if not isinstance(x, v.StateVariable)]
            if len(undefs) == 0:
                break
    except AttributeError:
        # Can't use xreplace on a float
        pass
    return obj

The calls to piecewise_fold and simplify here are crucial to getting the equations formatted into simple intervals that can be written to a DAT. I tried switching to symbol_replace as you highlighted, but it returns a nested piecewise equation that can't be used.

For more details of what needs to happen, you might look at my recent question on StackExchange.

There's probably another way to accomplish the goal here, but I don't fully understand the purpose of this function yet. I'd like to avoid reintroducing sympy as a dependency as much as possible

This isn't a great function. Basically I ran all these lines together in a couple of places, so I just grouped them into a function. All it is attempting to do is get the Gibbs reference energy equation into the same format whether it originated from a TDB (with nested piecewise) or a DAT (with just simple coefficients).

Piecewise equations have to be simplified as far as possible, but then I needed expand to get coefficients of simple powers of T.

After playing around with it, I'll add that simplified_parameter.simplify() doesn't yield the same results as simplify(simplified_parameter) (and the difference results in an error).