raise ValueError in case (in)equality is not decidable

src/sage/data_structures/stream.py

@@ -937,6 +937,23 @@ def iterate_coefficients(self):
             yield self._target[n]
             n += 1
 
+    def is_nonzero(self):
+        r"""
+        Return ``True`` if and only if this stream is known
+        to be nonzero.
+
+        An assumption of this class is that it is nonzero.
+
+        EXAMPLES::
+
+            sage: from sage.data_structures.stream import Stream_uninitialized
+            sage: g = Stream_uninitialized(0)
+            sage: g.is_nonzero()
+            True
+        """
+        if self._target is None:
+            return True
+        return super().is_nonzero()
 
 class Stream_unary(Stream_inexact):
     r"""

src/sage/rings/lazy_series.py

@@ -938,9 +938,13 @@ def _richcmp_(self, other, op):
 
             sage: fz = L(lambda n: 0, valuation=0)
             sage: L.zero() == fz
-            False
+            Traceback (most recent call last):
+            ...
+            ValueError: undecidable
             sage: fz == L.zero()
-            False
+            Traceback (most recent call last):
+            ...
+            ValueError: undecidable
 
         TESTS::
 
@@ -952,13 +956,15 @@ def _richcmp_(self, other, op):
 
         """
         if op is op_EQ:
-            prec = self.parent().options['halting_precision']
-            if prec is None:
-                return self._coeff_stream == other._coeff_stream
-
             # they may be trivially equal
             if self._coeff_stream == other._coeff_stream:
                 return True
+            # they may be trivially different
+            if self._coeff_stream != other._coeff_stream:
+                return False
+            prec = self.parent().options['halting_precision']
+            if prec is None:
+                raise ValueError("undecidable")
             # otherwise we check the first prec coefficients
             m = min(self._coeff_stream._approximate_order,
                     other._coeff_stream._approximate_order)
@@ -1003,7 +1009,9 @@ def __bool__(self):
             sage: M = L(lambda n: 2*n if n < 10 else 1, valuation=0); M
             O(z^7)
             sage: bool(M)
-            True
+            Traceback (most recent call last):
+            ...
+            ValueError: undecidable
             sage: M[15]
             1
             sage: bool(M)
@@ -1013,7 +1021,9 @@ def __bool__(self):
             sage: M = L(lambda n: 2*n if n < 10 else 1, valuation=0); M
             O(z^7)
             sage: bool(M)
-            True
+            Traceback (most recent call last):
+            ...
+            ValueError: undecidable
             sage: M[15]
             1
             sage: bool(M)
@@ -1040,9 +1050,11 @@ def __bool__(self):
             True
             sage: g.define(1 + z*g)
             sage: bool(g)
-            True
+            Traceback (most recent call last):
+            ...
+            ValueError: undecidable
         """
-        return bool(self._coeff_stream)
+        return not (self == self.parent().zero())
 
     def define(self, s):
         r"""
@@ -1716,7 +1728,9 @@ def _acted_upon_(self, scalar, self_on_left):
         Different scalars potentially give different series::
 
             sage: 2 * M == 3 * M
-            False
+            Traceback (most recent call last):
+            ...
+            ValueError: undecidable
 
         Sparse series can be multiplied with a scalar::
 

src/sage/rings/lazy_series_ring.py

@@ -664,8 +664,8 @@ class options(GlobalOptions):
                                description='the number of coefficients to display for nonzero constant series',
                                checker=lambda x: x in ZZ and x > 0)
         halting_precision = dict(default=None,
-                               description='the number of coefficients, beginning with the approximate valuation, to check in equality tests',
-                               checker=lambda x: x is None or x in ZZ and x > 0)
+                                 description='the number of coefficients, beginning with the approximate valuation, to check in equality tests',
+                                 checker=lambda x: x is None or x in ZZ and x > 0)
 
     @cached_method
     def one(self):
@@ -1117,7 +1117,9 @@ class LazyLaurentSeriesRing(LazySeriesRing):
         sage: f2 = f * 2  # currently no coefficients computed
         sage: f3 = f * 3  # currently no coefficients computed
         sage: f2 == f3
-        False
+        Traceback (most recent call last):
+        ...
+        ValueError: undecidable
         sage: f2  # computes some of the coefficients of f2
         2*z^-1 - 2 + 2*z - 2*z^2 + 2*z^3 - 2*z^4 + 2*z^5 + O(z^6)
         sage: f3  # computes some of the coefficients of f3