zeroRow := function(n)
   local
      row, rowEntry;
   row := [];
   for rowEntry in [1..n] do
      Add(row, 0);
   od;
   return row;
   end;

idMatrixRow := function(n, i)
   local
      row;
   row := zeroRow(n);
   row[i] := 1;
   return row;
   end;

zeroMatrix := function(n)
   local 
      matrix, row, rowNumber;

   row := zeroRow(n);

   matrix := [];
   for rowNumber in [1..n] do
      Add( matrix, row);
   od;

   return matrix;
   end;

lambdaMatrix := function(n)
#  Initialize a matrix with  1's  on the diagonal and  -1's
#  on the subdiagonal.
   local 
      matrix, row, rowNumber;

   matrix := [];
   Add( matrix, idMatrixRow( n, 1 ) );

   for rowNumber in [2..n] do
      row := idMatrixRow( n, rowNumber );
      row[ rowNumber - 1 ] := -1;
      Add(matrix, row);
   od;

   return matrix;
   end;

addBlock:= function( V, M, iPut, jPut )
#  Add the values of  M  to the block of  V  with upper 
#  left corner (iPut, jPut).

   local 
      i, j, row, mRows, mColumns;
   mRows := Size(M);
   mColumns := Size(M[1]);
   
   for i in [iPut..iPut + mRows - 1] do
      row := zeroRow(Size(V));
      for j in [1..Size(V)] do
         row[j] := V[i][j];
      od;
      for j in [0..mColumns-1] do
         row[jPut + j] := row[jPut + j] + M[i - iPut + 1][j + 1];
      od;
      V[i] := row;
   od;
   end;