Annotation of OpenXM_contrib/PHC/Ada/Homotopy/reduction_of_polynomial_systems.ads, Revision 1.1
1.1 ! maekawa 1: with Standard_Complex_Vectors; use Standard_Complex_Vectors;
! 2: with Standard_Complex_Poly_Systems; use Standard_Complex_Poly_Systems;
! 3:
! 4: package Reduction_of_Polynomial_Systems is
! 5:
! 6: -- DESCRIPTION :
! 7: -- Linear and nonlinear reduction to reduce the total degree.
! 8:
! 9: function Total_Degree ( p : Poly_Sys ) return natural;
! 10:
! 11: -- DESCRIPTION :
! 12: -- Returns the total degree of the polynomial system,
! 13: -- i.e. the product of the degrees of the polynomials.
! 14:
! 15: procedure Reduce ( p : in out Poly_Sys;
! 16: diagonal,inconsistent,infinite : in out boolean );
! 17:
! 18: -- DESCRIPTION :
! 19: -- This procedure tries to lower the total degree of p by means
! 20: -- of linear reduction.
! 21:
! 22: -- ON ENTRY :
! 23: -- p a polynomial system.
! 24:
! 25: -- ON RETURN :
! 26: -- p a polynomial system with a possible lower total degree;
! 27: -- diagonal true if all leading terms in p are different;
! 28: -- inconsistent is true if the reduced system has equations `4=0';
! 29: -- infinite is true if some equations of the original system
! 30: -- disappeared during the reduction process.
! 31:
! 32: procedure Sparse_Reduce ( p : in out Poly_Sys;
! 33: inconsistent,infinite : in out boolean );
! 34:
! 35: -- DESCRIPTION :
! 36: -- This procedure makes the coefficient matrix of p as sparse as
! 37: -- possible.
! 38:
! 39: procedure Reduce ( p : in Poly_Sys; res : in out Poly_Sys;
! 40: cnt_eq : in out natural; max_eq : in natural;
! 41: cnt_sp : in out natural; max_sp : in natural;
! 42: cnt_rp : in out natural; max_rp : in natural );
! 43:
! 44: -- DESCRIPTION :
! 45: -- This procedure tries to lower the total degree of the system p
! 46: -- by means of nonlinear reduction.
! 47:
! 48: -- REQUIRED : the counters must equal 0, on entry.
! 49:
! 50: -- ON ENTRY :
! 51: -- p a polynomial system;
! 52: -- cnt_eq counts the number of equal degree substitutions;
! 53: -- max_eq limit on the number of equal degree substitutions;
! 54: -- cnt_sp counts the number of S-polynomial computations;
! 55: -- max_sp limit on the number of S-polynomial computations.
! 56: -- cnt_rp counts the number of R-polynomial computations;
! 57: -- max_rp limit on the number of R-polynomial computations.
! 58:
! 59: -- ON RETURN :
! 60: -- res the reduced system;
! 61: -- cnt_eq the number of equal degree substitutions;
! 62: -- cnt_sp the number of computed S-polynomials;
! 63: -- cnt_rp the number of computed R-polynomials.
! 64:
! 65: procedure Sparse_Reduce ( p : in Poly_Sys; res : in out Poly_Sys;
! 66: cnt_eq : in out natural; max_eq : in natural );
! 67:
! 68: -- DESCRIPTION :
! 69: -- the polynomial system is reduced by computing S-polynomials.
! 70: -- After each replacement, the coefficient matrix is made as sparse
! 71: -- as possible.
! 72:
! 73: end Reduction_of_Polynomial_Systems;
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