.. automodule:: sympy.sets.sets

.. autoclass:: Set
   :members:

.. autofunction:: imageset

.. autoclass:: Interval
   :members:

.. autoclass:: FiniteSet
   :members:

.. module:: sympy.sets.sets
    :noindex:

.. autoclass:: Union
   :members:

.. autoclass:: Intersection
   :members:

.. autoclass:: ProductSet
   :members:

.. autoclass:: Complement
   :members:

.. autoclass:: SymmetricDifference
   :members:

.. autoclass:: EmptySet
   :members:

.. autoclass:: UniversalSet
   :members:

.. automodule:: sympy.sets.fancysets

.. autoclass:: Naturals
   :members:

.. autoclass:: Naturals0
   :members:

.. autoclass:: Integers
   :members:

.. autoclass:: Reals
   :members:

.. autoclass:: Complexes
   :members:

.. autoclass:: ImageSet
   :members:

.. autoclass:: Range
   :members:

.. autoclass:: ComplexRegion
   :members:

.. autoclass:: CartesianComplexRegion
   :members:

.. autoclass:: PolarComplexRegion
   :members:

.. autofunction:: normalize_theta_set

.. automodule:: sympy.sets.powerset

.. autoclass:: PowerSet
   :members:

For set unions, {a, b} cup {x, y} can be treated as {a, b, x, y} for iteration regardless of the distinctiveness of the elements, however, for set intersections, assuming that {a, b} cap {x, y} is varnothing or {a, b } would not always be valid, since some of a, b, x or y may or may not be the elements of the intersection.

Iterating over the elements of a set involving intersection, complement, or symmetric difference yields (possibly duplicate) elements of the set provided that all elements are known to be the elements of the set. If any element cannot be determined to be a member of a set then the iteration gives TypeError. This happens in the same cases where x in y would give an error.

There are some reasons to implement like this, even if it breaks the consistency with how the python set iterator works. We keep in mind that sympy set comprehension like FiniteSet(*s) from a existing sympy sets could be a common usage. And this approach would make FiniteSet(*s) to be consistent with any symbolic set processing methods like FiniteSet(*simplify(s)).

.. automodule:: sympy.sets.conditionset

.. autoclass:: ConditionSet
    :members: