Update reference examples to match the tutorial

[linpy.git] / doc / reference.rst

diff --git a/doc/reference.rst b/doc/reference.rst
index 69f0f45..4a2c419 100644 (file)
--- a/doc/reference.rst
+++ b/doc/reference.rst
@@ -1,8 +1,12 @@
 
+.. _reference:
+
 Module Reference
 ================
 
 
+.. _reference_symbols:
+
 Symbols
 -------
 
@@ -68,6 +72,8 @@ This is achieved using ``Dummy('x')``.
     True
 
 
+.. _reference_linexprs:
+
 Linear Expressions
 ------------------
 
@@ -78,12 +84,12 @@ Linear expressions are generally built using overloaded operators.
 For example, if ``x`` is a :class:`Symbol`, then ``x + 1`` is an instance of :class:`LinExpr`.
 
 .. class:: LinExpr(coefficients=None, constant=0)
-              LinExpr(string)
+           LinExpr(string)
 
     Return a linear expression from a dictionary or a sequence, that maps symbols to their coefficients, and a constant term.
     The coefficients and the constant term must be rational numbers.
 
-    For example, the linear expression ``x + 2y + 1`` can be constructed using one of the following instructions:
+    For example, the linear expression ``x + 2*y + 1`` can be constructed using one of the following instructions:
 
     >>> x, y = symbols('x y')
     >>> LinExpr({x: 1, y: 2}, 1)
@@ -96,7 +102,7 @@ For example, if ``x`` is a :class:`Symbol`, then ``x + 1`` is an instance of :cl
 
     Alternatively, linear expressions can be constructed from a string:
 
-    >>> LinExpr('x + 2*y + 1')
+    >>> LinExpr('x + 2y + 1')
 
     :class:`LinExpr` instances are hashable, and should be treated as immutable.
 
@@ -171,8 +177,7 @@ For example, if ``x`` is a :class:`Symbol`, then ``x + 1`` is an instance of :cl
 
         >>> x, y = symbols('x y')
         >>> x < y
-        Le(x - y + 1, 0)
-
+        x + 1 <= y
 
     .. method:: scaleint()
 
@@ -215,7 +220,7 @@ Apart from :mod:`Symbol`, a particular case of linear expressions are rational v
 They are implemented by the :class:`Rational` class, that inherits from both :class:`LinExpr` and :class:`fractions.Fraction` classes.
 
 .. class:: Rational(numerator, denominator=1)
-              Rational(string)
+           Rational(string)
 
     The first version requires that the *numerator* and *denominator* are instances of :class:`numbers.Rational` and returns a new :class:`Rational` instance with the value ``numerator/denominator``.
     If the denominator is ``0``, it raises a :exc:`ZeroDivisionError`.
@@ -229,6 +234,8 @@ They are implemented by the :class:`Rational` class, that inherits from both :cl
     See the documentation of :class:`fractions.Fraction` for more information and examples.
 
 
+.. _reference_polyhedra:
+
 Polyhedra
 ---------
 
@@ -236,31 +243,34 @@ A *convex polyhedron* (or simply "polyhedron") is the space defined by a system
 This space can be unbounded.
 
 .. class:: Polyhedron(equalities, inequalities)
-              Polyhedron(string)
-              Polyhedron(geometric object)
+           Polyhedron(string)
+           Polyhedron(geometric object)
 
     Return a polyhedron from two sequences of linear expressions: *equalities* is a list of expressions equal to ``0``, and *inequalities* is a list of expressions greater or equal to ``0``.
     For example, the polyhedron ``0 <= x <= 2, 0 <= y <= 2`` can be constructed with:
 
     >>> x, y = symbols('x y')
-    >>> square = Polyhedron([], [x, 2 - x, y, 2 - y])
+    >>> square1 = Polyhedron([], [x, 2 - x, y, 2 - y])
+    >>> square1
+    And(0 <= x, x <= 2, 0 <= y, y <= 2)
 
     It may be easier to use comparison operators :meth:`LinExpr.__lt__`, :meth:`LinExpr.__le__`, :meth:`LinExpr.__ge__`, :meth:`LinExpr.__gt__`, or functions :func:`Lt`, :func:`Le`, :func:`Eq`, :func:`Ge` and :func:`Gt`, using one of the following instructions:
 
     >>> x, y = symbols('x y')
-    >>> square = (0 <= x) & (x <= 2) & (0 <= y) & (y <= 2)
-    >>> square = Le(0, x, 2) & Le(0, y, 2)
+    >>> square1 = (0 <= x) & (x <= 2) & (0 <= y) & (y <= 2)
+    >>> square1 = Le(0, x, 2) & Le(0, y, 2)
 
     It is also possible to build a polyhedron from a string.
 
-    >>> square = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
+    >>> square1 = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
 
     Finally, a polyhedron can be constructed from a :class:`GeometricObject` instance, calling the :meth:`GeometricObject.aspolyedron` method.
     This way, it is possible to compute the polyhedral hull of a :class:`Domain` instance, i.e., the convex hull of two polyhedra:
 
-    >>> square = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
-    >>> square2 = Polyhedron('2 <= x <= 4, 2 <= y <= 4')
-    >>> Polyhedron(square | square2)
+    >>> square1 = Polyhedron('0 <= x <= 2, 0 <= y <= 2')
+    >>> square2 = Polyhedron('1 <= x <= 3, 1 <= y <= 3')
+    >>> Polyhedron(square1 | square2)
+    And(0 <= x, 0 <= y, x <= y + 2, y <= x + 2, x <= 3, y <= 3)
 
     A polyhedron is a :class:`Domain` instance, and, therefore, inherits the functionalities of this class.
     It is also a :class:`GeometricObject` instance.
@@ -303,32 +313,35 @@ This space can be unbounded.
 
     The universe polyhedron, whose set of constraints is always satisfiable, i.e. is empty.
 
+
+.. _reference_domains:
+
 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)
-              Domain(geometric object)
+           Domain(string)
+           Domain(geometric object)
 
     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 :meth:`Domain.__and__`, :meth:`Domain.__or__` or functions :func:`And` and :func:`Or`, using one of the following instructions:
+    It is also possible to build domains from polyhedra using arithmetic operators :meth:`Domain.__or__`, :meth:`Domain.__invert__` or functions :func:`Or` and :func:`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 :class:`GeometricObject` instance, calling the :meth:`GeometricObject.asdomain` method.
 
@@ -485,6 +498,8 @@ Unlike polyhedra, domains allow exact computation of union and complementary ope
         Convert the domain to a sympy expression.
 
 
+.. _reference_operators:
+
 Comparison and Logic Operators
 ------------------------------
 
@@ -505,7 +520,7 @@ The following functions create :class:`Polyhedron` or :class:`Domain` instances
 .. 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, ...])
 
@@ -530,6 +545,8 @@ The following functions combine :class:`Polyhedron` or :class:`Domain` instances
     Create the complementary domain of the domain given in argument.
 
 
+.. _reference_geometry:
+
 Geometric Objects
 -----------------