+.. _reference:
+
Module Reference
================
+
Symbols
-------
>>> x < y
Le(x - y + 1, 0)
-
.. method:: scaleint()
Return the expression multiplied by its lowest common denominator to make all values integer.
See the documentation of :class:`fractions.Fraction` for more information and examples.
+
Polyhedra
---------
The tuple of constraints, i.e., equalities and inequalities.
This is semantically equivalent to: ``equalities + inequalities``.
+ .. method:: convex_union(polyhedron[, ...])
+
+ Return the convex union of two or more polyhedra.
+
+ .. method:: asinequalities()
+
+ Express the polyhedron using inequalities, given as a list of expressions greater or equal to 0.
+
.. method:: widen(polyhedron)
Compute the *standard widening* of two polyhedra, à la Halbwachs.
+ In its current implementation, this method is slow and should not be used on large polyhedra.
+
.. data:: Empty
The universe polyhedron, whose set of constraints is always satisfiable, i.e. is empty.
+
Domains
-------
A *domain* is a union of polyhedra.
-Unlike polyhedra, domains allow exact computation of union and complementary operations.
+Unlike polyhedra, domains allow exact computation of union, subtraction and complementary operations.
.. class:: Domain(*polyhedra)
Domain(string)
.. function:: Ne(expr1, expr2[, expr3, ...])
Create the domain such that ``expr1 != expr2 != expr3 ...``.
- The result is a :class:`Domain`, not a :class:`Polyhedron`.
+ The result is a :class:`Domain` object, not a :class:`Polyhedron`.
.. function:: Ge(expr1, expr2[, expr3, ...])
The following functions combine :class:`Polyhedron` or :class:`Domain` instances using logic operators:
-.. function:: Or(domain1, domain2[, ...])
-
- Create the union domain of the domains given in arguments.
-
.. function:: And(domain1, domain2[, ...])
Create the intersection domain of the domains given in arguments.
+.. function:: Or(domain1, domain2[, ...])
+
+ Create the union domain of the domains given in arguments.
+
.. function:: Not(domain)
Create the complementary domain of the domain given in argument.