Better uninitialized checking; fixing doctests.

src/sage/combinat/species/recursive_species.py

@@ -230,7 +230,7 @@ def _gs(self, series_ring, base_ring):
 
             sage: F = CombinatorialSpecies()
             sage: F.generating_series()
-            Uninitialized Lazy Laurent Series
+            Uninitialized Lazy Series
         """
         if base_ring not in self._generating_series:
             self._generating_series[base_ring] = series_ring.undefined(valuation=(0 if self._min is None else self._min))
@@ -247,7 +247,7 @@ def _itgs(self, series_ring, base_ring):
 
             sage: F = CombinatorialSpecies()
             sage: F.isotype_generating_series()
-            Uninitialized Lazy Laurent Series
+            Uninitialized Lazy Series
         """
         if base_ring not in self._isotype_generating_series:
             self._isotype_generating_series[base_ring] = series_ring.undefined(valuation=(0 if self._min is None else self._min))
@@ -264,7 +264,7 @@ def _cis(self, series_ring, base_ring):
 
             sage: F = CombinatorialSpecies()
             sage: F.cycle_index_series()
-            Uninitialized Lazy Laurent Series
+            Uninitialized Lazy Series
         """
         if base_ring not in self._cycle_index_series:
             self._cycle_index_series[base_ring] = series_ring.undefined(valuation=(0 if self._min is None else self._min))

src/sage/data_structures/stream.py

@@ -1080,6 +1080,7 @@ def __init__(self, approximate_order, true_order=False):
             raise ValueError("the valuation must be specified for undefined series")
         super().__init__(False, true_order)
         self._approximate_order = approximate_order
+        self._initializing = False
 
     def iterate_coefficients(self):
         """
@@ -1113,7 +1114,15 @@ def is_uninitialized(self):
             sage: C.is_uninitialized()
             True
         """
-        return self._target is None
+        if self._target is None:
+            return True
+        if self._initializing:
+            return False
+        # We implement semaphore-like behavior for coupled (undefined) series
+        self._initializing = True
+        result = self._target.is_uninitialized()
+        self._initializing = False
+        return result
 
 
 class Stream_unary(Stream_inexact):

src/sage/rings/lazy_series.py

@@ -3594,7 +3594,8 @@ def exp(self):
         coeff_stream = self._coeff_stream
         # TODO: coefficients should not be checked here, it prevents
         # us from using self.define in some cases!
-        if any(coeff_stream[i] for i in range(coeff_stream._approximate_order, 1)):
+        if ((not coeff_stream.is_uninitialized())
+            and any(coeff_stream[i] for i in range(coeff_stream._approximate_order, 1))):
             raise ValueError("can only compose with a positive valuation series")
         # WARNING: d_self need not be a proper element of P, e.g. for
         # multivariate power series
@@ -3646,8 +3647,9 @@ def log(self):
         coeff_stream = self._coeff_stream
         # TODO: coefficients should not be checked here, it prevents
         # us from using self.define in some cases!
-        if (any(coeff_stream[i] for i in range(coeff_stream._approximate_order, 0))
-            or coeff_stream[0] != R.one()):
+        if ((not coeff_stream.is_uninitialized())
+            and (any(coeff_stream[i] for i in range(coeff_stream._approximate_order, 0))
+                 or coeff_stream[0] != R.one())):
             raise ValueError("can only compose with a positive valuation series")
         # WARNING: d_self need not be a proper element of P, e.g. for
         # multivariate power series