/pypol.egg-info/
/venv/
__pycache__
+*~
+++ /dev/null
-Domains Module
-==============
-
-.. py:class :: Domain
-
- .. py:method:: polyhedra(self)
-
- Return .
-
-Domain Properties
------------------
- .. py:method:: symbols
-
- Returns a tuple of the symbols that exsist in a domain.
-
- .. py:method:: dimension
-
- Returns the number of variables that exist in a domain.
-
- .. py:method:: disjoint
-
- Returns a domain as disjoint.
-
- .. py:method:: num_parameters
-
- Returns the total number of parameters, input, output or dimensions in a domain.
-
- .. py:method:: involves_dims(self, dims)
-
- Returns ``True`` if a domain depends on the given dimensions.
-
-Unary Properties
-----------------
- .. py:method:: isempty(self)
-
- Return ``True`` is a domain is 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)
-
- Returns a domain as disjoint.
-
-Binary Properties
------------------
-
- .. 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*.
-
- .. py:method:: __lt__(self, other)
- self < 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*.
-
- .. py:method:: __gt__(self, other)
- self > 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.
-
- .. py:method:: complement(self)
- ¬self
-
- Return the complement of a domain.
-
- .. 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:: aspolyhedron(self)
-
- 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.
-
- .. py:method:: intersection(self, other)
- self | other
-
- Return a new domain with the elements that are common between *self* and *other*.
-
- .. py:method:: union(self, other)
- self & other
-
- Return a new domain with all the elements from *self* and *other*.
-
- .. py:method:: difference(self, other)
- self - 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.
-
- .. py:method:: lexmin(self)
-
- Return a new set containing the lexicographic minimum of the elements in the set.
-
- .. py:method:: lexmax(self)
-
- Return a new set containing the lexicographic maximum of the elements in the set.
-
-
- 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.
-
- .. py:method:: points(self)
-
- Return a list of the points contained in a 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.
-
-
-
+++ /dev/null
-Pypol Examples
-==============
-
-Creating a Square
------------------
- To create any polyhedron, first define the symbols used. Then use the polyhedron functions to define the constraints for the polyhedron. This example creates a square::
-
- >>> x, y = symbols('x y')
- >>> # define the constraints of the polyhedron
- >>> square = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2)
- >>> print(square)
- >>> And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0))
-
- Several unary operations can be performed on a polyhedron. For example: ::
-
- >>> square2 =
-
-
-Plot Examples
--------------
-
-
+++ /dev/null
-Geometry Module
-===============
-
-The geometry module is used to obtain information about the points and vertices of a ployhedra.
-
-.. py:class:: Points
-
-This class represents points in space.
-
- .. py:method:: isorigin(self)
-
- Return ``True`` if a point is the origin.
-
- .. py:method:: __eq__(self, other)
-
- Compares two Points for equality.
-
- .. py:method:: __add__(self, other)
-
- Adds a Point to a Vector and returns the result as a Point.
-
- .. py:method:: __sub__(self, other)
-
- Returns the difference between two Points as a Vector.
-
- .. py:method:: aspolyhedon(self)
-
- Returns a Point as a polyhedron.
-
-
-.. py:class:: Vector
-
-This class represents displacements in space.
-
- .. py:method:: __eq__(self, other)
-
- Compares two Vectors for equality.
-
- .. py:method:: __add__(self, other)
-
- Adds either a Point or Vector to a Vector. The resulting sum is returned as the same structure *other* is.
-
- .. py:method:: __sub__(self, other)
-
- Subtract a Point or Vector from a Vector. The resulting difference is returned in the same form as *other*.
-
- .. py:method:: __mul__(self, other)
-
- Multiples a Vector by a scalar value and returns the result as a Vector.
-
- .. py:method:: __neg__(self)
-
- Negates a Vector.
-
- .. py:method:: norm(self)
-
- Normalizes a Vector.
-
-
- .. py:method:: isnull(self)
-
- Tests whether a Vector is null.
-
- .. py:method:: angle(self, other)
-
- Retrieve the angle required to rotate the vector into the vector passed in argument. The result is an angle in radians, ranging between -pi and
- pi.
-
- .. py:method:: cross(self, other)
-
- Calculate the cross product of two Vector3D structures.
-
- .. py:method:: dot(self, other)
-
- Calculate the dot product of two vectors.
-
- .. py:method:: __trudiv__(self, other)
-
- Divide the vector by the specified scalar and returns the result as a vector.
-
+++ /dev/null
-.. pypol documentation master file, created by
- sphinx-quickstart on Wed Jun 25 20:34:21 2014.
- You can adapt this file completely to your liking, but it should at least
- contain the root `toctree` directive.
-
-Welcome to pypol's documentation!
-=================================
-
-Pypol is a Python library for symbolic mathematics.
-If you are new to Pypol, start with the Tutorial.
-
-This is the central page for all of SymPy's documentation.
-
-
-Contents:
-
-.. toctree::
- :maxdepth: 2
-
- install.rst
- examples.rst
- modules.rst
-
-
-
+++ /dev/null
-.. _installation:
-
-Installation
-------------
-
-Dependencies
-============
-
-Users will first need to install Integer Set Library (isl). The source files of isl are available as a tarball or a git repository. Both
-are available `here`_ .
-
-Source
-======
-
-Git
-===
-
-
-.. _here: http://freshmeat.net/projects/isl/
+++ /dev/null
-Linear Expression Module
-========================
-
-
-This class implements linear expressions.
-
- .. py:method:: coefficient(self, symbol)
-
- Return the coefficient value of the given symbol.
-
- .. py:method:: coefficients(self)
-
- Return a list of the coefficients of an expression
-
- .. py:method:: constant(self)
-
- Return the constant value of an expression.
-
- .. py:method:: symbols(self)
-
- Return a list of symbols in an expression.
-
- .. py:method:: dimension(self)
-
- Return the number of vriables in an expression.
-
- .. py:method:: __sub__(self, other)
-
- Return the difference between two expressions.
-
- .. py:method:: subs(self, symbol, expression=None)
-
- Subsitute the given value into an expression and return the resulting expression.
-
- .. py:method:: fromsympy(self)
-
- Convert sympy object to an expression.
-
- .. py:method:: tosympy(self)
-
- Return an expression as a sympy object.
-
-.. py:class:: Dummy(Symbol)
-
-This class returns a dummy symbol to ensure that each no variables are repeated in an expression
+++ /dev/null
-.. module-docs:
-
-Pypol Module Reference
-======================
-
-There are four main Pypol modules:
-
-.. toctree::
- :maxdepth: 2
-
- polyhedra.rst
- domain.rst
- linexpr.rst
- geometry.rst
-
+++ /dev/null
-Polyhedra Module
-================
-
-.. py:class:: Polyhedron
-
- Polyhedron class allows users to build and inspect polyherons. The following methods provide the properties of a polyhedron.
-
- .. py:method:: equalities(self)
-
- Return a list of the equalities in a polyhedron.
-
- .. py:method:: inequalities(self)
-
- Return a list of the inequalities in a polyhedron.
-
- .. py:method:: constraints(self)
-
- Return ta list of the constraints of a polyhedron.
-
- The following unary operations can be used to inspect a polyhedron.
-
- .. py:method:: disjoint(self)
-
- Returns a polyhedron as a disjoint.
-
- .. py:method:: isuniverse(self)
-
- Return ``True`` if a polyhedron is the Universe set.
-
- .. py:method:: subs(self, symbol, expression=None)
-
- Subsitutes an expression into a polyhedron and returns the result.
-
-To create a polyhedron, the user must use the folloing functions to define the equalities and inequalities which are the contraints of a polyhedron.
-
-.. py:function:: Lt(left, right)
-
- Assert first set is less than the second set.
-
-.. py:function:: Le(left, right)
-
- Assert first set is less than or equal to the second set.
-
-.. py:function:: Eq(left, right)
-
- Assert first set is equal to the second set.
-
-.. py:function:: Ne(left, right)
-
- Assert first set is not equal to the second set.
-
-.. py:function:: Gt(left, right)
-
- Assert first set is greater than the second set.
-
-.. py:function:: Ge(left, right)
-
- Assert first set is greater than or equal to the second set.
+++ /dev/null
-import ast
-import functools
-import re
-import math
-
-from fractions import Fraction
-
-from . import islhelper
-from .islhelper import mainctx, libisl
-from .linexprs import Expression, Symbol, Rational
-from .geometry import GeometricObject, Point, Vector
-
-
-__all__ = [
- 'Domain',
- 'And', 'Or', 'Not',
-]
-
-
-@functools.total_ordering
-class Domain(GeometricObject):
-
- __slots__ = (
- '_polyhedra',
- '_symbols',
- '_dimension',
- )
-
- def __new__(cls, *polyhedra):
- from .polyhedra import Polyhedron
- if len(polyhedra) == 1:
- argument = polyhedra[0]
- if isinstance(argument, str):
- return cls.fromstring(argument)
- elif isinstance(argument, GeometricObject):
- return argument.aspolyhedron()
- else:
- raise TypeError('argument must be a string '
- 'or a GeometricObject instance')
- else:
- for polyhedron in polyhedra:
- if not isinstance(polyhedron, Polyhedron):
- raise TypeError('arguments must be Polyhedron instances')
- symbols = cls._xsymbols(polyhedra)
- islset = cls._toislset(polyhedra, symbols)
- return cls._fromislset(islset, symbols)
-
- @classmethod
- def _xsymbols(cls, iterator):
- """
- Return the ordered tuple of symbols present in iterator.
- """
- symbols = set()
- for item in iterator:
- symbols.update(item.symbols)
- return tuple(sorted(symbols, key=Symbol.sortkey))
-
- @property
- def polyhedra(self):
- return self._polyhedra
-
- @property
- def symbols(self):
- return self._symbols
-
- @property
- def dimension(self):
- return self._dimension
-
- def disjoint(self):
- """
- Returns this set as disjoint.
- """
- islset = self._toislset(self.polyhedra, self.symbols)
- islset = libisl.isl_set_make_disjoint(mainctx, islset)
- return self._fromislset(islset, self.symbols)
-
- def isempty(self):
- """
- Returns true if this set is an Empty set.
- """
- islset = self._toislset(self.polyhedra, self.symbols)
- empty = bool(libisl.isl_set_is_empty(islset))
- libisl.isl_set_free(islset)
- return empty
-
- def __bool__(self):
- return not self.isempty()
-
- def isuniverse(self):
- """
- Returns true if this set is the Universe set.
- """
- islset = self._toislset(self.polyhedra, self.symbols)
- universe = bool(libisl.isl_set_plain_is_universe(islset))
- libisl.isl_set_free(islset)
- return universe
-
- def isbounded(self):
- """
- Returns true if this set is bounded.
- """
- islset = self._toislset(self.polyhedra, self.symbols)
- bounded = bool(libisl.isl_set_is_bounded(islset))
- libisl.isl_set_free(islset)
- return bounded
-
- def __eq__(self, other):
- """
- Returns true if two sets are equal.
- """
- symbols = self._xsymbols([self, other])
- islset1 = self._toislset(self.polyhedra, symbols)
- islset2 = other._toislset(other.polyhedra, symbols)
- equal = bool(libisl.isl_set_is_equal(islset1, islset2))
- libisl.isl_set_free(islset1)
- libisl.isl_set_free(islset2)
- return equal
-
- def isdisjoint(self, other):
- """
- Return True if two sets have a null intersection.
- """
- symbols = self._xsymbols([self, other])
- islset1 = self._toislset(self.polyhedra, symbols)
- islset2 = self._toislset(other.polyhedra, symbols)
- equal = bool(libisl.isl_set_is_disjoint(islset1, islset2))
- libisl.isl_set_free(islset1)
- libisl.isl_set_free(islset2)
- return equal
-
- def issubset(self, other):
- """
- Report whether another set contains this set.
- """
- symbols = self._xsymbols([self, other])
- islset1 = self._toislset(self.polyhedra, symbols)
- islset2 = self._toislset(other.polyhedra, symbols)
- equal = bool(libisl.isl_set_is_subset(islset1, islset2))
- libisl.isl_set_free(islset1)
- libisl.isl_set_free(islset2)
- return equal
-
- def __le__(self, other):
- """
- Returns true if this set is less than or equal to another set.
- """
- return self.issubset(other)
-
- def __lt__(self, other):
- """
- Returns true if this set is less than another set.
- """
- symbols = self._xsymbols([self, other])
- islset1 = self._toislset(self.polyhedra, symbols)
- islset2 = self._toislset(other.polyhedra, symbols)
- equal = bool(libisl.isl_set_is_strict_subset(islset1, islset2))
- libisl.isl_set_free(islset1)
- libisl.isl_set_free(islset2)
- return equal
-
- def complement(self):
- """
- Returns the complement of this set.
- """
- islset = self._toislset(self.polyhedra, self.symbols)
- islset = libisl.isl_set_complement(islset)
- return self._fromislset(islset, self.symbols)
-
- def __invert__(self):
- """
- Returns the complement of this set.
- """
- return self.complement()
-
- def simplify(self):
- """
- Returns a set without redundant constraints.
- """
- islset = self._toislset(self.polyhedra, self.symbols)
- islset = libisl.isl_set_remove_redundancies(islset)
- return self._fromislset(islset, self.symbols)
-
- def aspolyhedron(self):
- """
- Returns polyhedral hull of set.
- """
- from .polyhedra import Polyhedron
- islset = self._toislset(self.polyhedra, self.symbols)
- islbset = libisl.isl_set_polyhedral_hull(islset)
- return Polyhedron._fromislbasicset(islbset, self.symbols)
-
- def asdomain(self):
- return self
-
- def project(self, dims):
- """
- Return new set with given dimensions removed.
- """
- islset = self._toislset(self.polyhedra, self.symbols)
- n = 0
- for index, symbol in reversed(list(enumerate(self.symbols))):
- if symbol in dims:
- n += 1
- elif n > 0:
- islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, index + 1, n)
- n = 0
- if n > 0:
- islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, 0, n)
- dims = [symbol for symbol in self.symbols if symbol not in dims]
- return Domain._fromislset(islset, dims)
-
- def sample(self):
- """
- Returns a single subset of the input.
- """
- islset = self._toislset(self.polyhedra, self.symbols)
- islpoint = libisl.isl_set_sample_point(islset)
- if bool(libisl.isl_point_is_void(islpoint)):
- libisl.isl_point_free(islpoint)
- raise ValueError('domain must be non-empty')
- point = {}
- for index, symbol in enumerate(self.symbols):
- coordinate = libisl.isl_point_get_coordinate_val(islpoint,
- libisl.isl_dim_set, index)
- coordinate = islhelper.isl_val_to_int(coordinate)
- point[symbol] = coordinate
- libisl.isl_point_free(islpoint)
- return point
-
- def intersection(self, *others):
- """
- Return the intersection of two sets as a new set.
- """
- if len(others) == 0:
- return self
- symbols = self._xsymbols((self,) + others)
- islset1 = self._toislset(self.polyhedra, symbols)
- for other in others:
- islset2 = other._toislset(other.polyhedra, symbols)
- islset1 = libisl.isl_set_intersect(islset1, islset2)
- return self._fromislset(islset1, symbols)
-
- def __and__(self, other):
- """
- Return the intersection of two sets as a new set.
- """
- return self.intersection(other)
-
- def union(self, *others):
- """
- Return the union of sets as a new set.
- """
- if len(others) == 0:
- return self
- symbols = self._xsymbols((self,) + others)
- islset1 = self._toislset(self.polyhedra, symbols)
- for other in others:
- islset2 = other._toislset(other.polyhedra, symbols)
- islset1 = libisl.isl_set_union(islset1, islset2)
- return self._fromislset(islset1, symbols)
-
- def __or__(self, other):
- """
- Return a new set with elements from both sets.
- """
- return self.union(other)
-
- def __add__(self, other):
- """
- Return new set containing all elements in both sets.
- """
- return self.union(other)
-
- def difference(self, other):
- """
- Return the difference of two sets as a new set.
- """
- symbols = self._xsymbols([self, other])
- islset1 = self._toislset(self.polyhedra, symbols)
- islset2 = other._toislset(other.polyhedra, symbols)
- islset = libisl.isl_set_subtract(islset1, islset2)
- return self._fromislset(islset, symbols)
-
- def __sub__(self, other):
- """
- Return the difference of two sets as a new set.
- """
- return self.difference(other)
-
- def lexmin(self):
- """
- Return a new set containing the lexicographic minimum of the elements in the set.
- """
- islset = self._toislset(self.polyhedra, self.symbols)
- islset = libisl.isl_set_lexmin(islset)
- return self._fromislset(islset, self.symbols)
-
- def lexmax(self):
- """
- Return a new set containing the lexicographic maximum of the elements in the set.
- """
- islset = self._toislset(self.polyhedra, self.symbols)
- islset = libisl.isl_set_lexmax(islset)
- return self._fromislset(islset, self.symbols)
-
- def num_parameters(self):
- """
- Return the total number of parameters, input, output or set dimensions.
- """
- islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
- num = libisl.isl_basic_set_dim(islbset, libisl.isl_dim_set)
- return num
-
- def involves_dims(self, dims):
- """
- Returns true if set depends on given dimensions.
- """
- islset = self._toislset(self.polyhedra, self.symbols)
- dims = sorted(dims)
- symbols = sorted(list(self.symbols))
- n = 0
- if len(dims)>0:
- for dim in dims:
- if dim in symbols:
- first = symbols.index(dims[0])
- n +=1
- else:
- first = 0
- else:
- return False
- value = bool(libisl.isl_set_involves_dims(islset, libisl.isl_dim_set, first, n))
- libisl.isl_set_free(islset)
- return value
-
- _RE_COORDINATE = re.compile(r'\((?P<num>\-?\d+)\)(/(?P<den>\d+))?')
-
- def vertices(self):
- """
- Return a list of vertices for this Polygon.
- """
- from .polyhedra import Polyhedron
- islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
- vertices = libisl.isl_basic_set_compute_vertices(islbset);
- vertices = islhelper.isl_vertices_vertices(vertices)
- points = []
- for vertex in vertices:
- expr = libisl.isl_vertex_get_expr(vertex)
- coordinates = []
- if islhelper.isl_version < '0.13':
- constraints = islhelper.isl_basic_set_constraints(expr)
- for constraint in constraints:
- constant = libisl.isl_constraint_get_constant_val(constraint)
- constant = islhelper.isl_val_to_int(constant)
- for index, symbol in enumerate(self.symbols):
- coefficient = libisl.isl_constraint_get_coefficient_val(constraint,
- libisl.isl_dim_set, index)
- coefficient = islhelper.isl_val_to_int(coefficient)
- if coefficient != 0:
- coordinate = -Fraction(constant, coefficient)
- coordinates.append((symbol, coordinate))
- else:
- string = islhelper.isl_multi_aff_to_str(expr)
- matches = self._RE_COORDINATE.finditer(string)
- for symbol, match in zip(self.symbols, matches):
- numerator = int(match.group('num'))
- denominator = match.group('den')
- denominator = 1 if denominator is None else int(denominator)
- coordinate = Fraction(numerator, denominator)
- coordinates.append((symbol, coordinate))
- points.append(Point(coordinates))
- return points
-
- def points(self):
- """
- Returns the points contained in the set.
- """
- if not self.isbounded():
- raise ValueError('domain must be bounded')
- from .polyhedra import Universe, Eq
- islset = self._toislset(self.polyhedra, self.symbols)
- islpoints = islhelper.isl_set_points(islset)
- points = []
- for islpoint in islpoints:
- coordinates = {}
- for index, symbol in enumerate(self.symbols):
- coordinate = libisl.isl_point_get_coordinate_val(islpoint,
- libisl.isl_dim_set, index)
- coordinate = islhelper.isl_val_to_int(coordinate)
- coordinates[symbol] = coordinate
- points.append(Point(coordinates))
- return points
-
- @classmethod
- def _polygon_inner_point(cls, points):
- symbols = points[0].symbols
- coordinates = {symbol: 0 for symbol in symbols}
- for point in points:
- for symbol, coordinate in point.coordinates():
- coordinates[symbol] += coordinate
- for symbol in symbols:
- coordinates[symbol] /= len(points)
- return Point(coordinates)
-
- @classmethod
- def _sort_polygon_2d(cls, points):
- if len(points) <= 3:
- return points
- o = cls._polygon_inner_point(points)
- angles = {}
- for m in points:
- om = Vector(o, m)
- dx, dy = (coordinate for symbol, coordinate in om.coordinates())
- angle = math.atan2(dy, dx)
- angles[m] = angle
- return sorted(points, key=angles.get)
-
- @classmethod
- def _sort_polygon_3d(cls, points):
- if len(points) <= 3:
- return points
- o = cls._polygon_inner_point(points)
- a = points[0]
- oa = Vector(o, a)
- norm_oa = oa.norm()
- for b in points[1:]:
- ob = Vector(o, b)
- u = oa.cross(ob)
- if not u.isnull():
- u = u.asunit()
- break
- else:
- raise ValueError('degenerate polygon')
- angles = {a: 0.}
- for m in points[1:]:
- om = Vector(o, m)
- normprod = norm_oa * om.norm()
- cosinus = max(oa.dot(om) / normprod, -1.)
- sinus = u.dot(oa.cross(om)) / normprod
- angle = math.acos(cosinus)
- angle = math.copysign(angle, sinus)
- angles[m] = angle
- return sorted(points, key=angles.get)
-
- def faces(self):
- faces = []
- for polyhedron in self.polyhedra:
- vertices = polyhedron.vertices()
- for constraint in polyhedron.constraints:
- face = []
- for vertex in vertices:
- if constraint.subs(vertex.coordinates()) == 0:
- face.append(vertex)
- if len(face) >= 3:
- faces.append(face)
- return faces
-
- def _plot_2d(self, plot=None, **kwargs):
- import matplotlib.pyplot as plt
- from matplotlib.patches import Polygon
- if plot is None:
- fig = plt.figure()
- plot = fig.add_subplot(1, 1, 1)
- xmin, xmax = plot.get_xlim()
- ymin, ymax = plot.get_ylim()
- for polyhedron in self.polyhedra:
- vertices = polyhedron._sort_polygon_2d(polyhedron.vertices())
- xys = [tuple(vertex.values()) for vertex in vertices]
- xs, ys = zip(*xys)
- xmin, xmax = min(xmin, float(min(xs))), max(xmax, float(max(xs)))
- ymin, ymax = min(ymin, float(min(ys))), max(ymax, float(max(ys)))
- plot.add_patch(Polygon(xys, closed=True, **kwargs))
- plot.set_xlim(xmin, xmax)
- plot.set_ylim(ymin, ymax)
- return plot
-
- def _plot_3d(self, plot=None, **kwargs):
- import matplotlib.pyplot as plt
- from mpl_toolkits.mplot3d import Axes3D
- from mpl_toolkits.mplot3d.art3d import Poly3DCollection
- if plot is None:
- fig = plt.figure()
- axes = Axes3D(fig)
- else:
- axes = plot
- xmin, xmax = axes.get_xlim()
- ymin, ymax = axes.get_ylim()
- zmin, zmax = axes.get_zlim()
- poly_xyzs = []
- for vertices in self.faces():
- vertices = self._sort_polygon_3d(vertices)
- vertices.append(vertices[0])
- face_xyzs = [tuple(vertex.values()) for vertex in vertices]
- xs, ys, zs = zip(*face_xyzs)
- xmin, xmax = min(xmin, float(min(xs))), max(xmax, float(max(xs)))
- ymin, ymax = min(ymin, float(min(ys))), max(ymax, float(max(ys)))
- zmin, zmax = min(zmin, float(min(zs))), max(zmax, float(max(zs)))
- poly_xyzs.append(face_xyzs)
- collection = Poly3DCollection(poly_xyzs, **kwargs)
- axes.add_collection3d(collection)
- axes.set_xlim(xmin, xmax)
- axes.set_ylim(ymin, ymax)
- axes.set_zlim(zmin, zmax)
- return axes
-
- def plot(self, plot=None, **kwargs):
- """
- Display plot of this set.
- """
- if not self.isbounded():
- raise ValueError('domain must be bounded')
- elif self.dimension == 2:
- return self._plot_2d(plot=plot, **kwargs)
- elif self.dimension == 3:
- return self._plot_3d(plot=plot, **kwargs)
- else:
- raise ValueError('polyhedron must be 2 or 3-dimensional')
-
- def __contains__(self, point):
- for polyhedron in self.polyhedra:
- if point in polyhedron:
- return True
- return False
-
- def subs(self, symbol, expression=None):
- polyhedra = [polyhedron.subs(symbol, expression)
- for polyhedron in self.polyhedra]
- return Domain(*polyhedra)
-
- @classmethod
- def _fromislset(cls, islset, symbols):
- from .polyhedra import Polyhedron
- islset = libisl.isl_set_remove_divs(islset)
- islbsets = islhelper.isl_set_basic_sets(islset)
- libisl.isl_set_free(islset)
- polyhedra = []
- for islbset in islbsets:
- polyhedron = Polyhedron._fromislbasicset(islbset, symbols)
- polyhedra.append(polyhedron)
- if len(polyhedra) == 0:
- from .polyhedra import Empty
- return Empty
- elif len(polyhedra) == 1:
- return polyhedra[0]
- else:
- self = object().__new__(Domain)
- self._polyhedra = tuple(polyhedra)
- self._symbols = cls._xsymbols(polyhedra)
- self._dimension = len(self._symbols)
- return self
-
- @classmethod
- def _toislset(cls, polyhedra, symbols):
- polyhedron = polyhedra[0]
- islbset = polyhedron._toislbasicset(polyhedron.equalities,
- polyhedron.inequalities, symbols)
- islset1 = libisl.isl_set_from_basic_set(islbset)
- for polyhedron in polyhedra[1:]:
- islbset = polyhedron._toislbasicset(polyhedron.equalities,
- polyhedron.inequalities, symbols)
- islset2 = libisl.isl_set_from_basic_set(islbset)
- islset1 = libisl.isl_set_union(islset1, islset2)
- return islset1
-
- @classmethod
- def _fromast(cls, node):
- from .polyhedra import Polyhedron
- if isinstance(node, ast.Module) and len(node.body) == 1:
- return cls._fromast(node.body[0])
- elif isinstance(node, ast.Expr):
- return cls._fromast(node.value)
- elif isinstance(node, ast.UnaryOp):
- domain = cls._fromast(node.operand)
- if isinstance(node.operand, ast.invert):
- return Not(domain)
- elif isinstance(node, ast.BinOp):
- domain1 = cls._fromast(node.left)
- domain2 = cls._fromast(node.right)
- if isinstance(node.op, ast.BitAnd):
- return And(domain1, domain2)
- elif isinstance(node.op, ast.BitOr):
- return Or(domain1, domain2)
- elif isinstance(node, ast.Compare):
- equalities = []
- inequalities = []
- left = Expression._fromast(node.left)
- for i in range(len(node.ops)):
- op = node.ops[i]
- right = Expression._fromast(node.comparators[i])
- if isinstance(op, ast.Lt):
- inequalities.append(right - left - 1)
- elif isinstance(op, ast.LtE):
- inequalities.append(right - left)
- elif isinstance(op, ast.Eq):
- equalities.append(left - right)
- elif isinstance(op, ast.GtE):
- inequalities.append(left - right)
- elif isinstance(op, ast.Gt):
- inequalities.append(left - right - 1)
- else:
- break
- left = right
- else:
- return Polyhedron(equalities, inequalities)
- raise SyntaxError('invalid syntax')
-
- _RE_BRACES = re.compile(r'^\{\s*|\s*\}$')
- _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
- _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
- _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
- _RE_NOT = re.compile(r'\bnot\b|!|¬')
- _RE_NUM_VAR = Expression._RE_NUM_VAR
- _RE_OPERATORS = re.compile(r'(&|\||~)')
-
- @classmethod
- def fromstring(cls, string):
- # remove curly brackets
- string = cls._RE_BRACES.sub(r'', string)
- # replace '=' by '=='
- string = cls._RE_EQ.sub(r'\1==\2', string)
- # replace 'and', 'or', 'not'
- string = cls._RE_AND.sub(r' & ', string)
- string = cls._RE_OR.sub(r' | ', string)
- string = cls._RE_NOT.sub(r' ~', string)
- # add implicit multiplication operators, e.g. '5x' -> '5*x'
- string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
- # add parentheses to force precedence
- tokens = cls._RE_OPERATORS.split(string)
- for i, token in enumerate(tokens):
- if i % 2 == 0:
- token = '({})'.format(token)
- tokens[i] = token
- string = ''.join(tokens)
- tree = ast.parse(string, 'eval')
- return cls._fromast(tree)
-
- def __repr__(self):
- assert len(self.polyhedra) >= 2
- strings = [repr(polyhedron) for polyhedron in self.polyhedra]
- return 'Or({})'.format(', '.join(strings))
-
- def _repr_latex_(self):
- strings = []
- for polyhedron in self.polyhedra:
- strings.append('({})'.format(polyhedron._repr_latex_().strip('$')))
- return '${}$'.format(' \\vee '.join(strings))
-
- @classmethod
- def fromsympy(cls, expr):
- import sympy
- from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
- funcmap = {
- sympy.And: And, sympy.Or: Or, sympy.Not: Not,
- sympy.Lt: Lt, sympy.Le: Le,
- sympy.Eq: Eq, sympy.Ne: Ne,
- sympy.Ge: Ge, sympy.Gt: Gt,
- }
- if expr.func in funcmap:
- args = [Domain.fromsympy(arg) for arg in expr.args]
- return funcmap[expr.func](*args)
- elif isinstance(expr, sympy.Expr):
- return Expression.fromsympy(expr)
- raise ValueError('non-domain expression: {!r}'.format(expr))
-
- def tosympy(self):
- import sympy
- polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
- return sympy.Or(*polyhedra)
-
-
-def And(*domains):
- """
- Return the intersection of two sets as a new set.
- """
- if len(domains) == 0:
- from .polyhedra import Universe
- return Universe
- else:
- return domains[0].intersection(*domains[1:])
-
-def Or(*domains):
- """
- Return the union of sets as a new set.
- """
- if len(domains) == 0:
- from .polyhedra import Empty
- return Empty
- else:
- return domains[0].union(*domains[1:])
-
-def Not(domain):
- """
- Returns the complement of this set.
- """
- return ~domain
+++ /dev/null
-import math
-import numbers
-import operator
-
-from abc import ABC, abstractproperty, abstractmethod
-from collections import OrderedDict, Mapping
-
-from .linexprs import Symbol
-
-
-__all__ = [
- 'GeometricObject',
- 'Point',
- 'Vector',
-]
-
-
-class GeometricObject(ABC):
-
- @abstractproperty
- def symbols(self):
- pass
-
- @property
- def dimension(self):
- return len(self.symbols)
-
- @abstractmethod
- def aspolyhedron(self):
- pass
-
- def asdomain(self):
- return self.aspolyhedron()
-
-
-class Coordinates:
-
- __slots__ = (
- '_coordinates',
- )
-
- def __new__(cls, coordinates):
- if isinstance(coordinates, Mapping):
- coordinates = coordinates.items()
- self = object().__new__(cls)
- self._coordinates = OrderedDict()
- for symbol, coordinate in sorted(coordinates,
- key=lambda item: item[0].sortkey()):
- if not isinstance(symbol, Symbol):
- raise TypeError('symbols must be Symbol instances')
- if not isinstance(coordinate, numbers.Real):
- raise TypeError('coordinates must be real numbers')
- self._coordinates[symbol] = coordinate
- return self
-
- @property
- def symbols(self):
- return tuple(self._coordinates)
-
- @property
- def dimension(self):
- return len(self.symbols)
-
- def coordinates(self):
- yield from self._coordinates.items()
-
- def coordinate(self, symbol):
- if not isinstance(symbol, Symbol):
- raise TypeError('symbol must be a Symbol instance')
- return self._coordinates[symbol]
-
- __getitem__ = coordinate
-
- def values(self):
- yield from self._coordinates.values()
-
- def __bool__(self):
- return any(self._coordinates.values())
-
- def __hash__(self):
- return hash(tuple(self.coordinates()))
-
- def __repr__(self):
- string = ', '.join(['{!r}: {!r}'.format(symbol, coordinate)
- for symbol, coordinate in self.coordinates()])
- return '{}({{{}}})'.format(self.__class__.__name__, string)
-
- def _map(self, func):
- for symbol, coordinate in self.coordinates():
- yield symbol, func(coordinate)
-
- def _iter2(self, other):
- if self.symbols != other.symbols:
- raise ValueError('arguments must belong to the same space')
- coordinates1 = self._coordinates.values()
- coordinates2 = other._coordinates.values()
- yield from zip(self.symbols, coordinates1, coordinates2)
-
- def _map2(self, other, func):
- for symbol, coordinate1, coordinate2 in self._iter2(other):
- yield symbol, func(coordinate1, coordinate2)
-
-
-class Point(Coordinates, GeometricObject):
- """
- This class represents points in space.
- """
-
- def isorigin(self):
- """
- Return True if a Point is the origin.
- """
- return not bool(self)
-
- def __hash__(self):
- return super().__hash__()
-
- def __add__(self, other):
- if not isinstance(other, Vector):
- return NotImplemented
- coordinates = self._map2(other, operator.add)
- return Point(coordinates)
-
- def __sub__(self, other):
- coordinates = []
- if isinstance(other, Point):
- coordinates = self._map2(other, operator.sub)
- return Vector(coordinates)
- elif isinstance(other, Vector):
- coordinates = self._map2(other, operator.sub)
- return Point(coordinates)
- else:
- return NotImplemented
-
- def __eq__(self, other):
- """
- Compares two Points for equality.
- """
- return isinstance(other, Point) and \
- self._coordinates == other._coordinates
-
- def aspolyhedron(self):
- """
- Return a Point as a polyhedron.
- """
- from .polyhedra import Polyhedron
- equalities = []
- for symbol, coordinate in self.coordinates():
- equalities.append(symbol - coordinate)
- return Polyhedron(equalities)
-
-
-class Vector(Coordinates):
- """
- This class represents displacements in space.
- """
-
- def __new__(cls, initial, terminal=None):
- if not isinstance(initial, Point):
- initial = Point(initial)
- if terminal is None:
- coordinates = initial._coordinates
- else:
- if not isinstance(terminal, Point):
- terminal = Point(terminal)
- coordinates = terminal._map2(initial, operator.sub)
- return super().__new__(cls, coordinates)
-
- def isnull(self):
- """
- Returns true if a Vector is null.
- """
- return not bool(self)
-
- def __hash__(self):
- return super().__hash__()
-
- def __add__(self, other):
- """
- Adds either a Point or Vector to a Vector.
- """
- if isinstance(other, (Point, Vector)):
- coordinates = self._map2(other, operator.add)
- return other.__class__(coordinates)
- return NotImplemented
-
- def angle(self, other):
- """
- Retrieve the angle required to rotate the vector into the vector passed in argument. The result is an angle in radians, ranging between -pi and pi.
- """
- if not isinstance(other, Vector):
- raise TypeError('argument must be a Vector instance')
- cosinus = self.dot(other) / (self.norm()*other.norm())
- return math.acos(cosinus)
-
- def cross(self, other):
- """
- Calculate the cross product of two Vector3D structures.
- """
- if not isinstance(other, Vector):
- raise TypeError('other must be a Vector instance')
- if self.dimension != 3 or other.dimension != 3:
- raise ValueError('arguments must be three-dimensional vectors')
- if self.symbols != other.symbols:
- raise ValueError('arguments must belong to the same space')
- x, y, z = self.symbols
- coordinates = []
- coordinates.append((x, self[y]*other[z] - self[z]*other[y]))
- coordinates.append((y, self[z]*other[x] - self[x]*other[z]))
- coordinates.append((z, self[x]*other[y] - self[y]*other[x]))
- return Vector(coordinates)
-
- def __truediv__(self, other):
- """
- Divide the vector by the specified scalar and returns the result as a
- vector.
- """
- if not isinstance(other, numbers.Real):
- return NotImplemented
- coordinates = self._map(lambda coordinate: coordinate / other)
- return Vector(coordinates)
-
- def dot(self, other):
- """
- Calculate the dot product of two vectors.
- """
- if not isinstance(other, Vector):
- raise TypeError('argument must be a Vector instance')
- result = 0
- for symbol, coordinate1, coordinate2 in self._iter2(other):
- result += coordinate1 * coordinate2
- return result
-
- def __eq__(self, other):
- """
- Compares two Vectors for equality.
- """
- return isinstance(other, Vector) and \
- self._coordinates == other._coordinates
-
- def __hash__(self):
- return hash(tuple(self.coordinates()))
-
- def __mul__(self, other):
- """
- Multiplies a Vector by a scalar value.
- """
- if not isinstance(other, numbers.Real):
- return NotImplemented
- coordinates = self._map(lambda coordinate: other * coordinate)
- return Vector(coordinates)
-
- __rmul__ = __mul__
-
- def __neg__(self):
- """
- Returns the negated form of a Vector.
- """
- coordinates = self._map(operator.neg)
- return Vector(coordinates)
-
- def norm(self):
- """
- Normalizes a Vector.
- """
- return math.sqrt(self.norm2())
-
- def norm2(self):
- result = 0
- for coordinate in self._coordinates.values():
- result += coordinate ** 2
- return result
-
- def asunit(self):
- return self / self.norm()
-
- def __sub__(self, other):
- """
- Subtract a Point or Vector from a Vector.
- """
- if isinstance(other, (Point, Vector)):
- coordinates = self._map2(other, operator.sub)
- return other.__class__(coordinates)
- return NotImplemented
+++ /dev/null
-import functools
-import math
-import numbers
-
-from . import islhelper
-
-from .islhelper import mainctx, libisl
-from .geometry import GeometricObject, Point
-from .linexprs import Expression, Rational
-from .domains import Domain
-
-
-__all__ = [
- 'Polyhedron',
- 'Lt', 'Le', 'Eq', 'Ne', 'Ge', 'Gt',
- 'Empty', 'Universe',
-]
-
-
-class Polyhedron(Domain):
-
- __slots__ = (
- '_equalities',
- '_inequalities',
- '_constraints',
- '_symbols',
- '_dimension',
- )
-
- def __new__(cls, equalities=None, inequalities=None):
- if isinstance(equalities, str):
- if inequalities is not None:
- raise TypeError('too many arguments')
- return cls.fromstring(equalities)
- elif isinstance(equalities, GeometricObject):
- if inequalities is not None:
- raise TypeError('too many arguments')
- return equalities.aspolyhedron()
- if equalities is None:
- equalities = []
- else:
- for i, equality in enumerate(equalities):
- if not isinstance(equality, Expression):
- raise TypeError('equalities must be linear expressions')
- equalities[i] = equality.scaleint()
- if inequalities is None:
- inequalities = []
- else:
- for i, inequality in enumerate(inequalities):
- if not isinstance(inequality, Expression):
- raise TypeError('inequalities must be linear expressions')
- inequalities[i] = inequality.scaleint()
- symbols = cls._xsymbols(equalities + inequalities)
- islbset = cls._toislbasicset(equalities, inequalities, symbols)
- return cls._fromislbasicset(islbset, symbols)
-
- @property
- def equalities(self):
- return self._equalities
-
- @property
- def inequalities(self):
- return self._inequalities
-
- @property
- def constraints(self):
- return self._constraints
-
- @property
- def polyhedra(self):
- return self,
-
- def disjoint(self):
- """
- Return this set as disjoint.
- """
- return self
-
- def isuniverse(self):
- """
- Return true if this set is the Universe set.
- """
- islbset = self._toislbasicset(self.equalities, self.inequalities,
- self.symbols)
- universe = bool(libisl.isl_basic_set_is_universe(islbset))
- libisl.isl_basic_set_free(islbset)
- return universe
-
- def aspolyhedron(self):
- """
- Return polyhedral hull of this set.
- """
- return self
-
- def __contains__(self, point):
- if not isinstance(point, Point):
- raise TypeError('point must be a Point instance')
- if self.symbols != point.symbols:
- raise ValueError('arguments must belong to the same space')
- for equality in self.equalities:
- if equality.subs(point.coordinates()) != 0:
- return False
- for inequality in self.inequalities:
- if inequality.subs(point.coordinates()) < 0:
- return False
- return True
-
- def subs(self, symbol, expression=None):
- equalities = [equality.subs(symbol, expression)
- for equality in self.equalities]
- inequalities = [inequality.subs(symbol, expression)
- for inequality in self.inequalities]
- return Polyhedron(equalities, inequalities)
-
- def _asinequalities(self):
- inequalities = list(self.equalities)
- inequalities.extend([-expression for expression in self.equalities])
- inequalities.extend(self.inequalities)
- return inequalities
-
- def widen(self, other):
- if not isinstance(other, Polyhedron):
- raise ValueError('argument must be a Polyhedron instance')
- inequalities1 = self._asinequalities()
- inequalities2 = other._asinequalities()
- inequalities = []
- for inequality1 in inequalities1:
- if other <= Polyhedron(inequalities=[inequality1]):
- inequalities.append(inequality1)
- for inequality2 in inequalities2:
- for i in range(len(inequalities1)):
- inequalities3 = inequalities1[:i] + inequalities[i + 1:]
- inequalities3.append(inequality2)
- polyhedron3 = Polyhedron(inequalities=inequalities3)
- if self == polyhedron3:
- inequalities.append(inequality2)
- break
- return Polyhedron(inequalities=inequalities)
-
- @classmethod
- def _fromislbasicset(cls, islbset, symbols):
- if libisl.isl_basic_set_is_empty(islbset):
- return Empty
- if libisl.isl_basic_set_is_universe(islbset):
- return Universe
- islconstraints = islhelper.isl_basic_set_constraints(islbset)
- equalities = []
- inequalities = []
- for islconstraint in islconstraints:
- constant = libisl.isl_constraint_get_constant_val(islconstraint)
- constant = islhelper.isl_val_to_int(constant)
- coefficients = {}
- for index, symbol in enumerate(symbols):
- coefficient = libisl.isl_constraint_get_coefficient_val(islconstraint,
- libisl.isl_dim_set, index)
- coefficient = islhelper.isl_val_to_int(coefficient)
- if coefficient != 0:
- coefficients[symbol] = coefficient
- expression = Expression(coefficients, constant)
- if libisl.isl_constraint_is_equality(islconstraint):
- equalities.append(expression)
- else:
- inequalities.append(expression)
- libisl.isl_basic_set_free(islbset)
- self = object().__new__(Polyhedron)
- self._equalities = tuple(equalities)
- self._inequalities = tuple(inequalities)
- self._constraints = tuple(equalities + inequalities)
- self._symbols = cls._xsymbols(self._constraints)
- self._dimension = len(self._symbols)
- return self
-
- @classmethod
- def _toislbasicset(cls, equalities, inequalities, symbols):
- dimension = len(symbols)
- indices = {symbol: index for index, symbol in enumerate(symbols)}
- islsp = libisl.isl_space_set_alloc(mainctx, 0, dimension)
- islbset = libisl.isl_basic_set_universe(libisl.isl_space_copy(islsp))
- islls = libisl.isl_local_space_from_space(islsp)
- for equality in equalities:
- isleq = libisl.isl_equality_alloc(libisl.isl_local_space_copy(islls))
- for symbol, coefficient in equality.coefficients():
- islval = str(coefficient).encode()
- islval = libisl.isl_val_read_from_str(mainctx, islval)
- index = indices[symbol]
- isleq = libisl.isl_constraint_set_coefficient_val(isleq,
- libisl.isl_dim_set, index, islval)
- if equality.constant != 0:
- islval = str(equality.constant).encode()
- islval = libisl.isl_val_read_from_str(mainctx, islval)
- isleq = libisl.isl_constraint_set_constant_val(isleq, islval)
- islbset = libisl.isl_basic_set_add_constraint(islbset, isleq)
- for inequality in inequalities:
- islin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(islls))
- for symbol, coefficient in inequality.coefficients():
- islval = str(coefficient).encode()
- islval = libisl.isl_val_read_from_str(mainctx, islval)
- index = indices[symbol]
- islin = libisl.isl_constraint_set_coefficient_val(islin,
- libisl.isl_dim_set, index, islval)
- if inequality.constant != 0:
- islval = str(inequality.constant).encode()
- islval = libisl.isl_val_read_from_str(mainctx, islval)
- islin = libisl.isl_constraint_set_constant_val(islin, islval)
- islbset = libisl.isl_basic_set_add_constraint(islbset, islin)
- return islbset
-
- @classmethod
- def fromstring(cls, string):
- domain = Domain.fromstring(string)
- if not isinstance(domain, Polyhedron):
- raise ValueError('non-polyhedral expression: {!r}'.format(string))
- return domain
-
- def __repr__(self):
- strings = []
- for equality in self.equalities:
- strings.append('Eq({}, 0)'.format(equality))
- for inequality in self.inequalities:
- strings.append('Ge({}, 0)'.format(inequality))
- if len(strings) == 1:
- return strings[0]
- else:
- return 'And({})'.format(', '.join(strings))
-
- def _repr_latex_(self):
- strings = []
- for equality in self.equalities:
- strings.append('{} = 0'.format(equality._repr_latex_().strip('$')))
- for inequality in self.inequalities:
- strings.append('{} \\ge 0'.format(inequality._repr_latex_().strip('$')))
- return '$${}$$'.format(' \\wedge '.join(strings))
-
- @classmethod
- def fromsympy(cls, expr):
- domain = Domain.fromsympy(expr)
- if not isinstance(domain, Polyhedron):
- raise ValueError('non-polyhedral expression: {!r}'.format(expr))
- return domain
-
- def tosympy(self):
- import sympy
- constraints = []
- for equality in self.equalities:
- constraints.append(sympy.Eq(equality.tosympy(), 0))
- for inequality in self.inequalities:
- constraints.append(sympy.Ge(inequality.tosympy(), 0))
- return sympy.And(*constraints)
-
-
-class EmptyType(Polyhedron):
-
- __slots__ = Polyhedron.__slots__
-
- def __new__(cls):
- self = object().__new__(cls)
- self._equalities = (Rational(1),)
- self._inequalities = ()
- self._constraints = self._equalities
- self._symbols = ()
- self._dimension = 0
- return self
-
- def widen(self, other):
- if not isinstance(other, Polyhedron):
- raise ValueError('argument must be a Polyhedron instance')
- return other
-
- def __repr__(self):
- return 'Empty'
-
- def _repr_latex_(self):
- return '$$\\emptyset$$'
-
-Empty = EmptyType()
-
-
-class UniverseType(Polyhedron):
-
- __slots__ = Polyhedron.__slots__
-
- def __new__(cls):
- self = object().__new__(cls)
- self._equalities = ()
- self._inequalities = ()
- self._constraints = ()
- self._symbols = ()
- self._dimension = ()
- return self
-
- def __repr__(self):
- return 'Universe'
-
- def _repr_latex_(self):
- return '$$\\Omega$$'
-
-Universe = UniverseType()
-
-
-def _polymorphic(func):
- @functools.wraps(func)
- def wrapper(left, right):
- if not isinstance(left, Expression):
- if isinstance(left, numbers.Rational):
- left = Rational(left)
- else:
- raise TypeError('left must be a a rational number '
- 'or a linear expression')
- if not isinstance(right, Expression):
- if isinstance(right, numbers.Rational):
- right = Rational(right)
- else:
- raise TypeError('right must be a a rational number '
- 'or a linear expression')
- return func(left, right)
- return wrapper
-
-@_polymorphic
-def Lt(left, right):
- """
- Return true if the first set is less than the second.
- """
- return Polyhedron([], [right - left - 1])
-
-@_polymorphic
-def Le(left, right):
- """
- Return true the first set is less than or equal to the second.
- """
- return Polyhedron([], [right - left])
-
-@_polymorphic
-def Eq(left, right):
- """
- Return true if the sets are equal.
- """
- return Polyhedron([left - right], [])
-
-@_polymorphic
-def Ne(left, right):
- """
- Return true if the sets are NOT equal.
- """
- return ~Eq(left, right)
-
-@_polymorphic
-def Gt(left, right):
- """
- Return true if the first set is greater than the second set.
- """
- return Polyhedron([], [left - right - 1])
-
-@_polymorphic
-def Ge(left, right):
- """
- Return true if the first set is greater than or equal the second set.
- """
- return Polyhedron([], [left - right])
projects / linpy.git / commitdiff