Domains Module
==============
+This module provides classes and functions to deal with polyhedral
+domains, i.e. unions of polyhedra.
+
.. py:class :: Domain
- The properties of a domain can be are found using the following
+ This class represents polyhedral domains, i.e. unions of polyhedra.
- .. py:method:: symbols
+ .. py:method:: __new__(cls, *polyhedra)
- Returns a tuple of the symbols that exsist in a domain.
+ Create and return a new domain from a string or a list of polyhedra.
- .. py:method:: dimension
+ .. attribute:: polyhedra
+
+ The tuple of polyhedra which constitute the domain.
+ .. attribute:: symbols
+
+ Returns a tuple of the symbols that exsist in a domain.
+
+ .. attribute:: dimension
+
Returns the number of variables that exist in a domain.
- .. py:method:: disjoint
-
- Returns a domain as disjoint.
-
- .. py:method:: involvesvars(self, vars)
-
- Returns ``True`` if a domain depends on the given dimensions.
-
- The unary properties of a domain can be inspected using the following methods.
-
.. py:method:: isempty(self)
-
+
Return ``True`` is a domain is empty.
- .. py:method:: isuniverse(self)
+ .. py:method:: __bool__(self)
+ Return ``True`` if the domain is non-empty.
+
+ .. py:method:: isuniverse(self)
+
Return ``True`` if a domain is the Universe set.
-
+
.. py:method:: isbounded(self)
-
- Return ``True`` if a domain is bounded.
- .. py:method:: disjoint(self)
-
- It is not guarenteed that a domain is disjoint. If it is necessary, this method will return a domain as disjoint.
+ Return ``True`` if a domain is bounded.
- The following methods compare two domains to find the binary properties.
+ .. py:method:: make_disjoint(self)
+
+ It is not guarenteed that a domain is disjoint. If it is necessary, this method will return an equivalent domain, whose polyhedra are disjoint.
.. py:method:: isdisjoint(self, other)
-
+
Return ``True`` if the intersection of *self* and *other* results in an empty set.
-
+
.. py:method:: issubset(self, other)
-
+
Test whether every element in a domain is in *other*.
.. py:method:: __eq__(self, other)
self == other
-
- Test whether a domain is equal to *other*.
-
+
+ Test whether a domain is equal to *other*.
+
.. py:method:: __lt__(self, other)
self < other
-
- Test whether a domain is a strict subset of *other*.
-
+
+ Test whether a domain is a strict subset of *other*.
+
.. py:method:: __le__(self, other)
self <= other
-
- Test whether every element in a domain is in *other*.
-
+
+ Test whether every element in a domain is in *other*.
+
.. py:method:: __gt__(self, other)
self > other
-
- Test whether a domain is a strict superset of *other*.
-
+
+ Test whether a domain is a strict superset of *other*.
+
.. py:method:: __ge__(self, other)
self >= other
-
- Test whether every element in *other* is in a domain.
-
- The following methods implement unary operations on a domain.
+ Test whether every element in *other* is in a domain.
.. py:method:: complement(self)
- ¬self
+ ~self
+
+ Return the complementary domain of a domain.
+
+ .. py:method:: coalesce(self)
- Return the complement of a domain.
+ Simplify the representation of the domain by trying to combine pairs of
+ polyhedra into a single polyhedron.
+
+ .. py:method:: detect_equalities(self)
+
+ Simplify the representation of the domain by detecting implicit
+ equalities.
+
.. py:method:: simplify(self)
Return a new domain without any redundant constraints.
- .. py:method:: project(self, dims)
-
- Return a new domain with the given dimensions removed.
+ .. py:method:: project(self, variables)
+
+ Return a new domain with the given variables removed.
.. py:method:: aspolyhedron(self)
-
- Return polyhedral hull of a domain.
-
+
+ Return polyhedral hull of a domain.
+
.. py:method:: sample(self)
-
- Return a single sample subset of a domain.
- The following methods implement binary operations on two domains.
+ Return a single sample subset of a domain.
.. py:method:: intersection(self, other)
+ __or__
self | other
-
- Return a new domain with the elements that are common between *self* and *other*.
+
+ Return a new domain with the elements that are common between *self* and *other*.
.. py:method:: union(self, other)
+ __and__
self & other
-
- Return a new domain with all the elements from *self* and *other*.
-
+
+ Return a new domain with all the elements from *self* and *other*.
+
.. py:method:: difference(self, other)
+ __sub__
self - other
-
- Return a new domain with the elements in a domain that are not in *other* .
-
+
+ Return a new domain with the elements in a domain that are not in *other* .
+
.. py:method:: __add__(self, other)
self + other
-
- Return the sum of two domains.
-
- The following methods use lexicographical ordering to find the maximum or minimum element in a domain.
+
+ Return the sum of two domains.
.. py:method:: lexmin(self)
-
- Return a new set containing the lexicographic minimum of the elements in the set.
-
+
+ Return a new domain containing the lexicographic minimum of the elements in the domain.
+
.. py:method:: lexmax(self)
+
+ Return a new domain containing the lexicographic maximum of the elements in the domain.
+
+ .. py:method:: subs(self, symbol, expression=None):
+
+ Subsitute symbol by expression in equations and return the resulting
+ domain.
+
+ .. py:method:: fromstring(cls, string)
+
+ Convert a string into a domain.
+
+ .. py:method:: fromsympy(cls, expr)
- Return a new set containing the lexicographic maximum of the elements in the set.
+ Convert a SymPy expression into a domain.
+ .. py:method:: tosympy(self)
+
+ Convert a domain into a SymPy expression.
- 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.
+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.
.. py:method:: points(self)
+
+ Return a list of the points with integer coordinates contained in a domain as :class:`Points` objects.
+
+ .. py:method:: __contains__(self, point)
- Return a list of the points contained in a domain as :class:`Points` objects.
+ Return ``True`` if point if contained within the domain.
.. py:method:: vertices(self)
-
+
Return a list of the verticies of a domain.
-
+
.. py:method:: faces(self)
-
+
Return a list of the vertices for each face of a domain.
-
+
.. py:method:: plot(self, plot=None, **kwargs)
-
- Return a plot of the given domain.
-
-
-
+
+ Return a plot of the given domain or add a plot to a plot instance, using matplotlib.
projects / linpy.git / blobdiff