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File: [local] / OpenXM_contrib / PHC / Ada / Root_Counts / Stalift / contributions_to_mixed_volume.ads (download)
Revision 1.1.1.1 (vendor branch), Sun Oct 29 17:45:29 2000 UTC (23 years, 10 months ago) by maekawa
Import the second public release of PHCpack. OKed by Jan Verschelde. |
with Standard_Integer_Vectors; use Standard_Integer_Vectors; with Arrays_of_Integer_Vector_Lists; use Arrays_of_Integer_Vector_Lists; with Integer_Faces_of_Polytope; use Integer_Faces_of_Polytope; package Contributions_to_Mixed_Volume is -- DESCRIPTION : -- This package provides utilities to determine whether a point -- contributes to the mixed volume of a tuple of point sets, i.e.: whether -- it can be removed of the tuple without decreasing the mixed volume. -- THE CRITERION : (simple/exhaustive) function Simple_Zero_Contribution ( pts : Array_of_Lists; x : Vector; i : natural ) return boolean; function Simple_Zero_Contribution ( pts : Array_of_Lists; ifacets : Faces; x : Vector; i : natural ) return boolean; function Exhaustive_Zero_Contribution ( pts : Array_of_Lists; x : Vector; i : natural ) return boolean; function Exhaustive_Zero_Contribution ( pts : Array_of_Lists; ifacets : Faces; x : Vector; i : natural ) return boolean; -- DESCRIPTION : -- Returns true if the point x does not influence the mixed volume of -- the tuple pts, when considered w.r.t. the ith component. -- There is a simple and an exhaustive criterion to check the contribution -- of the point. When the simple criterion returns false, the point does -- not necessarily make a contribution to the mixed volume, whereas when -- the exhaustive criterion returns false, we can be sure that the point -- contributes to the mixed volume. -- ON ENTRY : -- pts tuple of points sets, with dimension = x'length; -- ifacets all facets of the polytope spanned by pts(i), that contain x; -- x a point, considered w.r.t. pts(i); -- i component of pts, i is in pts'range. -- ON RETURN : -- true if Mixed_Volume(pts) = Mixed_Volume(pts, pts(i) contains x); -- false when the criterion fails to decide. -- SWEEPING THROUGH THE POINT LISTS : (with simple/exhaustive criterion) function Simple_Sweep ( pts : Array_of_Lists ) return Array_of_Lists; function Simple_Sweep ( pts : Array_of_Lists; facets : Array_of_Faces ) return Array_of_Lists; function Exhaustive_Sweep ( pts : Array_of_Lists ) return Array_of_Lists; function Exhaustive_Sweep ( pts : Array_of_Lists; facets : Array_of_Faces ) return Array_of_Lists; -- DESCRIPTION : -- Applies the simple/exhaustive criterion to the points. -- Returns those points for which the criterion has failed to -- demonstrate that the contribution to the mixed volume was zero. -- ON ENTRY : -- pts tuple of point sets; -- facets tuple of facets of the polytopes spanned by pts, -- facets'range = pts'range. -- ON RETURN : -- A tuple of point sets where the points that do not contribute to the -- mixed volume have been eliminated, according to the simple or exhaustive -- criterion that has been used. -- Note that essential sets are not necessarily unique, because they depend -- on the order in which points with zero contribution are eliminated. end Contributions_to_Mixed_Volume;