more tweaks

doc/_templates/layout.html

@@ -4,9 +4,9 @@
 <li>[<a href="{{ pathto('index') }}">Uncertainties</a></li>
 <li>[<a href="{{ pathto('install') }}">Installation & Credits</a></li>
 <li>|<a href="{{ pathto('user_guide') }}">User Guide</a></li>
-<li>|<a href="{{ pathto('Formatting') }}">Formatting Values</a></li>
+<li>|<a href="{{ pathto('formatting') }}">Formatting</a></li>
 <li>|<a href="{{ pathto('numpy_guide') }}"> Numpy Arrays</a></li>
-<li>|<a href="{{ pathto('tech_guide') }}">Technical Guide</a>]</li> &nbsp;
+<li>|<a href="{{ pathto('tech_guide') }}">Advanced</a>]</li> &nbsp;
 &nbsp;
 &nbsp; &nbsp;
 {% endblock %}

doc/numpy_guide.rst

@@ -1,14 +1,38 @@
 .. index: NumPy support
 
 =======================
-Uncertainties in arrays
+Uncertainties and numpy arrays
 =======================
 
 .. index:: unumpy
+.. index:: arrays; simple use, matrices; simple use
+
+.. _simple_array_use:
+
+Arrays of uncertainties Variables
+====================================
+
+It is possible to put uncertainties Variable  in NumPy_ arrays and
+matrices:
+
+>>> arr = numpy.array([ufloat(1, 0.01), ufloat(2, 0.1)])
+>>> 2*arr
+[2.0+/-0.02 4.0+/-0.2]
+>>> print arr.sum()
+3.00+/-0.10
+
+Many common operations on NumPy arrays can be performed transparently
+even when these arrays contain numbers with uncertainties.
+
 
 The unumpy package
 ==================
 
+
+While :ref:`basic operations on arrays <simple_array_use>` that
+contain numbers with uncertainties can be performed without it, the
+:mod:`unumpy` package is useful for more advanced uses.
+
 This package contains:
 
 1. utilities that help with the **creation and manipulation** of
@@ -17,9 +41,6 @@ NumPy_ arrays and matrices of numbers with uncertainties;
 2. **generalizations** of multiple NumPy functions so that they also
 work with arrays that contain numbers with uncertainties.
 
-While :ref:`basic operations on arrays <simple_array_use>` that
-contain numbers with uncertainties can be performed without it, the
-:mod:`unumpy` package is useful for more advanced uses.
 
 Operations on arrays (including their cosine, etc.)  can thus be
 performed transparently.

doc/user_guide.rst

@@ -79,7 +79,7 @@ The most common and important functions for creating uncertain
 Basic math with uncertain Variables
 =========================================
 
-:class:`Variables` can be used in basic mathematical calculations
+:class:`Variable`s can be used in basic mathematical calculations
 ('+', '-', '*', '/', '**') as with other Python numbers and variables.
 
 >>> t = ufloat(0.2, 0.01)
@@ -177,33 +177,46 @@ The functions in the :mod:`uncertainties.umath` module include:
 Comparison operators
 ====================
 
-Comparison operators ('==', '!=', '>', '<', '>=', and '<=') for values with
+Comparison operators ('==', '!=', '>', '<', '>=', and '<=') for Variables with
 uncertainties are somewhat complicated, and need special atention.  As we
 hinted at above, and will explore in more detai below and in the
 :ref:`Technical Guide <comparison_operators>`, this relates to the correlation
-between variables with
+between Variables.
 
 
 
 Equality and inequality comparisons
 ------------------------------------
 
+If we compare the equality of two Variables with the same nominal value and
+uncertainty, we see
+
 >>> x = ufloat(5, 0.5)
 >>> y = ufloat(5, 0.5)
 >>> x == x
 True
 >>> x == y
 False
 
-While it may seem like this based on identity, note that
+The difference here is that although the two Python objects have the same
+nominal value and uncertainty, these are indepedent, uncorrelated values.  It
+is not exactly true that the difference is based on identity, note that
 
 >>> x == (1.0*x)
 True
 >>> x is (1.0*x)
 False
 
 In order for the resuls of two calculations with uncertainties to be considered
-equal, the nomimal value *and* the uncertainty must have the same value.
+equal, the :mod:`uncertainties` package does not test whether the nomimal value
+and the uncertainty have the same value.  Instead it checks whether the
+difference of the two calculations has a nominal value of 0 *and* an
+uncertainty of 0.
+
+>>> (x -x)
+0.0+/-0
+>>> (x -y)
+0.0+/-0.7071067811865476
 
 
 Comparisons of magnitude
@@ -261,11 +274,6 @@ To check whether the uncertainty is NaN or Inf, use one of :func:`math.isnan`,
 ``std_dev`` attribute.
 
 
-.. index:: arrays; simple use, matrices; simple use
-
-.. _simple_array_use:
-
-
 .. index:: correlations; detailed example