Drop useless slot inheritance in EmptyType and UniverseType

[linpy.git] / doc / reference.rst

diff --git a/doc/reference.rst b/doc/reference.rst
index 4dcfbdc..18e69c0 100644 (file)
--- a/doc/reference.rst
+++ b/doc/reference.rst
@@ -103,7 +103,7 @@ 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)
-                   __getitem__(symbol)
+                __getitem__(symbol)
 
         Return the coefficient value of the given symbol, or ``0`` if the symbol does not appear in the expression.
 
@@ -148,11 +148,11 @@ For example, if ``x`` is a :class:`Symbol`, then ``x + 1`` is an instance of :cl
 
     .. method:: __mul__(value)
 
-        Return the product of the linear expression as a rational.
+        Return the product of the linear expression by a rational.
 
     .. method:: __truediv__(value)
 
-        Return the quotient of the linear expression as a rational.
+        Return the quotient of the linear expression by a rational.
 
     .. method:: __eq__(expr)
 
@@ -161,9 +161,9 @@ 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)
-                   __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.
@@ -178,7 +178,7 @@ 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)
-                   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.
@@ -203,7 +203,7 @@ 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.
-        Raise :exc:`ValueError` is the :mod:`sympy` expression is not linear.
+        Raise :exc:`TypeError` is the :mod:`sympy` expression is not linear.
 
     .. method:: tosympy()
 
@@ -280,7 +280,9 @@ This space can be unbounded.
 
     .. 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
@@ -329,7 +331,7 @@ Unlike polyhedra, domains allow exact computation of union and complementary ope
 
     .. 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
 
@@ -435,7 +437,7 @@ Unlike polyhedra, domains allow exact computation of union and complementary ope
 
     .. 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()
 
@@ -567,7 +569,7 @@ Geometric Objects
         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.
@@ -590,10 +592,10 @@ Geometric Objects
 
     .. 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)
-                   __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.
@@ -604,9 +606,10 @@ Geometric Objects
 
 
 .. 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.
 
@@ -619,7 +622,7 @@ Geometric Objects
         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.
@@ -641,13 +644,13 @@ Geometric Objects
         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)
-                   __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.
@@ -656,6 +659,18 @@ Geometric Objects
 
         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.
@@ -664,31 +679,19 @@ Geometric Objects
     .. 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:: __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()
 
-        Return the square norm of the vector.
+        Return the squared norm of the vector.
 
     .. method:: asunit()