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Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Implift/transformations.ads, Revision 1.1

1.1     ! maekawa     1: with Standard_Integer_Vectors;           use Standard_Integer_Vectors;
        !             2: with Standard_Integer_VecVecs;           use Standard_Integer_VecVecs;
        !             3: with Standard_Integer_Matrices;          use Standard_Integer_Matrices;
        !             4: with Standard_Complex_Vectors;
        !             5:
        !             6: package Transformations is
        !             7:
        !             8: -- DESCRIPTION :
        !             9: --   This package implements monomial transformations.
        !            10:
        !            11:   type Transfo is private;
        !            12:
        !            13: -- CONSTRUCTORS :
        !            14:
        !            15:   function Id ( n : natural ) return Transfo;
        !            16:
        !            17:   -- DESCRIPTION :
        !            18:   --   Returns the identical transformation.
        !            19:
        !            20:   function Create ( v : Vector; i : integer ) return Transfo;
        !            21:
        !            22:   -- DESCRIPTION :
        !            23:   --   returns a transformation T such that after w = Apply(T,v),
        !            24:   --   there exists a j /= i: w(i) = 1 and w(j) = 0;
        !            25:   --   if v(i) = 0, then the identity transformation will be returned;
        !            26:   --   T is an isomorphism.
        !            27:
        !            28:   function Create ( v : VecVec ) return Transfo;
        !            29:
        !            30:   -- DESCRIPTION :
        !            31:   --   returns a transformation T, where v(i) is the image of
        !            32:   --   the i-th basis vector, for i in da'range.
        !            33:
        !            34:   function Create ( m : Matrix ) return Transfo;
        !            35:
        !            36:   -- DESCRIPTION :
        !            37:   --   Returns the transformation defined by the matrix m.
        !            38:   --   Apply(Create(m),v) = m*v.
        !            39:
        !            40:   function Rotate ( v : Vector; i : integer ) return Transfo;
        !            41:   function Rotate ( v : Link_to_Vector; i : integer ) return Transfo;
        !            42:
        !            43:   -- DESCRIPTION :
        !            44:   --   Returns a transformation T which will reduce v into e_i;
        !            45:   --   if v(i) /= 0; T is an isomorphism.
        !            46:
        !            47:   function Build_Transfo ( v : Vector; i : integer ) return Transfo;
        !            48:   function Build_Transfo ( v : Link_to_Vector; i : integer ) return Transfo;
        !            49:
        !            50:   -- DESCRIPTION :
        !            51:   --   Returns a transformation T so that for all vectors x
        !            52:   --   < x , v > = pv, after application of T on all x, the
        !            53:   --   following holds: x(i) = pv / d, where d is the gcd of
        !            54:   --   the components of v; T is an isomorphism.
        !            55:
        !            56: -- SELECTORS :
        !            57:
        !            58:   function Dimension ( t : Transfo ) return natural;
        !            59:
        !            60:   -- DESCRIPTION :
        !            61:   --   Returns the dimension of the transformation.
        !            62:
        !            63:   function Sign ( t : Transfo ) return integer;
        !            64:
        !            65:   -- DESCRIPTION :
        !            66:   --   Returns the determinant of the matrix representation of t,
        !            67:   --   which is either +1 or -1.
        !            68:
        !            69: -- OPERATIONS :
        !            70:
        !            71:   function Transpose ( t : Transfo ) return Transfo;
        !            72:
        !            73:   -- DESCRIPTION :
        !            74:   --   Returns the transposed transformation.
        !            75:
        !            76:   function Invert ( t : Transfo ) return Transfo;
        !            77:
        !            78:   -- DESCRIPTION :
        !            79:   --   Computes the inverse transformation of t;
        !            80:   --   after t1 := Invert(t), t1*t = t*t1 = Id.
        !            81:
        !            82:   -- REQUIRED : t is an isomorphism.
        !            83:
        !            84:   function "*" ( t1,t2 : Transfo ) return Transfo;
        !            85:
        !            86:   -- DESCRIPTION :
        !            87:   --   Returns t1 after t2
        !            88:
        !            89:   procedure Mult1 ( t1 : in out Transfo; t2 : in Transfo );
        !            90:
        !            91:   -- DESCRIPTION :
        !            92:   --   t1 := t1 * t2;  but with an efficient memory management
        !            93:
        !            94:   procedure Mult2 ( t1 : in Transfo; t2 : in out Transfo );
        !            95:
        !            96:   -- DESCRIPTION :
        !            97:   --   t2 := t1 * t2;  but with an efficient memory management
        !            98:
        !            99:   function "*"( t : Transfo; v : Vector ) return Vector;  -- return t*v;
        !           100:   function "*"( t : Transfo; v : Link_to_Vector ) return Link_to_Vector;
        !           101:   procedure Apply ( t : in Transfo; v : in out Vector );  -- v := t*v;
        !           102:   procedure Apply ( t : in Transfo; v : in out Link_to_Vector );
        !           103:
        !           104:   function "*" ( t : Transfo; v : Standard_Complex_Vectors.Vector )
        !           105:                return Standard_Complex_Vectors.Vector;
        !           106:   procedure Apply ( t : in Transfo;
        !           107:                     v : in out Standard_Complex_Vectors.Vector ); -- v := t*v;
        !           108:
        !           109: -- DESTRUCTOR :
        !           110:
        !           111:   procedure Clear ( t : in out Transfo );
        !           112:
        !           113:   -- DESCRIPTION :
        !           114:   --   Frees all allocated memory space
        !           115:
        !           116: private
        !           117:
        !           118:   type Transfo_tp;
        !           119:   type Transfo is access Transfo_tp;
        !           120:
        !           121: end Transformations;