doc/domain.rst

   1 Domains Module
   2 ==============
   3
   4 .. py:class :: Domain
   5
   6     The properties of a domain can be are found using the following
   7
   8     .. py:method:: symbols
   9
  10         Returns a tuple of the symbols that exsist in a domain.
  11
  12     .. py:method:: dimension
  13
  14         Returns the number of variables that exist in a domain.
  15
  16     .. py:method:: disjoint
  17
  18         Returns a domain as disjoint.
  19
  20     .. py:method:: involves_vars(self, vars)
  21
  22        Returns ``True`` if a domain depends on the given variables.
  23
  24
  25     The unary properties of a domain can be inspected using the following methods.
  26
  27     .. py:method:: isempty(self)
  28
  29         Return ``True`` is a domain is empty.
  30
  31     .. py:method:: isuniverse(self)
  32
  33         Return ``True`` if a domain is the Universe set.
  34
  35     .. py:method:: isbounded(self)
  36
  37         Return ``True`` if a domain is bounded.
  38
  39     .. py:method:: disjoint(self)
  40
  41         It is not guarenteed that a domain is disjoint. If it is necessary, this method will return a domain as disjoint.
  42
  43     The following methods compare two domains to find the binary properties.
  44
  45     .. py:method:: isdisjoint(self, other)
  46
  47         Return ``True`` if the intersection of *self* and *other* results in an empty set.
  48
  49     .. py:method:: issubset(self, other)
  50
  51         Test whether every element in a domain is in *other*.
  52
  53     .. py:method:: __eq__(self, other)
  54                    self == other
  55
  56         Test whether a domain is equal to *other*.
  57
  58     .. py:method:: __lt__(self, other)
  59                    self < other
  60
  61         Test whether a domain is a strict subset of *other*.
  62
  63     .. py:method:: __le__(self, other)
  64                    self <= other
  65
  66         Test whether every element in a domain is in *other*.
  67
  68     .. py:method:: __gt__(self, other)
  69                    self > other
  70
  71         Test whether a domain is a strict superset of *other*.
  72
  73     .. py:method:: __ge__(self, other)
  74                    self >= other
  75
  76        Test whether every element in *other* is in a domain.
  77
  78
  79     The following methods implement unary operations on a domain.
  80
  81     .. py:method:: complement(self)
  82                    ¬self
  83
  84         Return the complement of a domain.
  85
  86     .. py:method:: simplify(self)
  87
  88         Return a new domain without any redundant constraints.
  89
  90     .. py:method:: project(self, dims)
  91
  92         Return a new domain with the given dimensions removed.
  93
  94     .. py:method:: aspolyhedron(self)
  95
  96         Return polyhedral hull of a domain.
  97
  98     .. py:method:: sample(self)
  99
 100         Return a single sample subset of a domain.
 101
 102     The following methods implement binary operations on two domains.
 103
 104     .. py:method:: intersection(self, other)
 105                    self | other
 106
 107         Return a new domain with the elements that are common between *self* and *other*.
 108
 109     .. py:method:: union(self, other)
 110                    self & other
 111
 112         Return a new domain with all the elements from *self* and *other*.
 113
 114     .. py:method:: difference(self, other)
 115                    self - other
 116
 117         Return a new domain with the elements in a domain that are not in *other* .
 118
 119     .. py:method:: __add__(self, other)
 120                    self + other
 121
 122         Return the sum of two domains.
 123
 124     The following methods use lexicographical ordering to find the maximum or minimum element in a domain.
 125
 126     .. py:method:: lexmin(self)
 127
 128         Return a new set containing the lexicographic minimum of the elements in the set.
 129
 130     .. py:method:: lexmax(self)
 131
 132         Return a new set containing the lexicographic maximum of the elements in the set.
 133
 134
 135     A 2D or 3D domain can be plotted using the :meth:`plot` function. The points, verticies, and faces of a domain can be inspected using the following functions.
 136
 137     .. py:method:: points(self)
 138
 139         Return a list of the points contained in a domain as :class:`Points` objects.
 140
 141     .. py:method:: vertices(self)
 142
 143         Return a list of the verticies of a domain.
 144
 145     .. py:method:: faces(self)
 146
 147         Return a list of the vertices for each face of a domain.
 148
 149     .. py:method:: plot(self, plot=None, **kwargs)
 150
 151         Return a plot of the given domain.
 152
 153
 154