diff --git a/doc/reference/c++/det_manip/cookbook/basic.rst b/doc/reference/c++/det_manip/cookbook/basic.rst
index 87e3d7c6..91d41d38 100644
--- a/doc/reference/c++/det_manip/cookbook/basic.rst
+++ b/doc/reference/c++/det_manip/cookbook/basic.rst
@@ -1,7 +1,5 @@
-Basics
-------
-
-Here, an exemple of creation of a class det_manip, of use of insert and remove. 
+Creation of an empty det_manip class
+-------------------------------------
 
 .. compileblock:: 
 
@@ -9,58 +7,204 @@ Here, an exemple of creation of a class det_manip, of use of insert and remove.
 
     struct fun {
 
-    typedef double result_type;
-    typedef double argument_type;
+      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);
+      }
 
-    //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);
+      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;
+      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;
     }
 
+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<<" (f(x,y)="<<f(x0,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/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();
   }