sympify TypeError "Invalid comparison of complex zoo" with '1<zoo'

[ducktalez]

I reduced my problem to this expression:
sympy.sympify('1<zoo')
Which will raise a TypeError:
TypeError: Invalid comparison of complex zoo

zoo occurs during an 'accidental' division by zero that seldomly occurs. The original comparisson also has nothing to do with complex numbers: 1<1/(a-a). And, of course, this expression does not make sense.

However, I expected sympy to evaluate to 'nan' and not to crash.
Is this intentionally?
Is there a way to return 'nan' without a try-block? Or specify fail-evaluations as proposed somewhere in #5195 so I could choose a (signed) oo instead of zoo to have a secure evaluation?

.

Complete Exception:

>>> import sympy
>>> sympy.sympify('1<zoo')
Traceback (most recent call last):
  File "C:\ProgramData\Anaconda3\lib\site-packages\IPython\core\interactiveshell.py", line 3296, in run_code
    exec(code_obj, self.user_global_ns, self.user_ns)
  File "<ipython-input-112-fa2832916d99>", line 1, in <module>
    sympy.sympify('1<zoo')
  File "C:\ProgramData\Anaconda3\lib\site-packages\sympy\core\sympify.py", line 368, in sympify
    expr = parse_expr(a, local_dict=locals, transformations=transformations, evaluate=evaluate)
  File "C:\ProgramData\Anaconda3\lib\site-packages\sympy\parsing\sympy_parser.py", line 965, in parse_expr
    return eval_expr(code, local_dict, global_dict)
  File "C:\ProgramData\Anaconda3\lib\site-packages\sympy\parsing\sympy_parser.py", line 878, in eval_expr
    code, global_dict, local_dict)  # take local objects in preference
  File "<string>", line 1, in <module>
  File "C:\ProgramData\Anaconda3\lib\site-packages\sympy\core\numbers.py", line 2185, in __lt__
    return Rational.__lt__(self, other)
  File "C:\ProgramData\Anaconda3\lib\site-packages\sympy\core\numbers.py", line 1818, in __lt__
    return Expr.__lt__(expr, other)
  File "C:\ProgramData\Anaconda3\lib\site-packages\sympy\core\expr.py", line 334, in __lt__
    raise TypeError("Invalid comparison of complex %s" % me)
TypeError: Invalid comparison of complex zoo

[oscarbenjamin]

There is no way to know whether 1/0 is positive or negative so evaluating to oo rather than -oo is not correct.

I think there is an issue somewhere that proposes that something like 1 < zoo could just be False.