Fix typo in doc/reference.rst

[linpy.git] / doc / reference.rst

diff --git a/doc/reference.rst b/doc/reference.rst
index 8184c43..20168e4 100644 (file)
--- a/doc/reference.rst
+++ b/doc/reference.rst
@@ -12,7 +12,7 @@ They correspond to mathematical variables.
 
     Return a symbol with the name string given in argument.
     Alternatively, the function :func:`symbols` allows to create several symbols at once.
 
     Return a symbol with the name string given in argument.
     Alternatively, the function :func:`symbols` allows to create several symbols at once.

-    Symbols are instances of class :class:`LinExpr` and, as such, inherit its functionalities.
+    Symbols are instances of class :class:`LinExpr` and inherit its functionalities.

 
     >>> x = Symbol('x')
     >>> x
 
     >>> x = Symbol('x')
     >>> x


@@ -46,12 +46,12 @@ They correspond to mathematical variables.
     >>> x, y = symbols(['x', 'y'])
 
 
     >>> x, y = symbols(['x', 'y'])
 
 

-Sometimes, you need to have a unique symbol, for example as a temporary one in some calculation, which is going to be substituted for something else at the end anyway.
+Sometimes you need to have a unique symbol. For example, you might need a temporary one in some calculation, which is going to be substituted for something else at the end anyway.

 This is achieved using ``Dummy('x')``.
 
 .. class:: Dummy(name=None)
 
 This is achieved using ``Dummy('x')``.
 
 .. class:: Dummy(name=None)
 

-    A variation of :class:`Symbol` which are all unique, identified by an internal count index.
+    A variation of :class:`Symbol` in which all symbols are unique and identified by an internal count index.

     If a name is not supplied then a string value of the count index will be used.
     This is useful when a unique, temporary variable is needed and the name of the variable used in the expression is not important.
 
     If a name is not supplied then a string value of the count index will be used.
     This is useful when a unique, temporary variable is needed and the name of the variable used in the expression is not important.
 


@@ -79,8 +79,8 @@ For example, if ``x`` is a :class:`Symbol`, then ``x + 1`` is an instance of :cl
 .. class:: LinExpr(coefficients=None, constant=0)
               LinExpr(string)
 
 .. class:: LinExpr(coefficients=None, constant=0)
               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 must be rational numbers.
+    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 + 2y + 1`` can be constructed using one of the following instructions:
 


@@ -88,7 +88,7 @@ For example, if ``x`` is a :class:`Symbol`, then ``x + 1`` is an instance of :cl
     >>> LinExpr({x: 1, y: 2}, 1)
     >>> LinExpr([(x, 1), (y, 2)], 1)
 
     >>> LinExpr({x: 1, y: 2}, 1)
     >>> LinExpr([(x, 1), (y, 2)], 1)
 

-    although it may be easier to use overloaded operators:
+    However, it may be easier to use overloaded operators:

 
     >>> x, y = symbols('x y')
     >>> x + 2*y + 1
 
     >>> x, y = symbols('x y')
     >>> x + 2*y + 1


@@ -181,7 +181,7 @@ For example, if ``x`` is a :class:`Symbol`, then ``x + 1`` is an instance of :cl
                    subs(pairs)
 
         Substitute the given symbol by an expression and return the resulting expression.
                    subs(pairs)
 
         Substitute the given symbol by an expression and return the resulting expression.

-        Raise :exc:`TypeError` is the resulting expression is not linear.
+        Raise :exc:`TypeError` if the resulting expression is not linear.

 
         >>> x, y = symbols('x y')
         >>> e = x + 2*y + 1
 
         >>> x, y = symbols('x y')
         >>> e = x + 2*y + 1


@@ -216,21 +216,21 @@ They are implemented by the :class:`Rational` class, that inherits from both :cl
 .. class:: Rational(numerator, denominator=1)
               Rational(string)
 
 .. class:: Rational(numerator, denominator=1)
               Rational(string)
 

-    The first version requires that *numerator* and *denominator* are instances of :class:`numbers.Rational` and returns a new :class:`Rational` instance with value ``numerator/denominator``.
-    If denominator is ``0``, it raises a :exc:`ZeroDivisionError`.
+    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`.

     The other version of the constructor expects a string.
     The usual form for this instance is::
 
         [sign] numerator ['/' denominator]
 
     The other version of the constructor expects a string.
     The usual form for this instance is::
 
         [sign] numerator ['/' denominator]
 

-    where the optional ``sign`` may be either '+' or '-' and ``numerator`` and ``denominator`` (if present) are strings of decimal digits.
+    where the optional ``sign`` may be either '+' or '-' and the ``numerator`` and ``denominator`` (if present) are strings of decimal digits.

 
     See the documentation of :class:`fractions.Fraction` for more information and examples.
 
 Polyhedra
 ---------
 
 
     See the documentation of :class:`fractions.Fraction` for more information and examples.
 
 Polyhedra
 ---------
 

-A *convex polyhedron* (or simply polyhedron) is the space defined by a system of linear equalities and inequalities.
+A *convex polyhedron* (or simply "polyhedron") is the space defined by a system of linear equalities and inequalities.

 This space can be unbounded.
 
 .. class:: Polyhedron(equalities, inequalities)
 This space can be unbounded.
 
 .. class:: Polyhedron(equalities, inequalities)


@@ -260,7 +260,7 @@ This space can be unbounded.
     >>> square2 = Polyhedron('2 <= x <= 4, 2 <= y <= 4')
     >>> Polyhedron(square | square2)
 
     >>> square2 = Polyhedron('2 <= x <= 4, 2 <= y <= 4')
     >>> Polyhedron(square | square2)
 

-    A polyhedron is a :class:`Domain` instance, and, as such, inherits the functionalities of this class.
+    A polyhedron is a :class:`Domain` instance, and, therefore, inherits the functionalities of this class.

     It is also a :class:`GeometricObject` instance.
 
     .. attribute:: equalities
     It is also a :class:`GeometricObject` instance.
 
     .. attribute:: equalities


@@ -476,7 +476,7 @@ Unlike polyhedra, domains allow exact computation of union and complementary ope
 Comparison and Logic Operators
 ------------------------------
 
 Comparison and Logic Operators
 ------------------------------
 

-The following functions allow to create :class:`Polyhedron` or :class:`Domain` instances by comparison of :class:`LinExpr` instances:
+The following functions create :class:`Polyhedron` or :class:`Domain` instances using the comparisons of two or more :class:`LinExpr` instances:

 
 .. function:: Lt(expr1, expr2[, expr3, ...])
 
 
 .. function:: Lt(expr1, expr2[, expr3, ...])
 


@@ -503,15 +503,15 @@ The following functions allow to create :class:`Polyhedron` or :class:`Domain` i
 
     Create the polyhedron with constraints ``expr1 > expr2 > expr3 ...``.
 
 
     Create the polyhedron with constraints ``expr1 > expr2 > expr3 ...``.
 

-The following functions allow to 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[, ...])
 
 
 .. function:: Or(domain1, domain2[, ...])
 

-    Create the union domain of domains given in arguments.
+    Create the union domain of the domains given in arguments.

 
 .. function:: And(domain1, domain2[, ...])
 
 
 .. function:: And(domain1, domain2[, ...])
 

-    Create the intersection domain of domains given in arguments.
+    Create the intersection domain of the domains given in arguments.

 
 .. function:: Not(domain)
 
 
 .. function:: Not(domain)
 


@@ -545,7 +545,7 @@ Geometric Objects
 
 .. class:: Point(coordinates)
 
 
 .. class:: Point(coordinates)
 

-    Create a point from a dictionnary or a sequence that maps symbols to their coordinates.
+    Create a point from a dictionary or a sequence that maps the symbols to their coordinates.

     Coordinates must be rational numbers.
 
     For example, the point ``(x: 1, y: 2)`` can be constructed using one of the following instructions:
     Coordinates must be rational numbers.
 
     For example, the point ``(x: 1, y: 2)`` can be constructed using one of the following instructions:


@@ -554,7 +554,7 @@ Geometric Objects
     >>> p = Point({x: 1, y: 2})
     >>> p = Point([(x, 1), (y, 2)])
 
     >>> p = Point({x: 1, y: 2})
     >>> p = Point([(x, 1), (y, 2)])
 

-    :class:`Point` instances are hashable, and should be treated as immutable.
+    :class:`Point` instances are hashable and should be treated as immutable.

 
     A point is a :class:`GeometricObject` instance.
 
 
     A point is a :class:`GeometricObject` instance.
 


@@ -595,7 +595,7 @@ Geometric Objects
     .. method:: __sub__(point)
                    __sub__(vector)
 
     .. method:: __sub__(point)
                    __sub__(vector)
 

-        The first version substract a point from another and return the resulting 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.
 
     .. method:: __eq__(point)
         The second version translates the point by the opposite vector of *vector* and returns the resulting point.
 
     .. method:: __eq__(point)


@@ -605,10 +605,10 @@ Geometric Objects
 
 .. class:: Vector(coordinates)
 
 
 .. class:: Vector(coordinates)
 

-    Create a point from a dictionnary or a sequence that maps symbols to their coordinates, similarly to :meth:`Point`.
+    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.
 
     Coordinates must be rational numbers.
 

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

 
     .. attribute:: symbols
 
 
     .. attribute:: symbols