1====
2Sets
3====
4
5Basic Sets
6----------
7
8.. automodule:: sympy.sets.sets
9
10Set
11^^^
12.. autoclass:: Set
13   :members:
14
15.. autofunction:: imageset
16
17Elementary Sets
18---------------
19
20Interval
21^^^^^^^^
22.. autoclass:: Interval
23   :members:
24
25FiniteSet
26^^^^^^^^^
27.. autoclass:: FiniteSet
28   :members:
29
30Compound Sets
31-------------
32
33.. module:: sympy.sets.sets
34    :noindex:
35
36Union
37^^^^^
38.. autoclass:: Union
39   :members:
40
41Intersection
42^^^^^^^^^^^^
43.. autoclass:: Intersection
44   :members:
45
46ProductSet
47^^^^^^^^^^
48.. autoclass:: ProductSet
49   :members:
50
51Complement
52^^^^^^^^^^
53.. autoclass:: Complement
54   :members:
55
56SymmetricDifference
57^^^^^^^^^^^^^^^^^^^
58.. autoclass:: SymmetricDifference
59   :members:
60
61Singleton Sets
62--------------
63
64EmptySet
65^^^^^^^^
66.. autoclass:: EmptySet
67   :members:
68
69UniversalSet
70^^^^^^^^^^^^
71.. autoclass:: UniversalSet
72   :members:
73
74Special Sets
75------------
76.. automodule:: sympy.sets.fancysets
77
78Naturals
79^^^^^^^^
80.. autoclass:: Naturals
81   :members:
82
83Naturals0
84^^^^^^^^^
85.. autoclass:: Naturals0
86   :members:
87
88Integers
89^^^^^^^^
90.. autoclass:: Integers
91   :members:
92
93
94Reals
95^^^^^
96.. autoclass:: Reals
97   :members:
98
99Complexes
100^^^^^^^^^
101.. autoclass:: Complexes
102   :members:
103
104ImageSet
105^^^^^^^^
106.. autoclass:: ImageSet
107   :members:
108
109Range
110^^^^^
111.. autoclass:: Range
112   :members:
113
114ComplexRegion
115^^^^^^^^^^^^^
116.. autoclass:: ComplexRegion
117   :members:
118
119.. autoclass:: CartesianComplexRegion
120   :members:
121
122.. autoclass:: PolarComplexRegion
123   :members:
124
125.. autofunction:: normalize_theta_set
126
127Power sets
128----------
129
130.. automodule:: sympy.sets.powerset
131
132PowerSet
133^^^^^^^^
134.. autoclass:: PowerSet
135   :members:
136
137Iteration over sets
138^^^^^^^^^^^^^^^^^^^
139
140For set unions, `\{a, b\} \cup \{x, y\}` can be treated as
141`\{a, b, x, y\}` for iteration regardless of the distinctiveness of
142the elements, however, for set intersections, assuming that
143`\{a, b\} \cap \{x, y\}` is `\varnothing` or `\{a, b \}` would not
144always be valid, since some of `a`, `b`, `x` or `y` may or may not be
145the elements of the intersection.
146
147Iterating over the elements of a set involving intersection, complement,
148or symmetric difference yields (possibly duplicate) elements of the set
149provided that all elements are known to be the elements of the set.
150If any element cannot be determined to be a member of a set then the
151iteration gives ``TypeError``.
152This happens in the same cases where ``x in y`` would give an error.
153
154There are some reasons to implement like this, even if it breaks the
155consistency with how the python set iterator works.
156We keep in mind that sympy set comprehension like ``FiniteSet(*s)`` from
157a existing sympy sets could be a common usage.
158And this approach would make ``FiniteSet(*s)`` to be consistent with any
159symbolic set processing methods like ``FiniteSet(*simplify(s))``.
160
161Condition Sets
162--------------
163
164.. automodule:: sympy.sets.conditionset
165
166ConditionSet
167^^^^^^^^^^^^
168
169.. autoclass:: ConditionSet
170   :members:
171
172Relations on sets
173^^^^^^^^^^^^^^^^^
174
175.. autoclass:: Contains
176   :members:
177