DATUM ABOUT HILBERT BASES

      
      For n=2 to 5 fixed, Lambda_even is the set of vectors v=(v_i) in Z^3n such that \sum_iv_i is even.     

      The files Ineq_n_Z3n.in contains the inequalities in the standard basis of Z^3n.
      The files Hilbertbasis_n_Z3n.out contains the Hilbert basis of the saturated subsemigroup of Z^3n defined by the inequalities of Ineq_n_Z3n.in.
      The files Ineq_n_Lambda_even.in contains the inequalities in a basis of Lambda_even.
      The files Hilbertbasis_n_Lambda_even.out contains the Hilbert basis of the saturated subsemigroup of Lambda_even defined by the inequalities of Ineq_n_Lambda_even.in.


PROGRAMS

	The file checkSat.py is a Sagemath program that checks that any element of an Hilbert basis from a file Hilbertbasis_n_Lambda_even.out has nonzero NL-coefficient

        The file checkSat_without_lattice.py is a Sagemath program that checks that bath any element even element of an Hilbert basis from a file Hilbertbasis_n_Z3n.out
	and any sum of two odd element of an Hilbert basi  has nonzero NL-coefficient

	The program gen_ineq_EH.py computes the list of inequalities defining  NL-sat 
        
