with Standard_Integer_Vectors;           use Standard_Integer_Vectors;
with Standard_Integer_VecVecs;           use Standard_Integer_VecVecs;
with Lists_of_Integer_Vectors;           use Lists_of_Integer_Vectors;
with Arrays_of_Integer_Vector_Lists;     use Arrays_of_Integer_Vector_Lists;
with Standard_Complex_Polynomials;       use Standard_Complex_Polynomials;
with Standard_Complex_Poly_Functions;    use Standard_Complex_Poly_Functions;
with Standard_Complex_Poly_Systems;      use Standard_Complex_Poly_Systems;
with Standard_Complex_Poly_SysFun;       use Standard_Complex_Poly_SysFun;

package Integer_Lifting_Functions is

-- DESCRIPTION :
--   This package offers three different types of integer-valued
--   lifting functions: linear, polynomial, and point-wise.

-- LINEAR LIFTING :

  function Linear_Lift ( lf,v : Vector ) return Vector;
  function Linear_Lift ( lf : Vector; l : List ) return List;
  function Linear_Lift ( lf : VecVec;
                         l : Array_of_Lists ) return Array_of_Lists;

  -- DESCRIPTION :
  --   The last entry of the enlarged vector on return equals <lf,v>,
  --   for every vector v in the lists.

  -- REQUIRED : lf'range = v'range.

-- POLYNOMIAL LIFTING :

  function Polynomial_Lift ( lf : Poly; v : Vector ) return Vector;
  function Polynomial_Lift ( lf : Eval_Poly; v : Vector ) return Vector;
  function Polynomial_Lift ( lf : Poly; l : List ) return List;
  function Polynomial_Lift ( lf : Eval_Poly; l : List ) return List;
  function Polynomial_Lift ( lf : Poly_Sys; l : Array_of_Lists )
                           return Array_of_Lists;
  function Polynomial_Lift ( lf : Eval_Poly_Sys; l : Array_of_Lists )
                           return Array_of_Lists;

  -- DESCRIPTION :
  --   As lf is complex valued, the rounded real part is used as lifting.

-- RANDOM LIFTING :

  function Random_Lift ( lflow,lfupp : integer; v : Vector ) return Vector;
  function Random_Lift ( lflow,lfupp : integer; l : List ) return List;
  function Random_Lift ( lflow,lfupp : Vector; l : Array_of_Lists )
                       return Array_of_Lists;

  -- DESCRIPTION :
  --   The lifting values are random integers between lflow and lfupp.

-- RANDOM LINEAR LIFTING :

  function Random_Linear_Lift ( lflow,lfupp : integer; v : Vector ) 
                              return Vector;
  function Random_Linear_Lift ( lflow,lfupp : integer; l : List ) return List;
  function Random_Linear_Lift ( lflow,lfupp : Vector; l : Array_of_Lists )
                              return Array_of_Lists;

  -- DESCRIPTION :
  --   Linear lifting with random vectors of integers between lflow and lfupp.

-- POINT-WISE LIFTING :

  function Point_Lift ( lf : integer; v : Vector ) return Vector;
  function Point_Lift ( lf : Vector; l : List ) return List;
  function Point_Lift ( lf : VecVec;
                        l : Array_of_Lists ) return Array_of_Lists;

  -- DESCRIPTION :
  --   The enlarged vector on return has as last component the lifting lf(k),
  --   where k is the position of the vector v in the lists.

  -- REQUIRED : Length_Of(l) = lf'length.

end Integer_Lifting_Functions;