Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Product/interpolating_homotopies.ads, Revision 1.1.1.1
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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