Fixing a broken doctest by better testing for 0; using self.one().

src/sage/data_structures/stream.py

@@ -3358,7 +3358,7 @@ def _advance(self):
         """
         if self._cur is None:
             temp = next(self._op_iter)
-            if not temp:
+            if isinstance(temp._coeff_stream, Stream_zero):
                 self._advance()
                 return
             self.initial(temp)
@@ -3370,7 +3370,7 @@ def _advance(self):
             except StopIteration:
                 self._cur_order = infinity
                 return
-            if not next_factor:
+            if isinstance(next_factor._coeff_stream, Stream_zero):
                 continue
             coeff_stream = next_factor._coeff_stream
             while coeff_stream._approximate_order < order:

src/sage/rings/lazy_series_ring.py

@@ -974,7 +974,7 @@ def prod(self, f, a=None, b=infinity, add_one=False):
         elif a in ZZ:
             if b != infinity:
                 if add_one:
-                    return super().prod(1 + f(i) for i in range(a, b+1))
+                    return super().prod(self.one() + f(i) for i in range(a, b+1))
                 return super().prod(f(i) for i in range(a, b+1))
             from sage.sets.non_negative_integers import NonNegativeIntegers
             it = (f(i+a) for i in NonNegativeIntegers())
@@ -983,7 +983,7 @@ def prod(self, f, a=None, b=infinity, add_one=False):
 
         # NOTE: We must have a new variable name for each new iterator
         if not add_one:
-            data = (g - 1 for g in it)
+            data = (g - self.one() for g in it)
         else:
             data = it