ImageSubobject.cardinality: Handle infinite cardinalities explicitly

src/sage/sets/image_set.py

@@ -23,6 +23,7 @@
 from sage.categories.sets_cat import Sets
 from sage.categories.enumerated_sets import EnumeratedSets
 from sage.misc.cachefunc import cached_method
+from sage.rings.infinity import Infinity
 from sage.rings.integer import Integer
 from sage.modules.free_module import FreeModule
 from sage.structure.element import Expression
@@ -265,11 +266,27 @@ def cardinality(self) -> Integer:
  sage: Z4711 = ImageSet(lambda x: x**4 % 11, Z7, is_injective=False)
  sage: Z4711.cardinality()
  6
+
+ sage: Squares = ImageSet(lambda x: x^2, ZZ, is_injective=False,
+ ....: category=Sets().Infinite())
+ sage: Squares.cardinality()
+ +Infinity
+
+ sage: Mod2 = ZZ.map(lambda x: x % 2, is_injective=False)
+ sage: Mod2.cardinality()
+ Traceback (most recent call last):
+ ...
+ NotImplementedError: cannot determine cardinality of a non-injective image of an infinite set
  """
+ domain_cardinality = self._domain_subset.cardinality()
  if self._is_injective and self._is_injective != 'check':
- return self._domain_subset.cardinality()
+ return domain_cardinality
+ if self in Sets().Infinite():
+ return Infinity
+ if domain_cardinality == Infinity:
+ raise NotImplementedError('cannot determine cardinality of a non-injective image of an infinite set')
  # Fallback like EnumeratedSets.ParentMethods.__len__
- return Integer(len(list(self)))
+ return Integer(len(list(iter(self))))
 
  def __iter__(self) -> Iterator:
  r"""