doc: fixed a few typos+ put back tutorial for arrays+changed a few titles

doc/reference/c++/arrays/contents.rst

@@ -2,7 +2,7 @@ Multidimensional arrays
 *******************************************
 .. warning::
 
-   This library is of stable quality, except when mentionned otherwise (for some recent features).
+   This library is of stable quality, except when otherwise stated(for some recent features).
    
    Documentation is still work in progress.
    

doc/reference/c++/using_the_lib/triqs_library.rst

@@ -1,7 +1,7 @@
 .. highlight:: c
 
-A simple C++ code
---------------------
+Writing you own C++ code with TRIQS
+------------------------------------
 Basically, this structure means that you have successfully installed TRIQS in
 :file:`/home/triqs/install` and that you plan to have your new project under
 :file:`/home/project`. Obviously you can choose any other directory but this
@@ -86,9 +86,9 @@ That's it! You can modify your sources and then recompile with make. Obviously
 with bigger projects your :file:`CMakeLists.txt` file will change, but the
 principle remains the same.
 
-A simple C++ code, with its tests and documentation
+A simple C++ project, with its tests and documentation
 ------------------------------------------------------
 
-A mixed C++/Python code
+A mixed C++/Python project
 ------------------------------
 

doc/tutorials/c++/array_tutorial.rst

@@ -3,6 +3,7 @@ Using arrays
 
 .. highlight:: c
 
+TRIQS comes with a library of multidimensional arrays. This library, among others, allows for easy slicing, archiving and algebraic manipulations of multidimensional arrays. Here are a couple of simple examples showing the basic use of this class.
 
 
 Declaring and printing an array
@@ -172,4 +173,4 @@ Map and fold
       std::cout << "F(2*A) = "<<C<<std::endl;
     }
 
-
+The full reference of the array library can be found :doc:`here:  <../../reference/c++/arrays/contents>`

doc/tutorials/c++/contents.rst

@@ -8,7 +8,7 @@ C++ libraries
 .. toctree::
    :maxdepth: 1  
 
+   array_tutorial
 
 
 ..
-   array_tutorial

doc/tutorials/python/ipt/ipt.rst

@@ -1,6 +1,6 @@
 .. _ipt:
 
-Iterated perturbation theory: an extended DMFT example
+Iterated perturbation theory: an more elaborate DMFT example
 ========================================================
 
 Introduction

doc/tutorials/python/tour1.rst

@@ -3,7 +3,7 @@
 Tour 1: Manipulations with local Green functions 
 ------------------------------------------------
 
-Let use start with a problem of free electrons : an impurity `d`
+Let us start with a problem of free electrons: an impurity `d`
 level embedded in a flat conduction bath :math:`\Delta` of `s`-electrons.
 To construct and plot the corresponding 2x2 Green's function:
 
@@ -12,7 +12,7 @@ To construct and plot the corresponding 2x2 Green's function:
   \hat{G}^\mathrm{s+d} ( \omega) = \begin{pmatrix} \omega - \epsilon_d & V \\ V & \Delta^{-1} \end{pmatrix}^{-1}
 
 we first create the corresponding energy
-mesh `a` on the real axis in the energy interval :math:`\omega \in (-2:2]`  
+mesh on the real axis in the energy interval :math:`\omega \in (-2:2]`.  
 The Green's function is generated using classes of the ``gf.local`` module by setting up
 :math:`\left[\hat{G}^\mathrm{s+d}\right]^{-1}` and inverting it.
 Finally, the obtained bath and impurity densities of states are plotted using the TRIQS function ``oplot``: 

doc/tutorials/python/tour4.rst

@@ -12,16 +12,16 @@ In the case of Bethe lattice the dynamical mean-field theory (DMFT) self-consist
   G^{-1}_{0,\sigma} (i \omega_n) = i \omega_n + \mu - t^2 G_{\sigma} (i \omega_n).
 
 
-Hence, from a strictly technical point of view, in this case DMFT cycle can be implemented by modifying 
+Hence, from a strictly technical point of view, in this case the DMFT cycle can be implemented by modifying 
 the previous single-impurity example to the case of a bath with semi-circular density of states and adding a python loop to update :math:`G_0` as function of :math:`G`.
 
-Here is a complete program doing this plain vanilla DMFT  on a half-filled one-band Bethe lattice:
+Here is a complete program doing this plain-vanilla DMFT  on a half-filled one-band Bethe lattice:
 
 
 .. literalinclude:: ./single_site_bethe.py
 
 
-A general introduction to DMFT calculations with TRIQS can be found :ref:`here <dmftloop>`
+A general introduction to DMFT calculations with TRIQS can be found :ref:`here <dmftloop>`.
 
 Chapter :ref:`Wien2TRIQS <Wien2k>` discusses the TRIQS implementation for DMFT calculations of real materials and the interface between TRIQS and the Wien2k band structure code.