doc/domain.rst

   1 Domains Module
   2 ==============
   3
   4 This module provides classes and functions to deal with polyhedral
   5 domains, i.e. unions of polyhedra.
   6
   7 .. py:class :: Domain
   8
   9     This class represents polyhedral domains, i.e. unions of polyhedra.
  10
  11     .. py:method:: __new__(cls, *polyhedra)
  12
  13        Create and return a new domain from a string or a list of polyhedra.
  14
  15     .. attribute:: polyhedra
  16
  17        The tuple of polyhedra which constitute the domain.
  18
  19     .. attribute:: symbols
  20
  21         Returns a tuple of the symbols that exsist in a domain.
  22
  23     .. attribute:: dimension
  24
  25         Returns the number of variables that exist in a domain.
  26
  27     .. py:method:: isempty(self)
  28
  29         Return ``True`` is a domain is empty.
  30
  31     .. py:method:: __bool__(self)
  32
  33         Return ``True`` if the domain is non-empty.
  34
  35     .. py:method:: isuniverse(self)
  36
  37         Return ``True`` if a domain is the Universe set.
  38
  39     .. py:method:: isbounded(self)
  40
  41         Return ``True`` if a domain is bounded.
  42
  43     .. py:method:: make_disjoint(self)
  44
  45         It is not guarenteed that a domain is disjoint. If it is necessary, this method will return an equivalent domain, whose polyhedra are disjoint.
  46
  47     .. py:method:: isdisjoint(self, other)
  48
  49         Return ``True`` if the intersection of *self* and *other* results in an empty set.
  50
  51     .. py:method:: issubset(self, other)
  52
  53         Test whether every element in a domain is in *other*.
  54
  55     .. py:method:: __eq__(self, other)
  56                    self == other
  57
  58         Test whether a domain is equal to *other*.
  59
  60     .. py:method:: __lt__(self, other)
  61                    self < other
  62
  63         Test whether a domain is a strict subset of *other*.
  64
  65     .. py:method:: __le__(self, other)
  66                    self <= other
  67
  68         Test whether every element in a domain is in *other*.
  69
  70     .. py:method:: __gt__(self, other)
  71                    self > other
  72
  73         Test whether a domain is a strict superset of *other*.
  74
  75     .. py:method:: __ge__(self, other)
  76                    self >= other
  77
  78        Test whether every element in *other* is in a domain.
  79
  80     .. py:method:: complement(self)
  81                    ~self
  82
  83         Return the complementary domain of a domain.
  84
  85     .. py:method:: coalesce(self)
  86
  87        Simplify the representation of the domain by trying to combine pairs of
  88         polyhedra into a single polyhedron.
  89
  90
  91     .. py:method:: detect_equalities(self)
  92
  93         Simplify the representation of the domain by detecting implicit
  94         equalities.
  95
  96     .. py:method:: simplify(self)
  97
  98         Return a new domain without any redundant constraints.
  99
 100     .. py:method:: project(self, variables)
 101
 102         Return a new domain with the given variables removed.
 103
 104     .. py:method:: aspolyhedron(self)
 105
 106         Return polyhedral hull of a domain.
 107
 108     .. py:method:: sample(self)
 109
 110         Return a single sample subset of a domain.
 111
 112     .. py:method:: intersection(self, other)
 113                    __or__
 114                    self | other
 115
 116         Return a new domain with the elements that are common between *self* and *other*.
 117
 118     .. py:method:: union(self, other)
 119                    __and__
 120                    self & other
 121
 122         Return a new domain with all the elements from *self* and *other*.
 123
 124     .. py:method:: difference(self, other)
 125                    __sub__
 126                    self - other
 127
 128         Return a new domain with the elements in a domain that are not in *other* .
 129
 130     .. py:method:: __add__(self, other)
 131                    self + other
 132
 133         Return the sum of two domains.
 134
 135     .. py:method:: lexmin(self)
 136
 137         Return a new domain containing the lexicographic minimum of the elements in the domain.
 138
 139     .. py:method:: lexmax(self)
 140
 141         Return a new domain containing the lexicographic maximum of the elements in the domain.
 142
 143     .. py:method:: subs(self, symbol, expression=None):
 144
 145         Subsitute symbol by expression in equations and return the resulting
 146         domain.
 147
 148     .. py:method:: fromstring(cls, string)
 149
 150         Convert a string into a domain.
 151
 152     .. py:method:: fromsympy(cls, expr)
 153
 154         Convert a SymPy expression into a domain.
 155
 156     .. py:method:: tosympy(self)
 157
 158         Convert a domain into a SymPy expression.
 159
 160 A 2D or 3D domain can be plotted using the :meth:`plot` method. The points, vertices, and faces of a domain can be inspected using the following functions.
 161
 162     .. py:method:: points(self)
 163
 164         Return a list of the points with integer coordinates contained in a domain as :class:`Points` objects.
 165
 166     .. py:method:: __contains__(self, point)
 167
 168        Return ``True`` if point if contained within the domain.
 169
 170     .. py:method:: vertices(self)
 171
 172         Return a list of the verticies of a domain.
 173
 174     .. py:method:: faces(self)
 175
 176         Return a list of the vertices for each face of a domain.
 177
 178     .. py:method:: plot(self, plot=None, **kwargs)
 179
 180         Return a plot of the given domain or add a plot to a plot instance, using matplotlib.