Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Product/interpolating_homotopies.ads, Revision 1.1
1.1 ! maekawa 1: with Standard_Integer_Matrices; use Standard_Integer_Matrices;
! 2: with Standard_Complex_Poly_Systems; use Standard_Complex_Poly_Systems;
! 3: with Standard_Complex_Solutions; use Standard_Complex_Solutions;
! 4: with Partitions_of_Sets_of_Unknowns; use Partitions_of_Sets_of_Unknowns;
! 5:
! 6: package Interpolating_Homotopies is
! 7:
! 8: -- DESCRIPTION :
! 9: -- This package contains facilities for constructing interpolating
! 10: -- homotopies, based on a given m-homogeneous structure.
! 11: -- The routines are given in the order in which they should be applied.
! 12: -- Null polynomials are ignored, making scaled interpolation possible,
! 13: -- the scaling equation, used for generating the interpolating vectors,
! 14: -- can be added afterwards. For linear scalers, the last unknown of the
! 15: -- scaling equation should be ignored in those monomials that have degree
! 16: -- one in that unknown, to avoid singular interpolation matrices.
! 17:
! 18: function Dense_Representation
! 19: ( p : Poly_Sys; z : partition ) return Poly_Sys;
! 20: function Dense_Representation
! 21: ( p : Poly_Sys; z : partition; d : Matrix ) return Poly_Sys;
! 22:
! 23: -- DESCRIPTION :
! 24: -- A dense representation of an m-homogeneous structure is returned.
! 25: -- The coefficients of the polynomials in the returned system are all one.
! 26:
! 27: function Independent_Representation ( p : Poly_Sys ) return Poly_Sys;
! 28:
! 29: -- DESCRIPTION :
! 30: -- An independent representation of a polynomial system is returned.
! 31: -- This means that the initial term of each polynomial does not occur
! 32: -- in every other polynomial.
! 33:
! 34: function Independent_Roots ( p : Poly_Sys ) return natural;
! 35: function Independent_Roots ( p : Poly_Sys; i : natural ) return natural;
! 36:
! 37: -- DESCRIPTION :
! 38: -- Returns the number of independent roots the system p can have.
! 39: -- When the ith unknown is given as parameter, the monomials that
! 40: -- have degree one in x_i are not counted.
! 41:
! 42: -- IMPORTANT NOTE : p must be an independent representation of a polynomial
! 43: -- system, otherwise the result might not be reliable.
! 44:
! 45: function Interpolate ( p : Poly_Sys; b : natural; sols : Solution_List )
! 46: return Poly_Sys;
! 47: function Interpolate ( p : Poly_Sys; i,b : natural; sols : Solution_List )
! 48: return Poly_Sys;
! 49:
! 50: -- DESCRIPTION :
! 51: -- This routine constructs a start system q with the same monomial
! 52: -- structure as the system p.
! 53:
! 54: -- ON ENTRY :
! 55: -- p a polynomial system;
! 56: -- i monomials with degree one in x_i will be ignored;
! 57: -- b must equal Independent_Roots(p);
! 58: -- sols interpolation vectors, Length_Of(sols) = b.
! 59:
! 60: -- ON RETURN :
! 61: -- q system that has the given list sols as solutions.
! 62:
! 63: end Interpolating_Homotopies;
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