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:: num_parameters
  21
  22         Returns the total number of parameters, input, output or dimensions in a domain.
  23
  24     .. py:method:: involves_dims(self, dims)
  25
  26        Returns ``True`` if a domain depends on the given dimensions.
  27
  28     The unary properties of a domain can be inspected using the following methods.
  29
  30     .. py:method:: isempty(self)
  31
  32         Return ``True`` is a domain is empty.
  33
  34     .. py:method:: isuniverse(self)
  35
  36         Return ``True`` if a domain is the Universe set.
  37
  38     .. py:method:: isbounded(self)
  39
  40         Return ``True`` if a domain is bounded.
  41
  42     .. py:method:: disjoint(self)
  43
  44         It is not guarenteed that a domain is disjoint. If it is necessary, this method will return a domain as disjoint.
  45
  46     The following methods compare two domains to find the binary properties.
  47
  48     .. py:method:: isdisjoint(self, other)
  49
  50         Return ``True`` if the intersection of *self* and *other* results in an empty set.
  51
  52     .. py:method:: issubset(self, other)
  53
  54         Test whether every element in a domain is in *other*.
  55
  56     .. py:method:: __eq__(self, other)
  57                    self == other
  58
  59         Test whether a domain is equal to *other*.
  60
  61     .. py:method:: __lt__(self, other)
  62                    self < other
  63
  64         Test whether a domain is a strict subset of *other*.
  65
  66     .. py:method:: __le__(self, other)
  67                    self <= other
  68
  69         Test whether every element in a domain is in *other*.
  70
  71     .. py:method:: __gt__(self, other)
  72                    self > other
  73
  74         Test whether a domain is a strict superset of *other*.
  75
  76     .. py:method:: __ge__(self, other)
  77                    self >= other
  78
  79        Test whether every element in *other* is in a domain.
  80
  81
  82     The following methods implement unary operations on a domain.
  83
  84     .. py:method:: complement(self)
  85                    ¬self
  86
  87         Return the complement of a domain.
  88
  89     .. py:method:: simplify(self)
  90
  91         Return a new domain without any redundant constraints.
  92
  93     .. py:method:: project(self, dims)
  94
  95         Return a new domain with the given dimensions removed.
  96
  97     .. py:method:: aspolyhedron(self)
  98
  99         Return polyhedral hull of a domain.
 100
 101     .. py:method:: sample(self)
 102
 103         Return a single sample subset of a domain.
 104
 105     The following methods implement binary operations on two domains.
 106
 107     .. py:method:: intersection(self, other)
 108                    self | other
 109
 110         Return a new domain with the elements that are common between *self* and *other*.
 111
 112     .. py:method:: union(self, other)
 113                    self & other
 114
 115         Return a new domain with all the elements from *self* and *other*.
 116
 117     .. py:method:: difference(self, other)
 118                    self - other
 119
 120         Return a new domain with the elements in a domain that are not in *other* .
 121
 122     .. py:method:: __add__(self, other)
 123                    self + other
 124
 125         Return the sum of two domains.
 126
 127     The following methods use lexicographical ordering to find the maximum or minimum element in a domain.
 128
 129     .. py:method:: lexmin(self)
 130
 131         Return a new set containing the lexicographic minimum of the elements in the set.
 132
 133     .. py:method:: lexmax(self)
 134
 135         Return a new set containing the lexicographic maximum of the elements in the set.
 136
 137
 138     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.
 139
 140     .. py:method:: points(self)
 141
 142         Return a list of the points contained in a domain as :class:`Points` objects.
 143
 144     .. py:method:: vertices(self)
 145
 146         Return a list of the verticies of a domain.
 147
 148     .. py:method:: faces(self)
 149
 150         Return a list of the vertices for each face of a domain.
 151
 152     .. py:method:: plot(self, plot=None, **kwargs)
 153
 154         Return a plot of the given domain.
 155
 156
 157