Improve comparison methods in LinExpr

[linpy.git] / doc / reference.rst

diff --git a/doc/reference.rst b/doc/reference.rst
index 20168e4..e649227 100644 (file)
--- a/doc/reference.rst
+++ b/doc/reference.rst
@@ -2,6 +2,7 @@
 Module Reference
 ================
 
 Module Reference
 ================
 

+

 Symbols
 -------
 
 Symbols
 -------
 


@@ -103,7 +104,7 @@ For example, if ``x`` is a :class:`Symbol`, then ``x + 1`` is an instance of :cl
     A linear expression with no symbol, only a constant term, is automatically subclassed as a :class:`Rational` instance.
 
     .. method:: coefficient(symbol)
     A linear expression with no symbol, only a constant term, is automatically subclassed as a :class:`Rational` instance.
 
     .. method:: coefficient(symbol)

-                   __getitem__(symbol)
+                __getitem__(symbol)

 
         Return the coefficient value of the given symbol, or ``0`` if the symbol does not appear in the expression.
 
 
         Return the coefficient value of the given symbol, or ``0`` if the symbol does not appear in the expression.
 


@@ -161,9 +162,9 @@ For example, if ``x`` is a :class:`Symbol`, then ``x + 1`` is an instance of :cl
     As explained below, it is possible to create polyhedra from linear expressions using comparison methods.
 
     .. method:: __lt__(expr)
     As explained below, it is possible to create polyhedra from linear expressions using comparison methods.
 
     .. method:: __lt__(expr)

-                   __le__(expr)
-                   __ge__(expr)
-                   __gt__(expr)
+                __le__(expr)
+                __ge__(expr)
+                __gt__(expr)

 
         Create a new :class:`Polyhedron` instance whose unique constraint is the comparison between two linear expressions.
         As an alternative, functions :func:`Lt`, :func:`Le`, :func:`Ge` and :func:`Gt` can be used.
 
         Create a new :class:`Polyhedron` instance whose unique constraint is the comparison between two linear expressions.
         As an alternative, functions :func:`Lt`, :func:`Le`, :func:`Ge` and :func:`Gt` can be used.


@@ -178,7 +179,7 @@ For example, if ``x`` is a :class:`Symbol`, then ``x + 1`` is an instance of :cl
         Return the expression multiplied by its lowest common denominator to make all values integer.
 
     .. method:: subs(symbol, expression)
         Return the expression multiplied by its lowest common denominator to make all values integer.
 
     .. method:: subs(symbol, expression)

-                   subs(pairs)
+                subs(pairs)

 
         Substitute the given symbol by an expression and return the resulting expression.
         Raise :exc:`TypeError` if the resulting expression is not linear.
 
         Substitute the given symbol by an expression and return the resulting expression.
         Raise :exc:`TypeError` if the resulting expression is not linear.


@@ -203,7 +204,7 @@ For example, if ``x`` is a :class:`Symbol`, then ``x + 1`` is an instance of :cl
     .. classmethod:: fromsympy(expr)
 
         Create a linear expression from a :mod:`sympy` expression.
     .. classmethod:: fromsympy(expr)
 
         Create a linear expression from a :mod:`sympy` expression.

-        Raise :exc:`ValueError` is the :mod:`sympy` expression is not linear.
+        Raise :exc:`TypeError` is the :mod:`sympy` expression is not linear.

 
     .. method:: tosympy()
 
 
     .. method:: tosympy()
 


@@ -227,6 +228,7 @@ 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.
 
 
     See the documentation of :class:`fractions.Fraction` for more information and examples.
 

+

 Polyhedra
 ---------
 
 Polyhedra
 ---------
 


@@ -278,9 +280,19 @@ This space can be unbounded.
         The tuple of constraints, i.e., equalities and inequalities.
         This is semantically equivalent to: ``equalities + inequalities``.
 
         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)
 
     .. method:: widen(polyhedron)
 

-        Compute the standard widening of two polyhedra, à la Halbwachs.
+        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
 
 
 .. data:: Empty


@@ -329,7 +341,7 @@ Unlike polyhedra, domains allow exact computation of union and complementary ope
 
     .. attribute:: symbols
 
 
     .. attribute:: symbols
 

-        The tuple of symbols present in the domain expression, sorted according to :meth:`Symbol.sortkey`.
+        The tuple of symbols present in the domain equations, sorted according to :meth:`Symbol.sortkey`.

 
     .. attribute:: dimension
 
 
     .. attribute:: dimension
 


@@ -435,7 +447,7 @@ Unlike polyhedra, domains allow exact computation of union and complementary ope
 
     .. method:: __contains__(point)
 
 
     .. method:: __contains__(point)
 

-        Return ``True`` if the :class:`Point` is contained within the domain.
+        Return ``True`` if the point is contained within the domain.

 
     .. method:: faces()
 
 
     .. method:: faces()
 


@@ -493,7 +505,7 @@ The following functions create :class:`Polyhedron` or :class:`Domain` instances
 .. function:: Ne(expr1, expr2[, expr3, ...])
 
     Create the domain such that ``expr1 != expr2 != expr3 ...``.
 .. 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, ...])
 
 
 .. function:: Ge(expr1, expr2[, expr3, ...])
 


@@ -505,14 +517,14 @@ The following functions create :class:`Polyhedron` or :class:`Domain` instances
 
 The following functions combine :class:`Polyhedron` or :class:`Domain` instances using logic operators:
 
 
 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:: 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.
 .. function:: Not(domain)
 
     Create the complementary domain of the domain given in argument.


@@ -567,7 +579,7 @@ Geometric Objects
         The dimension of the point, i.e. the number of symbols present in it.
 
     .. method:: coordinate(symbol)
         The dimension of the point, i.e. the number of symbols present in it.
 
     .. method:: coordinate(symbol)

-                   __getitem__(symbol)
+                __getitem__(symbol)

 
         Return the coordinate value of the given symbol.
         Raise :exc:`KeyError` if the symbol is not involved in the point.
 
         Return the coordinate value of the given symbol.
         Raise :exc:`KeyError` if the symbol is not involved in the point.


@@ -590,10 +602,10 @@ Geometric Objects
 
     .. method:: __add__(vector)
 
 
     .. method:: __add__(vector)
 

-        Translate the point by a :class:`Vector` instance and return the resulting point.
+        Translate the point by a :class:`Vector` object and return the resulting point.

 
     .. method:: __sub__(point)
 
     .. method:: __sub__(point)

-                   __sub__(vector)
+                __sub__(vector)

 
         The first version substracts a point from another and returns the resulting vector.
         The second version translates the point by the opposite vector of *vector* and returns the resulting point.
 
         The first version substracts a point from another and returns the resulting vector.
         The second version translates the point by the opposite vector of *vector* and returns the resulting point.


@@ -604,9 +616,10 @@ Geometric Objects
 
 
 .. class:: Vector(coordinates)
 
 
 .. class:: Vector(coordinates)

+           Vector(point1, point2)

 
 

-    Create a point from a dictionary or a sequence that maps the symbols to their coordinates, similar to :meth:`Point`.
-    Coordinates must be rational numbers.
+    The first version creates a vector from a dictionary or a sequence that maps the symbols to their coordinates, similarly to :meth:`Point`.
+    The second version creates a vector between two points.

 
     :class:`Vector` instances are hashable and should be treated as immutable.
 
 
     :class:`Vector` instances are hashable and should be treated as immutable.
 


@@ -619,7 +632,7 @@ Geometric Objects
         The dimension of the point, i.e. the number of symbols present in it.
 
     .. method:: coordinate(symbol)
         The dimension of the point, i.e. the number of symbols present in it.
 
     .. method:: coordinate(symbol)

-                   __getitem__(symbol)
+                __getitem__(symbol)

 
         Return the coordinate value of the given symbol.
         Raise :exc:`KeyError` if the symbol is not involved in the point.
 
         Return the coordinate value of the given symbol.
         Raise :exc:`KeyError` if the symbol is not involved in the point.


@@ -641,13 +654,13 @@ Geometric Objects
         Return ``True`` if not all coordinates are ``0``.
 
     .. method:: __add__(point)
         Return ``True`` if not all coordinates are ``0``.
 
     .. method:: __add__(point)

-                   __add__(vector)
+                __add__(vector)

 
         The first version translates the point *point* to the vector and returns the resulting point.
         The second version adds vector *vector* to the vector and returns the resulting vector.
 
     .. method:: __sub__(point)
 
         The first version translates the point *point* to the vector and returns the resulting point.
         The second version adds vector *vector* to the vector and returns the resulting vector.
 
     .. method:: __sub__(point)

-                   __sub__(vector)
+                __sub__(vector)

 
         The first version substracts a point from a vector and returns the resulting point.
         The second version returns the difference vector between two vectors.
 
         The first version substracts a point from a vector and returns the resulting point.
         The second version returns the difference vector between two vectors.


@@ -656,6 +669,18 @@ Geometric Objects
 
         Return the opposite vector.
 
 
         Return the opposite vector.
 

+    .. method:: __mul__(value)
+
+        Multiply the vector by a scalar value and return the resulting vector.
+
+    .. method:: __truediv__(value)
+
+        Divide the vector by a scalar value and return the resulting vector.
+
+    .. method:: __eq__(vector)
+
+        Test whether two vectors are equal.
+

     .. method:: angle(vector)
 
         Retrieve the angle required to rotate the vector into the vector passed in argument.
     .. method:: angle(vector)
 
         Retrieve the angle required to rotate the vector into the vector passed in argument.


@@ -664,31 +689,19 @@ Geometric Objects
     .. method:: cross(vector)
 
         Compute the cross product of two 3D vectors.
     .. method:: cross(vector)
 
         Compute the cross product of two 3D vectors.

-        If either one of the vectors is not tridimensional, a :exc:`ValueError` exception is raised.
+        If either one of the vectors is not three-dimensional, a :exc:`ValueError` exception is raised.

 
     .. method:: dot(vector)
 
         Compute the dot product of two vectors.
 
 
     .. method:: dot(vector)
 
         Compute the dot product of two vectors.
 

-    .. method:: __eq__(vector)
-
-        Test whether two vectors are equal.
-
-    .. method:: __mul__(value)
-
-        Multiply the vector by a scalar value and return the resulting vector.
-
-    .. method:: __truediv__(value)
-
-        Divide the vector by a scalar value and return the resulting vector.
-

     .. method:: norm()
 
         Return the norm of the vector.
 
     .. method:: norm2()
 
     .. method:: norm()
 
         Return the norm of the vector.
 
     .. method:: norm2()
 

-        Return the square norm of the vector.
+        Return the squared norm of the vector.

 
     .. method:: asunit()
 
 
     .. method:: asunit()