Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Product/m_homogeneous_bezout_numbers.ads, Revision 1.1.1.1
1.1 maekawa 1: with Standard_Complex_Poly_Systems; use Standard_Complex_Poly_Systems;
2: with Partitions_of_Sets_Of_Unknowns; use Partitions_of_Sets_of_Unknowns;
3:
4: package m_Homogeneous_Bezout_Numbers is
5:
6: -- DESCRIPTION :
7: -- This package allows the computation of m-homogeneous Bezout numbers.
8: -- It provides various enumeration strategies for computing a minimal
9: -- m-homogeneous Bezout number.
10:
11: function Total_Degree ( p : Poly_Sys ) return natural;
12:
13: -- DESCRIPTION :
14: -- Returns the 1-homogeneous Bezout number of the system.
15:
16: function Bezout_Number ( p : Poly_Sys; z : Partition ) return natural;
17: function Bezout_Number ( p : Poly_Sys; z : Partition; max : natural )
18: return natural;
19:
20: -- DESCRIPTION :
21: -- Returns the m-homogeneous Bezout number w.r.t. the given partition.
22: -- When max is given as parameter, the computation stops when the
23: -- result becomes larger than or equal to max.
24:
25: function Bezout_Number ( p : Poly_Sys ) return natural;
26: function Bezout_Number ( max : natural; p : Poly_Sys ) return natural;
27: function Bezout_Number ( p : Poly_Sys; min : natural ) return natural;
28: function Bezout_Number ( max : natural; p : Poly_Sys; min : natural )
29: return natural;
30: -- DESCRIPTION :
31: -- A minimal m-homogeneous Bezout number of the polynomial system
32: -- p is computed, by generating partitions of the sets of unknowns.
33:
34: -- ON ENTRY :
35: -- p a polynomial system;
36: -- max a maximum number of partition to be evaluated,
37: -- if max=0, then the total degree is returned;
38: -- min the procedure stops when the Bezout number becomes
39: -- smaller than min.
40:
41: procedure Bezout_Number
42: ( p : in Poly_Sys; b,m : out natural; z : in out Partition );
43: procedure Bezout_Number
44: ( max : in natural; p : in Poly_Sys; b,m : out natural;
45: z : in out Partition );
46: procedure Bezout_Number
47: ( p : in Poly_Sys; min : in natural; b,m : out natural;
48: z : in out Partition );
49: procedure Bezout_Number
50: ( max : in natural; p : in Poly_Sys; min : in natural;
51: b,m : out natural; z : in out Partition );
52:
53: -- DESCRIPTION :
54: -- A minimal m-homogeneous Bezout number of the polynomial system
55: -- is computed. The partition with the calculated Bezout number
56: -- is returned.
57:
58: -- ON ENTRY :
59: -- p a polynomial system;
60: -- max a maximum number of partition to be evaluated,
61: -- if max=0, then the total degree is returned;
62: -- min the procedure stops when the Bezout number becomes
63: -- smaller than min.
64:
65: -- ON RETURN :
66: -- b a minimal m-homogeneous Bezout number;
67: -- m the number of sets in the partition z;
68: -- z the partition with the computed Bezout number b.
69:
70: procedure PB ( p : in Poly_Sys; b,m : out natural; z : in out Partition );
71:
72: -- DESCRIPTION :
73: -- This is a fast heuristic for computing `the' Bezout number of p.
74: -- It is fast because it does not generate all partitions,
75: -- it is a heuristic because it does not always give then
76: -- minimal partition.
77:
78: -- ON ENTRY :
79: -- p a polynomial system.
80:
81: -- ON RETURN :
82: -- b an m-homogeneous Bezout number;
83: -- m the number of sets in the partition z;
84: -- z the partition corresponding to b.
85:
86: end m_Homogeneous_Bezout_Numbers;
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