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