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File: [local] / OpenXM_contrib / PHC / Ada / Root_Counts / Symmetry / symmetric_lifting_functions.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 Standard_Floating_Numbers; use Standard_Floating_Numbers; with Standard_Integer_Vectors; with Standard_Floating_Vectors; with Arrays_of_Integer_Vector_Lists; with Arrays_of_Floating_Vector_Lists; with Symmetry_Group; use Symmetry_Group; package Symmetric_Lifting_Functions is -- DESCRIPTION : -- This package provides symmetric lifting functions. procedure Classify_Orbits ( supports : in Arrays_of_Integer_Vector_Lists.Array_of_Lists; mix : in Standard_Integer_Vectors.Vector; v,w : in List_of_Permutations; norb : out natural; orbits : out Arrays_of_Integer_Vector_Lists.Array_of_Lists ); -- DESCRIPTION : -- This procedure provides a symmetric lifting for the given supports, -- w.r.t. the symmetry group, represented by the lists of permutations -- v and w. -- ON ENTRY : -- supports supports of a polynomial system; -- mix type of mixture; -- v,w linear representations of the group actions: -- wk P(x) = P(vk x). -- ON RETURN : -- norb the number of different orbits; -- orbits the lifted supports, w.r.t. the symmetry group, -- as lifting value the orbit number has been used. procedure Float_Lift_Orbits ( orbits : in out Arrays_of_Floating_Vector_Lists.Array_of_Lists; lifting : in Standard_Floating_Vectors.Vector ); -- DESCRIPTION : -- Given supports with classified orbits, each orbit will receive -- the corresponding lifting value in the vector lifting. -- REQUIRED : -- lifting has range 1..#orbits procedure Integer_Lift_Orbits ( orbits : in out Arrays_of_Integer_Vector_Lists.Array_of_Lists; lifting : in Standard_Integer_Vectors.Vector ); -- DESCRIPTION : -- Given supports with classified orbits, each orbit will receive -- the corresponding lifting value in the vector lifting. -- REQUIRED : -- lifting has range 1..#orbits procedure Float_Random_Lift_Orbits ( orbits : in out Arrays_of_Floating_Vector_Lists.Array_of_Lists; norb : in natural; lower,upper : in double_float ); -- DESCRIPTION : -- Orbits are given random floating-point lifting values in [lower,upper]. -- Every point in the same orbit receives the same lifting. -- ON ENTRY : -- orbits classified orbits, last entry of vectors is orbit number; -- norb the number of orbits; -- lower lower bound for random number generator; -- upper upper bound for random number generator. -- ON RETURN : -- orbits each point in the same orbit has the same random number. procedure Integer_Random_Lift_Orbits ( orbits : in out Arrays_of_Integer_Vector_Lists.Array_of_Lists; norb : in natural; lower,upper : in integer ); -- DESCRIPTION : -- Orbits are given random integer lifting values in [lower,upper]. -- Every point in the same orbit receives the same lifting. -- ON ENTRY : -- orbits classified orbits, last entry of vectors is orbit number; -- norb the number of orbits; -- lower lower bound for random number generator; -- upper upper bound for random number generator. -- ON RETURN : -- orbits each point in the same orbit has the same random number. end Symmetric_Lifting_Functions;