detection of infinite solution request

[smichr]

>>> solve_poly_system((x - 1,), x, y)
Traceback (most recent call last):
...
NotImplementedError:
only zero-dimensional systems supported (finite number of solutions)
>>> solve_poly_system((y - 1,), x, y)  <--- this is not handled correctly
[(1,)]

diff --git a/sympy/solvers/polysys.py b/sympy/solvers/polysys.py
index b9809fd4e9..674322d4eb 100644
--- a/sympy/solvers/polysys.py
+++ b/sympy/solvers/polysys.py
@@ -240,7 +240,7 @@ def _solve_reduced_system(system, gens, entry=False):
 
         univariate = list(filter(_is_univariate, basis))
 
-        if len(univariate) == 1:
+        if len(univariate) == 1 and len(gens) == 1:
             f = univariate.pop()
         else:
             raise NotImplementedError(filldedent('''
diff --git a/sympy/solvers/tests/test_polysys.py b/sympy/solvers/tests/test_polysys.py
index 58419f8762..9e674a6fe6 100644
--- a/sympy/solvers/tests/test_polysys.py
+++ b/sympy/solvers/tests/test_polysys.py
@@ -48,6 +48,10 @@ def test_solve_poly_system():
     raises(NotImplementedError, lambda: solve_poly_system(
         [z, -2*x*y**2 + x + y**2*z, y**2*(-z - 4) + 2]))
     raises(PolynomialError, lambda: solve_poly_system([1/x], x))
+    raises(NotImplementedError, lambda: solve_poly_system(
+        Poly(x - 1, x, y), (x, y)))
+    raises(NotImplementedError, lambda: solve_poly_system(
+        Poly(y - 1, x, y), (x, y)))
 
 
 def test_solve_biquadratic():

[praneethratna]

This is not a possible solution i feel , since some of the tests are failing and also weirdly solve_poly_system([2*x - 3, y*Rational(3, 2) - 2*x, z - 5*y], x, y, z) is throwing a NotImplementedError .

[smichr]

Hmm. Well, they should yield similar results: an error or a solution. Looks like maybe a solution, then, should be returned? I am not sure. Maybe @jksuom would have some idea.

[jksuom]

It seems that the number of polynomials in the Gröbner basis should be the same as the number of variables so there should be something like

    if len(basis) != len(gens):
        raise NotImplementedError(...)

[praneethratna]

It seems that the number of polynomials in the Gröbner basis should be the same as the number of variables

This raises a NotImplementedError for solve_poly_system([x*y - 2*y, 2*y**2 - x**2], x, y) but which isn't the case since it has a solution.

[jksuom]

It looks like the test could be if len(basis) < len(gens) though I'm not sure if the implementation can handle all cases where len(basis) > len(gens).

[praneethratna]

Yes this works and now solve_poly_system((y - 1,), x, y) also returns NotImplementedError , I'll open a PR for this.
I'm not sure but all cases of len(basis) > len(gens) are being handled.