from . import islhelper
from .islhelper import mainctx, libisl
-from .linexprs import LinExpr, Symbol, Rational
+from .linexprs import LinExpr, Symbol
from .geometry import GeometricObject, Point, Vector
class Domain(GeometricObject):
"""
A domain is a union of polyhedra. Unlike polyhedra, domains allow exact
- computation of union and complementary operations.
+ computation of union, subtraction and complementary operations.
A domain with a unique polyhedron is automatically subclassed as a
Polyhedron instance.
"""
Return a domain from a sequence of polyhedra.
- >>> square = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
- >>> square2 = Polyhedron('2 <= x <= 4, 2 <= y <= 4')
- >>> dom = Domain([square, square2])
+ >>> square1 = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
+ >>> square2 = Polyhedron('1 <= x <= 3, 1 <= y <= 3')
+ >>> dom = Domain(square1, square2)
+ >>> dom
+ Or(And(x <= 2, 0 <= x, y <= 2, 0 <= y),
+ And(x <= 3, 1 <= x, y <= 3, 1 <= y))
It is also possible to build domains from polyhedra using arithmetic
- operators Domain.__and__(), Domain.__or__() or functions And() and Or(),
- using one of the following instructions:
+ operators Domain.__or__(), Domain.__invert__() or functions Or() and
+ Not(), using one of the following instructions:
- >>> square = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
- >>> square2 = Polyhedron('2 <= x <= 4, 2 <= y <= 4')
- >>> dom = square | square2
- >>> dom = Or(square, square2)
+ >>> dom = square1 | square2
+ >>> dom = Or(square1, square2)
Alternatively, a domain can be built from a string:
- >>> dom = Domain('0 <= x <= 2, 0 <= y <= 2; 2 <= x <= 4, 2 <= y <= 4')
+ >>> dom = Domain('0 <= x <= 2, 0 <= y <= 2; 1 <= x <= 3, 1 <= y <= 3')
Finally, a domain can be built from a GeometricObject instance, calling
the GeometricObject.asdomain() method.
Create a domain from a string. Raise SyntaxError if the string is not
properly formatted.
"""
- # remove curly brackets
+ # Remove curly brackets.
string = cls._RE_BRACES.sub(r'', string)
- # replace '=' by '=='
+ # Replace '=' by '=='.
string = cls._RE_EQ.sub(r'\1==\2', string)
- # replace 'and', 'or', 'not'
+ # 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'
+ # Add implicit multiplication operators, e.g. '5x' -> '5*x'.
string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
- # add parentheses to force precedence
+ # Add parentheses to force precedence.
tokens = cls._RE_OPERATORS.split(string)
for i, token in enumerate(tokens):
if i % 2 == 0:
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):
"""
- Create a domain from a sympy expression.
+ Create a domain from a SymPy expression.
"""
import sympy
from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
def tosympy(self):
"""
- Convert the domain to a sympy expression.
+ Convert the domain to a SymPy expression.
"""
import sympy
polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
return Universe
else:
return domains[0].intersection(*domains[1:])
-And.__doc__ = Domain.intersection.__doc__
def Or(*domains):
"""
return Empty
else:
return domains[0].union(*domains[1:])
-Or.__doc__ = Domain.union.__doc__
def Not(domain):
"""
Create the complementary domain of the domain given in argument.
"""
return ~domain
-Not.__doc__ = Domain.complement.__doc__
projects / linpy.git / blobdiff