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File: [local] / OpenXM_contrib / PHC / Ada / Root_Counts / Implift / volumes.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 Lists_of_Integer_Vectors; use Lists_of_Integer_Vectors; with Arrays_of_Integer_Vector_Lists; use Arrays_of_Integer_Vector_Lists; with Trees_of_Vectors; use Trees_of_Vectors; package Volumes is -- DESCRIPTION : -- This package contains a routine to compute the volume -- of a polytope and two routines for computing the mixed volume. function Volume ( n : natural; l : List ) return natural; function Volume ( n : natural; l : List; tv : Tree_of_Vectors ) return natural; procedure Volume ( n : in natural; l : in List; tv : in out Tree_of_Vectors; vlm : out natural ); -- DESCRIPTION : -- Computes n! times the volume of the polytope generated -- by the points in l; n equals the dimension of the space. -- The tree of degrees tv maintains the directions used to -- compute the volume. Once tv has been constructed, the volume -- can be computed more efficiently. -- REMARK : -- The tree of vectors contains directions normal to the polytope -- generated by a list wl where the first element of the list -- consists of all zeroes; so eventually l has been shifted. function Mixed_Volume ( n : natural; al : Array_of_Lists ) return natural; function Mixed_Volume ( n : natural; al : Array_of_Lists; tv : Tree_of_Vectors ) return natural; procedure Mixed_Volume ( n : in natural; al : in Array_of_Lists; tv : in out Tree_of_Vectors; mv : out natural ); -- DESCRIPTION : -- Computes the mixed volume of the polytopes generated -- by the points in al; n equals the dimension of the space. -- The tree of vectors tv maintains the directions used to -- compute the mixed volume. Once tv has been constructed, -- the mixed volume can be computed more efficiently. end Volumes;