UnboundLocalError in nonlinsolve

[proy87]

nonlinsolve((4*y*(2*x + 2*exp(y) + 1)*exp(2*x), 4*x*exp(2*x) + 4*y*exp(2*x + y) + 4*exp(2*x + y) + 1), x,y)

raises UnboundLocalError: local variable 'exp_invs' referenced before assignment.

[oscargus]

Do you think that

is the correct answer?

[proy87]

@oscargus , (x,0) doesn't satisfy the second equation.

[oscargus]

OK! Then my simple fix didn't work... (I was not sure how to interpret the results...)

[oscargus]

The problem is that g_ys is EmptySet here:

sympy/sympy/solvers/solveset.py

Lines 363 to 378 in 700a4a1

	if isinstance(f, exp) or (f.is_Pow and f.base == S.Exp1):
	if isinstance(g_ys, ImageSet):
	# can solve upto `(d*exp(exp(...(exp(a*x + b))...) + c)` format.
	# Further can be improved to `(d*exp(exp(...(exp(a*x**n + b*x**(n-1) + ... + f))...) + c)`.
	g_ys_expr = g_ys.lamda.expr
	g_ys_vars = g_ys.lamda.variables
	k = Dummy('k{}'.format(len(g_ys_vars)))
	g_ys_vars_1 = (k,) + g_ys_vars
	exp_invs = Union(*[imageset(Lambda((g_ys_vars_1,), (I*(2*k*pi + arg(g_ys_expr))
	+ log(Abs(g_ys_expr)))), S.Integers**(len(g_ys_vars_1)))])
	elif isinstance(g_ys, FiniteSet):
	exp_invs = Union(*[imageset(Lambda(n, I*(2*n*pi + arg(g_y)) +
	log(Abs(g_y))), S.Integers)
	for g_y in g_ys if g_y != 0])
	return _invert_complex(f.exp, exp_invs, symbol)

Just adding a check for EmptySet here:

sympy/sympy/solvers/solveset.py

Lines 326 to 327 in 700a4a1

	if f == symbol:
	return (f, g_ys)

is what I tried and it returns the incorrect result.

So something more clever should be returned by an additional if-statement at the end of the first piece of code.

[oscargus]

I'm tempted to believe that the correct way to get away with the error is to change 326 to:

if f == symbol or g_ys == EmptySet:

and that the incorrect result comes from elsewhere (I seem to recall that nonlinsolve/substitution sometimes give incorrect results).

One should maybe add a corresponding fast exit for _invert_real for performance reasons.

[proy87]

@oscargus , if g_ys is EmptySet, shouldn't it return EmptySet, because f(x)=EmptySet is EmptySet?

[oscargus]

It will since it returns (f, g_ys).

[oscargus]

I created a PR that avoids the error, but returns the incorrect solution. So this remains to be fixed in the issue. (I am quite sure that I have not introduced the incorrect result by fixing the error.)