Hugging Face's logo

Spaces:
kabuda777
/
Code2MCP-sympy
Sleeping

App Files Community
Code2MCP-sympy
File size: 2,668 Bytes
b66f126
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
.. _sets-module:

====
Sets
====

Basic Sets
----------

.. automodule:: sympy.sets.sets

.. autoclass:: Set
   :members:

.. autofunction:: imageset

Elementary Sets
---------------

.. autoclass:: Interval
   :members:

.. autoclass:: FiniteSet
   :members:

Compound Sets
-------------

.. autoclass:: Union
   :members:

.. autoclass:: Intersection
   :members:

.. autoclass:: ProductSet
   :members:

.. autoclass:: Complement
   :members:

.. autoclass:: SymmetricDifference
   :members:

.. autoclass:: DisjointUnion
   :members:

Singleton Sets
--------------

.. autoclass:: EmptySet
   :members:

.. autoclass:: UniversalSet
   :members:

Special Sets
------------
.. automodule:: sympy.sets.fancysets

.. autoclass:: Rationals
   :members:

.. 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

Power sets
----------

.. automodule:: sympy.sets.powerset

.. autoclass:: PowerSet
   :members:


Condition Sets
--------------

.. automodule:: sympy.sets.conditionset


.. autoclass:: ConditionSet
   :members:


.. autoclass:: Contains
   :members:

SetKind
-------

.. autoclass:: SetKind
   :members:

Iteration over sets
-------------------

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))``.