diff --git a/doc/reference/c++/arrays/contents.rst b/doc/reference/c++/arrays/contents.rst
index 2fd565b8..1ee2476f 100644
--- a/doc/reference/c++/arrays/contents.rst
+++ b/doc/reference/c++/arrays/contents.rst
@@ -10,7 +10,6 @@ Multidimensional arrays
 
 .. toctree::
    :maxdepth: 1
-   :numbered:
 
    introduction
    concepts
@@ -35,4 +34,4 @@ Multidimensional arrays
    multithreading
    FAQ
    implementation_notes/contents
-    
+   ./../../../tutorials/c++/array_tutorial
diff --git a/doc/reference/c++/det_manip/contents.rst b/doc/reference/c++/det_manip/contents.rst
index 85f9acf0..5075cb50 100644
--- a/doc/reference/c++/det_manip/contents.rst
+++ b/doc/reference/c++/det_manip/contents.rst
@@ -39,4 +39,4 @@ This class implements these general operations. It contains :
 
    det_manip
    behind
-   cookbook/contents
+   ./../../../tutorials/c++/det_manip_tutorial
diff --git a/doc/reference/c++/det_manip/cookbook/basic.rst b/doc/reference/c++/det_manip/cookbook/basic.rst
deleted file mode 100644
index 87e3d7c6..00000000
--- a/doc/reference/c++/det_manip/cookbook/basic.rst
+++ /dev/null
@@ -1,68 +0,0 @@
-Basics
-------
-
-Here, an exemple of creation of a class det_manip, of use of insert and remove. 
-
-.. compileblock:: 
-
-    #include <triqs/det_manip/det_manip.hpp>
-
-    struct fun {
-
-    typedef double result_type;
-    typedef double argument_type;
-
-    //gives the coefficients of the matrix
-    double operator()(double x, double y) const {
-      return(x-y);
-    }
-    };
-
-    int main() {
-      
-      //creation of the class det_manip
-      fun f;
-      int init_size=100;
-      triqs::det_manip::det_manip<fun> D(f,init_size);
-      //the initial matrix is empty:
-      std::cout<<std::endl<<"After construction: D.matrix()="<<D.matrix()<<std::endl<<std::endl;
-      
-      double detratio;
-      //insertion of a line and a column at position (1,1) in the matrix, with x[i]=x, y[j]=y. 
-      double x=2, y=9;
-      int i=0, j=0;
-      detratio = D.try_insert(i,j,x,y);
-      D.complete_operation();
-      std::cout<<"We add a line and a column for i="<<i<<", j="<<j<<", x="<<x<<", y="<<y<<" (f(x,y)="<<f(x,y)<<")."<<std::endl;
-      std::cout<<"D.matrix()="<<D.matrix()<<std::endl<<std::endl;
-      
-      x=3; y=4; i=0; j=0;
-      detratio = D.try_insert(i,j,x,y);
-      D.complete_operation();
-      std::cout<<"We add a line and a column for i="<<i<<", j="<<j<<", x="<<x<<", y="<<y<<" (f(x,y)="<<f(x,y)<<")."<<std::endl;
-      std::cout<<"D.matrix()="<<D.matrix()<<std::endl;
-      std::cout<<"The determinant is "<<D.determinant()<<std::endl;
-      std::cout<<"The inverse matrix is"<<D.inverse_matrix()<< std::endl<<std::endl;
-      
-      x=-7; y=1; i=1; j=2;
-      detratio = D.try_insert(i,j,x,y);
-      D.complete_operation();
-      std::cout<<"We add a line and a column for i="<<i<<", j="<<j<<", x="<<x<<", y="<<y<<" (f(x,y)="<<f(x,y)<<")."<<std::endl;
-      std::cout<<"D.matrix()="<<D.matrix()<<std::endl<<std::endl;
-      std::cout<<"The size of the matrix is now "<<D.size()<<std::endl;
-      std::cout<<"The value of the parameters for coefficient (i,j)=(0,2) is (x,y)=("<<D.get_x(0)<<","<<D.get_y(2)<<") (f("<<D.get_x(0)<<","<<D.get_y(2)<<")="<<f(D.get_x(0),D.get_y(2))<<")."<<std::endl<<std::endl;
-
-      i=0; j=1;
-      detratio = D.try_remove(i,j);
-      D.complete_operation();
-      std::cout<<"We remove a line and a column for i="<<i<<", j="<<j<<"."<<std::endl;
-      std::cout<<"D.matrix()="<<D.matrix()<<std::endl;
-      std::cout<<"The determinant is "<<D.determinant()<<std::endl;
-      std::cout<<"The inverse matrix is"<<D.inverse_matrix()<< std::endl<<std::endl;
-    }
-
-
-
-Learn more in the full reference, see :ref:`det_manip`
-
-
diff --git a/doc/reference/c++/det_manip/cookbook/contents.rst b/doc/reference/c++/det_manip/cookbook/contents.rst
deleted file mode 100644
index 4e7d8482..00000000
--- a/doc/reference/c++/det_manip/cookbook/contents.rst
+++ /dev/null
@@ -1,9 +0,0 @@
-.. highlight:: c
-
-Det_manip cookbook
-===================
-
-.. toctree::
-   :maxdepth: 2
-
-   basic
diff --git a/doc/reference/c++/det_manip/det_manip.rst b/doc/reference/c++/det_manip/det_manip.rst
index 1e8edd90..da2b36c7 100644
--- a/doc/reference/c++/det_manip/det_manip.rst
+++ b/doc/reference/c++/det_manip/det_manip.rst
@@ -79,9 +79,11 @@ Doxygen documentation
 The :doxy:`full C++ documentation<triqs::det_manip::det_manip>` is available here.
 
 Example  
--------------
+---------
 
-.. code-block:: c
+.. compileblock::
+
+ #include <triqs/det_manip/det_manip.hpp>
 
  struct fun {
 
@@ -89,7 +91,7 @@ Example
   typedef double argument_type;
 
   double operator()(double x, double y) const { 
-    const double pi = acos(-1); 
+    const double pi = acos(-1.); 
     const double beta = 10.0; 
     const double epsi = 0.1; 
     double tau = x-y;
@@ -103,14 +105,18 @@ Example
  int main() { 
 
    fun f;
-   triqs::det_manip::det_manip<fun> D;
+   triqs::det_manip::det_manip<fun> D(f,100);
 
-   /// ....
-   double x=2, y=9, detratio; 
-   detratio = D.try_insert(1,3, x,y); 
+   /// insertions of 3 lines and 3 columns
+   double x=2., y=9., detratio; 
+   detratio = D.try_insert(0, 0, x,  y ); 
+   D.complete_operation();
+   detratio = D.try_insert(0, 1, 2., 3.); 
+   D.complete_operation();
+   detratio = D.try_insert(0, 0, 4., 5.); 
    D.complete_operation();
    
-   ///...
+   /// removal of a line (the 3rd) and a column (the 2nd)
    detratio = D.try_remove(2,1);
    D.complete_operation();
   }
diff --git a/doc/reference/python/green/block.rst b/doc/reference/python/green/block.rst
index e6435551..00945426 100644
--- a/doc/reference/python/green/block.rst
+++ b/doc/reference/python/green/block.rst
@@ -183,7 +183,7 @@ behaves like
 
 .. math::
 
-  g(z) \sim ... + M_{-1} z + M_0 + \frac{M_1}{z} + \frac{M_2}{z} + ...
+  g(z) \sim ... + M_{-1} z + M_0 + \frac{M_1}{z} + \frac{M_2}{z^2} + ...
 
 where :math:`M_i` are matrices with the same dimensions as :math:`g`. 
 
diff --git a/doc/tutorials/c++/array_tutorial.rst b/doc/tutorials/c++/array_tutorial.rst
index 12f8cd5c..fcc3e91c 100644
--- a/doc/tutorials/c++/array_tutorial.rst
+++ b/doc/tutorials/c++/array_tutorial.rst
@@ -1,9 +1,14 @@
-Using arrays
-===============
+Examples of use of 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.
+.. toctree::
+   :maxdepth: 1
+
+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
@@ -173,4 +178,4 @@ 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>`
+The full reference of the array library can be found :doc:`here  <../../reference/c++/arrays/contents>`
diff --git a/doc/tutorials/c++/contents.rst b/doc/tutorials/c++/contents.rst
index debc413c..62823cd9 100644
--- a/doc/tutorials/c++/contents.rst
+++ b/doc/tutorials/c++/contents.rst
@@ -9,6 +9,6 @@ C++ libraries
    :maxdepth: 1  
 
    array_tutorial
-
+   det_manip_tutorial
 
 ..
diff --git a/doc/tutorials/c++/det_manip_tutorial.rst b/doc/tutorials/c++/det_manip_tutorial.rst
new file mode 100644
index 00000000..d01b71e1
--- /dev/null
+++ b/doc/tutorials/c++/det_manip_tutorial.rst
@@ -0,0 +1,227 @@
+Det_manip cookbook
+===================
+
+.. highlight:: c
+
+.. toctree::
+   :maxdepth: 1
+
+TRIQS comes with a class called det_manip to easily perform operations on a special type of matrices 
+(see  :doc:`here  <../../reference/c++/det_manip/contents>`). 
+This library, among others, allows to easily add or remove lines or columns to the matrix, to calculate the determinant and the inverse. 
+Here are a couple of simple examples showing the basic use of this class.
+
+
+
+Creation of an empty det_manip class
+-------------------------------------
+
+.. compileblock:: 
+
+    #include <triqs/det_manip/det_manip.hpp>
+
+    struct fun {
+
+      typedef double result_type;
+      typedef double argument_type;
+
+      //gives the coefficients of the matrix (function F of the documentation)
+      double operator()(double x, double y) const {
+        return(x-y);
+      }
+
+    };
+
+    int main() {
+    
+      fun f;
+      int init_size = 100; // maximum size of the matrix before a resize
+      
+      //creation of a class det_manip
+      triqs::det_manip::det_manip<fun> D(f, init_size);
+      
+      //the initial matrix is empty:
+      std::cout<<std::endl<< "After construction: D.matrix()=" << D.matrix()<<std::endl<<std::endl;
+      
+    }
+
+Creation of a non empty det_manip class
+----------------------------------------
+
+.. compileblock:: 
+
+    #include <triqs/det_manip/det_manip.hpp>
+    
+    struct fun {
+      
+      typedef double result_type;
+      typedef double argument_type;
+      
+      //gives the coefficients of the matrix (function F of the documentation)
+      double operator()(double x, double y) const {
+        return(x-y);
+      }
+      
+    };
+    
+    int main() {
+      
+      fun f;
+      std::vector<double> initial_x{1,2}, initial_y{3,4};
+      
+      //creation of a class det_manip with a 2 by 2 matrix
+      triqs::det_manip::det_manip<fun> D(f, initial_x, initial_y);
+      
+      //the initial matrix:
+      std::cout<<std::endl<< "After construction: D.matrix()=" << D.matrix()<<std::endl<<std::endl;
+      
+    }
+
+
+Get informations about a det_manip class
+-----------------------------------------
+
+.. compileblock:: 
+
+    #include <triqs/det_manip/det_manip.hpp>
+    
+    struct fun {
+     typedef double result_type;
+     typedef double argument_type;
+     double operator()(double x, double y) const { return(x-y); }
+    };
+    
+   int main() {
+    fun f;
+    int i=0, j=1;
+    std::vector<double> initial_x{1,2}, initial_y{3,4};
+    triqs::det_manip::det_manip<fun> D(f, initial_x, initial_y);
+    std::cout<<std::endl<<"D.matrix()=" << D.matrix() <<std::endl<<std::endl;
+    std::cout<<"The size of the matrix is "<< D.size() <<std::endl<<std::endl;
+    std::cout<<"The determinant is "<< D.determinant() <<std::endl<<std::endl;
+    std::cout<<"The inverse matrix is"<< D.inverse_matrix() << std::endl<<std::endl;
+    std::cout<<"The value of the parameters for coefficient (i,j)=("<<i<<","<<j<<") is (x,y)=("
+    <<D.get_x(i)<<","<<D.get_y(j)<<")"<<std::endl<<std::endl;
+   }
+
+Add a line and a column
+-------------------------
+
+.. compileblock:: 
+
+    #include <triqs/det_manip/det_manip.hpp>
+    
+    struct fun {
+      typedef double result_type;
+      typedef double argument_type;
+      double operator()(double x, double y) const { return(exp(x)-y*y); }
+    };
+    
+    int main() {
+      triqs::det_manip::det_manip<fun> D(fun(), std::vector<double>{1,2,2.5}, std::vector<double>{3,4,9});
+      std::cout<<std::endl<<"After construction, D.matrix()="<<D.matrix()<<std::endl<<std::endl;
+      double x0 = 2.1, y0 = 7;
+      int i = 2, j = 0; // number of the added line and column
+      std::cout<<"We want to add a line and a column for i="<<i<<", j="<<j
+      <<", x="<<x0<<", y="<<y0<<"."<<std::endl;
+      // (try of) insertion of a line and a column at position (3,1) in the matrix
+      // with x[i]=x0, y[j]=y0. 
+      double detratio = D.try_insert(i, j, x0, y0); // the ratio between new and old determinants
+      // while the operation is not complete, the matrix stays unchanged
+      std::cout<<"After try_insert, D.matrix()="<<D.matrix()<<std::endl;
+      // here we validate the insertion: the (inverse) matrix and determinant are updated
+      D.complete_operation();
+      std::cout<<"After complete_operation, D.matrix()="<<D.matrix()<<std::endl<<std::endl;
+
+    }
+
+Remove a line and a column
+---------------------------
+
+.. compileblock:: 
+
+    #include <triqs/det_manip/det_manip.hpp>
+    
+    struct fun {
+      typedef double result_type;
+      typedef double argument_type;
+      double operator()(double x, double y) const { return(exp(x)-y*y); }
+    };
+    
+    int main() {
+      triqs::det_manip::det_manip<fun> D(fun(), std::vector<double>{1,2,2.5}, std::vector<double>{3,4,9});
+      std::cout<<std::endl<<"After construction, D.matrix()="<<D.matrix()<<std::endl<<std::endl;
+      int i = 1, j = 0; // number of the removed line and column
+      std::cout<<"We want to remove a line and a column for i="<<i<<", j="<<j<<"."<<std::endl;
+      // (try of) removal of a line and a column at position (1,0) in the matrix.
+      double detratio = D.try_remove(i, j); // the ratio between new and old determinants
+      // while the operation is not complete, the matrix stays unchanged
+      std::cout<<"After try_remove, D.matrix()="<<D.matrix()<<std::endl;
+      // here we validate the removal: the (inverse) matrix and determinant are updated
+      D.complete_operation();
+      std::cout<<"After complete_operation, D.matrix()="<<D.matrix()<<std::endl<<std::endl;
+    }
+
+
+
+Add two lines and two columns
+------------------------------
+
+.. compileblock:: 
+
+    #include <triqs/det_manip/det_manip.hpp>
+    
+    struct fun {
+      typedef double result_type;
+      typedef double argument_type;
+      double operator()(double x, double y) const { return(exp(x)-y*y); }
+    };
+    
+    int main() {
+      triqs::det_manip::det_manip<fun> D(fun(), std::vector<double>{1,2,2.5}, std::vector<double>{3,4,9});
+      std::cout<<std::endl<<"After construction, D.matrix()="<<D.matrix()<<std::endl<<std::endl;
+      double x0 = 2.1, y0 = 7, x1 = 3.5, y1 = 5;
+      int i0 = 2, i1 = 1, j0 = 0, j1 = 3;      // number of the added lines and columns
+      std::cout<<"We want to add a line and a column for i0="<<i0<<", j0="<<j0<<", i1="<<i1<<", j1="<<j1
+      <<", x0="<<x0<<", y0="<<y0<<", x1="<<x1<<", y1="<<y1<<")."<<std::endl;
+      // (try of) insertion of 2 lines and 2 columns in the matrix
+      double detratio = D.try_insert2 (i0, i1, j0, j1, x0, x1, y0, y1); // the ratio between new and old determinants
+      // while the operation is not complete, the matrix stays unchanged
+      std::cout<<"After try_insert2, D.matrix()="<<D.matrix()<<std::endl;
+      // here we validate the insertion: the (inverse) matrix and determinant are updated
+      D.complete_operation();
+      std::cout<<"After complete_operation, D.matrix()="<<D.matrix()<<std::endl<<std::endl;
+    }
+
+Remove two lines and two columns
+--------------------------------
+
+.. compileblock:: 
+
+    #include <triqs/det_manip/det_manip.hpp>
+    
+    struct fun {
+      typedef double result_type;
+      typedef double argument_type;
+      double operator()(double x, double y) const { return(exp(x)-y*y); }
+    };
+    
+    int main() {
+      triqs::det_manip::det_manip<fun> D(fun(), std::vector<double>{1,2,2.5}, std::vector<double>{3,4,9});
+      std::cout<<std::endl<<"After construction, D.matrix()="<<D.matrix()<<std::endl<<std::endl;
+      int i0 = 2, i1 = 1, j0 = 0, j1 = 1;      // number of the removed lines and columns
+      std::cout<<"We want to remove 2 lines and 2 columns for i0="
+      <<i0<<", j0="<<j0<<", i1="<<i1<<", j1="<<j1<<"."<<std::endl;
+      // (try of) removal of a line and a column at position (1,0) in the matrix.
+      double detratio = D.try_remove2(i0, i1, j0, j1); // the ratio between new and old determinants
+      // while the operation is not complete, the matrix stays unchanged
+      std::cout<<"After try_remove2, D.matrix()="<<D.matrix()<<std::endl;
+      // here we validate the removal: the (inverse) matrix and determinant are updated
+      D.complete_operation();
+      std::cout<<"After complete_operation, D.matrix()="<<D.matrix()<<std::endl<<std::endl;
+    }
+
+
+Learn more in the full reference, see :ref:`det_manip`
+
+
diff --git a/test/triqs/det_manip/det_manip_constructors.cpp b/test/triqs/det_manip/det_manip_constructors.cpp
new file mode 100644
index 00000000..bf579fde
--- /dev/null
+++ b/test/triqs/det_manip/det_manip_constructors.cpp
@@ -0,0 +1,31 @@
+    #include <triqs/det_manip/det_manip.hpp>
+    
+    struct fun {
+      
+      typedef double result_type;
+      typedef double argument_type;
+      
+      //gives the coefficients of the matrix (function F of the documentation)
+      double operator()(double x, double y) const {
+        return(x-y);
+      }
+      
+    };
+    
+    int main() {
+      
+      fun f;
+      int init_size=10;
+      std::vector<double> initial_x{1,2,2.5}, initial_y{3,4,9};
+      
+      //creation of an empty class det_manip
+      triqs::det_manip::det_manip<fun> D1(f, init_size);
+      
+      //creation of a class det_manip with a 3 by 3 matrix
+      triqs::det_manip::det_manip<fun> D2(f, initial_x, initial_y);
+      
+      //the initial matrix:
+      std::cout<<std::endl<< "After construction: D.matrix()=" << D1.matrix()<<std::endl;
+      std::cout<<std::endl<< "After construction: D.matrix()=" << D2.matrix()<<std::endl;
+      
+    }
\ No newline at end of file
diff --git a/triqs/det_manip/det_manip.hpp b/triqs/det_manip/det_manip.hpp
index 8eb84123..9b8230d6 100644
--- a/triqs/det_manip/det_manip.hpp
+++ b/triqs/det_manip/det_manip.hpp
@@ -206,7 +206,7 @@ namespace triqs { namespace det_manip {
      * \param X, Y : container for X,Y. 
      */
     template<typename ArgumentContainer1, typename ArgumentContainer2>
-     det_manip(FunctionType F, ArgumentContainer1 const & X, ArgumentContainer2 const & Y) : f(std::move(F)) { 
+    det_manip(FunctionType F, ArgumentContainer1 const & X, ArgumentContainer2 const & Y) : f(std::move(F)), Nmax(0) { 
       if (X.size() != Y.size()) TRIQS_RUNTIME_ERROR<< " X.size != Y.size";
       _construct_common();
       N =X.size();