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File: [local] / OpenXM_contrib / PHC / Ada / Root_Counts / Implift / binomial_system_solvers.ads (download)
Revision 1.1.1.1 (vendor branch), Sun Oct 29 17:45:28 2000 UTC (23 years, 10 months ago) by maekawa
Import the second public release of PHCpack. OKed by Jan Verschelde. |
with Standard_Complex_Vectors; use Standard_Complex_Vectors; with Standard_Integer_VecVecs; use Standard_Integer_VecVecs; with Standard_Complex_Solutions; use Standard_Complex_Solutions; with Transformations; use Transformations; package Binomial_System_Solvers is -- DESCRIPTION : -- This package contains a routine for the solution of a binomial system, -- where the i-th equation is defined as follows: -- -- X^u_i - c_i = 0, for i = 1,2,..,n, -- with -- [ u ]_i a vector of degrees and [ c ]_i a vector of complex numbers, -- -- using a multi_index notation: X^u_i = x1^u_i1 x2^u_i2 . . . xn^u_in. procedure Factorize ( v : in out VecVec; n : in natural; t : in out Transfo ); -- DESCRIPTION : -- This routines factorizes the binomial system defined by the -- degrees in the vector v. -- ON ENTRY : -- v defines the degrees of binomial system; -- n the number of unknowns to be eliminated. -- ON RETURN : -- v the factorized binomial system; -- t the transformations used to factorize. procedure Solve ( v : in VecVec; cv : in Vector; n : in natural; sols : in out Solution_List ); -- DESCRIPTION : -- This routine solves the binomial system defined by the degrees -- in the vector v and by the constants in the vector cv. -- REQUIRED : -- The vector cv contains no zero components! -- ON ENTRY : -- v defines the degrees of binomial system; -- cv is the vector of constants; -- n the dimension of the system. -- ON RETURN : -- sols is the solution list of the binomial system. procedure Residuals ( v : in VecVec; cv : in Vector; n : in natural; sols : in Solution_List; res : out Vector ); -- DESCRIPTION : -- This routine computes the residuals of the solutions of -- the binomial system defined by v and cv. -- REQUIRED : -- The dimension of res equals the number of solutions in sols. -- ON ENTRY : -- v defines the degrees of the binomial system; -- cv the vector of constants; -- n the dimension of the system; -- sols is the solution list of the binomial system. -- ON RETURN : -- res a vector of residuals. end Binomial_System_Solvers;