with Standard_integer_Vectors; use Standard_integer_Vectors;
with Standard_Integer_Matrices; use Standard_Integer_Matrices;
package Integer_Linear_Inequalities is
-- DESCRIPTION :
-- This package provides some routines for implementing the Farkas lemma.
procedure Integer_Complementary_Slackness
( tableau : in out matrix; feasible : out boolean );
procedure Integer_Complementary_Slackness
( tableau : in out matrix; lastcol : in integer;
feasible : out boolean );
-- DESCRIPTION :
-- Solves the complementary slackness problem: determines
-- whether there exists a positive combination of the columns
-- such that the right-hand side is satisfied.
-- ON ENTRY :
-- tableau inequalities as columns, last column is right hand side;
-- lastcol last column of interest in the tableau,
-- when not provided, tableau'last(2)-1 is assumed.
-- ON RETURN :
-- tableau modified tableau of inequalities;
-- feasible if true then the solution is feasible.
end Integer_Linear_Inequalities;