Regression in solveset for quadratic with symbolic coefficients

[oscarbenjamin]

This is a regression since sympy 1.8. On 1.8 we have:

In [1]: x, t = symbols('x, t')

In [2]: solveset(-sqrt(t)*x**2 + 2*x + sqrt(t), x, Reals)
Out[2]: 
    ⎧    _______         _______     ⎫
    ⎪  ╲╱ t + 1    1   ╲╱ t + 1    1 ⎪
ℝ ∩ ⎨- ───────── + ──, ───────── + ──⎬
    ⎪      √t      √t      √t      √t⎪
    ⎩                                ⎭

However on master that's:

In [11]: x, t = symbols('x, t')

In [12]: solveset(-sqrt(t)*x**2 + 2*x + sqrt(t), x, Reals)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-2-689112688710> in <module>
----> 1 solveset(-sqrt(t)*x**2 + 2*x + sqrt(t), x, Reals)

~/current/sympy/sympy/sympy/solvers/solveset.py in solveset(f, symbol, domain)
   2215     if symbol not in _rc:
   2216         x = _rc[0] if domain.is_subset(S.Reals) else _rc[1]
-> 2217         rv = solveset(f.xreplace({symbol: x}), x, domain)
   2218         # try to use the original symbol if possible
   2219         try:

~/current/sympy/sympy/sympy/solvers/solveset.py in solveset(f, symbol, domain)
   2239     f = piecewise_fold(f)
   2240 
-> 2241     return _solveset(f, symbol, domain, _check=True)
   2242 
   2243 

~/current/sympy/sympy/sympy/solvers/solveset.py in _solveset(f, symbol, domain, _check)
   1068                     u = unrad(f)
   1069                     if u:
-> 1070                         result += _solve_radical(equation, u,
   1071                                                  symbol,
   1072                                                  solver)

~/current/sympy/sympy/sympy/solvers/solveset.py in _solve_radical(f, unradf, symbol, solveset_solver)
    868         f_set = []  # solutions for FiniteSet
    869         c_set = []  # solutions for ConditionSet
--> 870         for s in result:
    871             if checksol(f, symbol, s):
    872                 f_set.append(s)

~/current/sympy/sympy/sympy/sets/sets.py in __iter__(self)
   1424             if not candidates:
   1425                 raise TypeError("None of the constituent sets are iterable")
-> 1426             raise TypeError(
   1427                 "The computation had not completed because of the "
   1428                 "undecidable set membership is found in every candidates.")

TypeError: The computation had not completed because of the undecidable set membership is found in every candidates.

There is a bug in solveset attempting to iterate over an Intersection(FiniteSet(sol1, sol2), Reals).

Bisected to 651595d from #21276.

CC @smichr

[oscarbenjamin]

The problem is these lines:

sympy/sympy/solvers/solveset.py

Lines 865 to 875 in 9cb75ab

	if isinstance(result, (Complement, ConditionSet)):
	solution_set = result
	else:
	f_set = [] # solutions for FiniteSet
	c_set = [] # solutions for ConditionSet
	for s in result:
	if checksol(f, symbol, s):
	f_set.append(s)
	else:
	c_set.append(s)
	solution_set = FiniteSet(*f_set) + ConditionSet(symbol, Eq(f, 0), FiniteSet(*c_set))

Here it is assumed that if the result is not Complement or ConditionSet then it must be iterable.

Maybe Set.is_iterable should be improved so that the check could instead be something like

if result.is_iterable and result.is_finite_set:

[smichr]

Where did you find that test?

[oscarbenjamin]

The example is a simplified version of the problem in #20370