![]() ![]() | ![]() |
File: [local] / OpenXM_contrib / PHC / Ada / Root_Counts / Stalift / mixed_volume_computation.ads (download)
Revision 1.1.1.1 (vendor branch), Sun Oct 29 17:45:31 2000 UTC (23 years, 10 months ago) by maekawa
Import the second public release of PHCpack. OKed by Jan Verschelde. |
with text_io; use text_io; with Standard_Integer_Vectors; use Standard_Integer_Vectors; with Standard_Complex_Poly_Systems; use Standard_Complex_Poly_Systems; with Arrays_of_Integer_Vector_Lists; use Arrays_of_Integer_Vector_Lists; with Integer_Mixed_Subdivisions; use Integer_Mixed_Subdivisions; package Mixed_Volume_Computation is -- DESCRIPTION : -- This package offers a number of routines for the computation -- of the mixed volume of a system of polynomial equations. -- UTILITIES : procedure Compute_Mixture ( supports : in out Array_of_Lists; mix,perms : out Link_to_Vector ); -- DESCRIPTION : -- Computes the type of mixture of the supports of a system. -- ON ENTRY : -- supports the supports of a polynomial system. -- ON RETURN : -- supports a permuted array of supports, so that the same -- supports stand all toghether; -- mix mix(k) indicates number of occurrencies of the kth support; -- perms perms(k) gives the place of the kth support, -- after permutation to make supports correspond with mix. function Compute_Index ( k : natural; mix : Vector ) return natural; -- DESCRIPTION : -- Given k, an entry in the supports, the number this function returns -- indicates the number of different support, w.r.t. the type of mixture. function Compute_Permutation ( n : natural; mix : Vector; supports : Array_of_Lists ) return Link_to_Vector; -- DESCRIPTION : -- Given the type of mixture and the support, the permutation vector -- will be computed. -- ON RETURN : -- perms perms(k) gives the place of the kth support, -- after permutation to make supports correspond with mix. function Typed_Lists ( mix : Vector; points : Array_of_Lists ) return Array_of_Lists; -- DESCRIPTION : -- Returns a tuple of lists where each list occurs only once, -- according to the given type of mixture. function Permute ( p : Poly_Sys; perm : Link_to_Vector ) return Poly_Sys; function Permute ( supports : Array_of_Lists ; perm : Link_to_Vector ) return Array_of_Lists; -- DESCRIPTION : -- Permutes the polynomials in the system or the supports, -- according to the vector perm. -- MIXED VOLUME COMPUTATION, GIVEN A SUBDIVISION : function Mixed_Volume ( n : natural; mix : Vector; mic : Mixed_Cell ) return natural; function Mixed_Volume ( n : natural; mix : Vector; mixsub : Mixed_Subdivision ) return natural; -- DESCRIPTION : -- Computes the mixed volume based on a mixed cell and subdivision. -- When the cells are not fine enough, they will be refined but will -- be lost after returning the result. procedure Mixed_Volume ( n : in natural; mix : in Vector; mic : in out Mixed_Cell; mv : out natural ); procedure Mixed_Volume ( n : in natural; mix : in Vector; mixsub : in out Mixed_Subdivision; mv : out natural ); -- DESCRIPTION : -- Computes the mixed volume based on a mixed cell and subdivision. -- When the cells are not fine enough, they will be refined by lifting. -- The refinement is stored in the subdivision field of the cells. -- MIXED VOLUME COMPUTATIONS, GIVEN THE SUPPORTS : function Mixed_Volume ( n : natural; supports : Array_of_Lists ) return natural; function Mixed_Volume ( file : file_type; n : natural; supports : Array_of_Lists ) return natural; function Mixed_Volume ( n : natural; mix : Vector; supports : Array_of_Lists ) return natural; function Mixed_Volume ( file : file_type; n : natural; mix : Vector; supports : Array_of_Lists ) return natural; procedure Mixed_Volume ( n : in natural; mix : in Vector; supports : in Array_of_Lists; lifted : out Array_of_Lists; mixsub : out Mixed_Subdivision; mv : out natural ); procedure Mixed_Volume ( file : in file_type; n : in natural; mix : in Vector; supports : in Array_of_Lists; lifted : out Array_of_Lists; mixsub : out Mixed_Subdivision; mv : out natural ); -- DESCRIPTION : -- All these routines compute the mixed volume of support lists. -- ON ENTRY : -- file if specified, then the mixed subdivision will be -- written on file; -- n the dimension of the system; -- mix mix(k) is the number of times the kth support occurs; -- supports the supports of a system of n polynomials in n unknowns. -- ON RETURN : -- lifted array of listed points; -- mixsub mixed subdivision used; -- mv the mixed volume. end Mixed_Volume_Computation;