Return to minkowski_polynomials.ads CVS log

Up to [local] / OpenXM_contrib / PHC / Ada / Root_Counts / Dynlift

Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Dynlift/minkowski_polynomials.ads, Revision 1.1

1.1     ! maekawa     1: with Standard_Integer_Vectors;           use Standard_Integer_Vectors;
        !             2: with Standard_Complex_Polynomials;       use Standard_Complex_Polynomials;
        !             3: with Triangulations;                     use Triangulations;
        !             4: with Integer_Mixed_Subdivisions;         use Integer_Mixed_Subdivisions;
        !             5:
        !             6: package Minkowski_Polynomials is
        !             7:
        !             8: -- DESCRIPTION :
        !             9: --   This package allows the computation of the Minkowski-polynomial
        !            10: --   of a tuple of polytopes (P1,P2,..,Pr).  This polynomial is the
        !            11: --   expansion of the volume of a positive linear combination of the
        !            12: --   polytopes in the tuple: vol_n(l1*P1 + l2*P2 + .. + lr*Pr), which
        !            13: --   is a homogeneous polynomial of degree n in the coefficients l1,l2,..,lr,
        !            14: --   according to Minkowski's theorem.
        !            15:
        !            16:   function Minkowski_Polynomial ( n,r : natural ) return Poly;
        !            17:
        !            18:   -- DESCRIPTION :
        !            19:   --   Returns the structure of the Minkowski-polynomial, given the
        !            20:   --   dimension and the number of different polytopes in the tuple.
        !            21:
        !            22:   -- ON ENTRY :
        !            23:   --   n           dimension of the polytopes before lifting;
        !            24:   --   r           number of different polytopes in the tuple.
        !            25:
        !            26:   -- ON RETURN :
        !            27:   --   The structure of the Minkowski-polynomial, with all coefficients
        !            28:   --   equal to one.
        !            29:
        !            30:   procedure Minkowski_Polynomial
        !            31:                  ( p : in out Poly; t : in Triangulation; n : in natural;
        !            32:                    mix : in Vector; mixsub : out Mixed_Subdivision );
        !            33:
        !            34:   -- DESCRIPTION :
        !            35:   --   Computes the coefficients of the Minkowski-polynomial, given its
        !            36:   --   structure and based on the triangulation of the Cayley-polytope.
        !            37:   --   On return, one also obtains the mixed subdivision, corresponding
        !            38:   --   the given type of mixture.
        !            39:
        !            40:   generic
        !            41:     with procedure Process ( submix : in Vector; sub : in Mixed_Subdivision;
        !            42:                              vol : out natural );
        !            43:   procedure Minkowski_Polynomial_Subdivisions
        !            44:                  ( p : in out Poly; t : in Triangulation; n : in natural;
        !            45:                    mix : in Vector; mixsub : out Mixed_Subdivision );
        !            46:
        !            47:   -- DESCRIPTION :
        !            48:   --   Computes the coefficients of the Minkowski-polynomial, given its
        !            49:   --   structure and the triangulation of the Cayley polytope.
        !            50:   --   The generic procedure returns the subdivision for a given type of
        !            51:   --   mixture and asks to compute its volume.
        !            52:   --   On return, one also obtains the mixed subdivision, corresponding
        !            53:   --   the given type of mixture.
        !            54:
        !            55: end Minkowski_Polynomials;