Mention that we use Z-polyhedra

[linpy.git] / linpy / domains.py

diff --git a/linpy/domains.py b/linpy/domains.py
index 0da0a49..1f7a190 100644 (file)
--- a/linpy/domains.py
+++ b/linpy/domains.py
@@ -24,7 +24,7 @@ from fractions import Fraction
 
 from . import islhelper
 from .islhelper import mainctx, libisl
 
 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
 
 
 from .geometry import GeometricObject, Point, Vector
 
 


@@ -38,7 +38,7 @@ __all__ = [
 class Domain(GeometricObject):
     """
     A domain is a union of polyhedra. Unlike polyhedra, domains allow exact
 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.
 
     A domain with a unique polyhedron is automatically subclassed as a
     Polyhedron instance.


@@ -54,22 +54,23 @@ class Domain(GeometricObject):
         """
         Return a domain from a sequence of polyhedra.
 
         """
         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
 
         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:
 
 
         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.
 
         Finally, a domain can be built from a GeometricObject instance, calling
         the GeometricObject.asdomain() method.


@@ -703,17 +704,17 @@ class Domain(GeometricObject):
         Create a domain from a string. Raise SyntaxError if the string is not
         properly formatted.
         """
         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)
         string = cls._RE_BRACES.sub(r'', string)

-        # replace '=' by '=='
+        # Replace '=' by '=='.

         string = cls._RE_EQ.sub(r'\1==\2', string)
         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)
         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)
         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:
         tokens = cls._RE_OPERATORS.split(string)
         for i, token in enumerate(tokens):
             if i % 2 == 0:


@@ -772,7 +773,6 @@ def And(*domains):
         return Universe
     else:
         return domains[0].intersection(*domains[1:])
         return Universe
     else:
         return domains[0].intersection(*domains[1:])

-And.__doc__ = Domain.intersection.__doc__

 
 def Or(*domains):
     """
 
 def Or(*domains):
     """


@@ -783,11 +783,9 @@ def Or(*domains):
         return Empty
     else:
         return domains[0].union(*domains[1:])
         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
 
 def Not(domain):
     """
     Create the complementary domain of the domain given in argument.
     """
     return ~domain

-Not.__doc__ = Domain.complement.__doc__