Fix various generator bugs

src/sage/combinat/boltzmann_sampling/generator.pyx

@@ -273,6 +273,10 @@ cdef c_gen(first_rule, rules, int size_min, int size_max, int max_retry, builder
 cdef inline identity(x):
     return x
 
+cdef inline first(x):
+    a, __ = x
+    return a
+
 def UnionBuilder(*builders):
     """Helper for computing the builder of a union out of the builders of its
     components in Boltzmann samplers. For instance, in order to compute the
@@ -317,11 +321,11 @@ cdef make_default_builder(rule):
     if isinstance(rule, Ref):
         return identity
     elif isinstance(rule, Atom):
-        return identity
-    elif isinstance(rule, Product):
+        return first
+    elif isinstance(rule, Union):
         subbuilders = [make_default_builder(component) for component in rule.args]
         return UnionBuilder(*subbuilders)
-    elif isinstance(rule, Union):
+    elif isinstance(rule, Product):
         subbuilders = [make_default_builder(component) for component in rule.args]
         return ProductBuilder(subbuilders)
 
@@ -386,7 +390,7 @@ class Generator:
     def _precompute_oracle_values(self, z):
         return [
             self.oracle.eval_rule(self.id_to_name[rule_id], z)
-            for rule_id in range(len(self.flat_rules))
+            for rule_id in range(len(self.id_to_name))
         ]
 
     def gen(self, name, window, max_retry=2000, singular=True):
@@ -422,6 +426,7 @@ class Generator:
                 self.singularity = values[atom_name]
                 z = self.singularity
                 self.oracle_cache[z] = values
+            z = self.singularity
         else:
             raise NotImplementedError("Non-singular generation")
         if z not in self.oracle_cache:
@@ -434,7 +439,7 @@ class Generator:
             self.grammar.rules
         )
         # Generate
-        first_rule = flat_rules[self.name_to_id[name]]
+        first_rule = (REF, self.oracle_cache[z][name], self.name_to_id[name])
         statistics, obj = c_gen(
             first_rule,
             flat_rules,