Annotation of OpenXM_contrib/PHC/Ada/Schubert/pieri_homotopies.ads, Revision 1.1.1.1
1.1 maekawa 1: with Standard_Complex_Vectors; use Standard_Complex_Vectors;
2: with Standard_Complex_Matrices;
3: with Standard_Complex_VecMats; use Standard_Complex_VecMats;
4: with Standard_Complex_Poly_Matrices;
5: with Standard_Complex_Poly_Systems; use Standard_Complex_Poly_Systems;
6: with Brackets; use Brackets;
7: with Bracket_Polynomials; use Bracket_Polynomials;
8: with Bracket_Systems; use Bracket_Systems;
9: with Localization_Posets; use Localization_Posets;
10:
11: package Pieri_Homotopies is
12:
13: -- DESCRIPTION :
14: -- This package provides the homotopy constructors for the poset-oriented
15: -- Pieri homotopy algorithm for four cases of increasing complexity :
16: -- 1) hypersurface intersection conditions
17: -- 2) general co-dimension intersections
18: -- 3) q-curves satisfying interpolation-intersection conditions
19: -- 4) q-curves the meet general planes of varying dimensions
20: -- at specified interpolation points.
21: -- The prefixes One_ and Two_ refer to the cases of respectively one
22: -- and two moving equations in the homotopy.
23:
24: function One_Hypersurface_Pieri_Homotopy
25: ( n : natural; nd : Node; expbp : Bracket_Polynomial;
26: xpm : Standard_Complex_Poly_Matrices.Matrix;
27: planes : VecMat ) return Poly_Sys;
28:
29: -- DESCRIPTION :
30: -- Returns the Pieri homotopy for the hypersurface case,
31: -- when the type of the node is either top or bottom,
32: -- which means that only one intersection condition is folded in.
33:
34: -- ON ENTRY :
35: -- n dimension of the working space, equals m+p;
36: -- nd node in the localization poset, must be top or bottom;
37: -- expbp general format of the intersection condition;
38: -- xpm localization pattern corresponding to the pivots in nd;
39: -- planes the planes that form the intersection conditions.
40:
41: function Two_Hypersurface_Pieri_Homotopy
42: ( n : natural; nd : Node; expbp : Bracket_Polynomial;
43: xpm : Standard_Complex_Poly_Matrices.Matrix;
44: planes : VecMat ) return Poly_Sys;
45:
46: -- DESCRIPTION :
47: -- Returns the Pieri homotopy for the hypersurface case,
48: -- when the type of the node is mixed,
49: -- which means that two intersection conditions are folded in.
50:
51: -- ON ENTRY :
52: -- n dimension of the working space, equals m+p;
53: -- nd node in the localization poset, must be mixed;
54: -- expbp general format of the intersection condition;
55: -- xpm localization pattern corresponding to the pivots in nd;
56: -- planes the planes that form the intersection conditions.
57:
58: function One_General_Pieri_Homotopy
59: ( n,ind : natural; nd : Node; bs : Bracket_System;
60: start,target : Standard_Complex_Matrices.Matrix;
61: xpm : Standard_Complex_Poly_Matrices.Matrix;
62: planes : VecMat ) return Link_to_Poly_Sys;
63:
64: -- DESCRIPTION :
65: -- Returns the Pieri homotopy to satisfy one general linear subspace
66: -- intersection, when the type of the node is either top or bottom.
67:
68: -- ON ENTRY :
69: -- n dimension of the working space, equals m+p;
70: -- ind indicates the plane planes(ind) that is folded in;
71: -- nd node in the localization poset, must be top or bottom;
72: -- bs collects the structure of the equations;
73: -- start specialized plane that is met at the start of the homotopy;
74: -- target plane that has to be met at the end of the homotopy;
75: -- xpm localization pattern corresponding to the pivots in nd;
76: -- planes the planes that form the intersection conditions.
77:
78: function Two_General_Pieri_Homotopy
79: ( n,ind : natural; nd : Node; top_bs,bot_bs : Bracket_System;
80: top_start,top_target,bot_start,bot_target
81: : Standard_Complex_Matrices.Matrix;
82: xpm : Standard_Complex_Poly_Matrices.Matrix;
83: planes : VecMat ) return Link_to_Poly_Sys;
84:
85: -- DESCRIPTION :
86: -- Returns the Pieri homotopy to satisfy two general linear subspace
87: -- intersections, when the type of the node is mixed.
88:
89: -- ON ENTRY :
90: -- n dimension of the working space, equals m+p;
91: -- ind indicates the plane planes(ind) that is folded in;
92: -- nd node in the localization poset, must be mixed;
93: -- top_bs the structure of the equations for top pivots;
94: -- bot_bs the structure of the equations for bottom pivots;
95: -- top_start special plane met at the start for top pivots;
96: -- top_target plane to be met at the end for top pivots;
97: -- bot_start special plane met at the start for bottom pivots;
98: -- bot_target plane to be met at the end for bottom pivots;
99: -- xpm localization pattern corresponding to the pivots in nd;
100: -- planes the planes that form the intersection conditions.
101:
102: function One_Quantum_Pieri_Homotopy
103: ( n : natural; nd : Node; expbp : Bracket_Polynomial;
104: xpm : Standard_Complex_Poly_Matrices.Matrix;
105: planes : VecMat; s : Vector ) return Poly_Sys;
106:
107: -- DESCRIPTION :
108: -- Returns the Pieri homotopy to compute q-curves for one interpolation-
109: -- intersection condition, when the node is either top or bottom.
110:
111: -- ON ENTRY :
112: -- n dimension of the working space, equals m+p;
113: -- nd node in the localization poset, must be top or bottom;
114: -- expbp general format of the intersection condition;
115: -- xpm localization pattern corresponding to the pivots in nd;
116: -- planes the planes that form the intersection conditions;
117: -- s interpolation points where the planes are sampled.
118:
119: function Two_Quantum_Pieri_Homotopy
120: ( n : natural; nd : Node; expbp : Bracket_Polynomial;
121: xpm : Standard_Complex_Poly_Matrices.Matrix;
122: planes : VecMat; s : Vector ) return Poly_Sys;
123:
124: -- DESCRIPTION :
125: -- Returns the Pieri homotopy to compute q-curves for one interpolation-
126: -- intersection condition, when the node is either top or bottom.
127:
128: -- ON ENTRY :
129: -- n dimension of the working space, equals m+p;
130: -- nd node in the localization poset, must be mixed;
131: -- expbp general format of the intersection condition;
132: -- xpm localization pattern corresponding to the pivots in nd;
133: -- planes the planes that form the intersection conditions;
134: -- s interpolation points where the planes are sampled.
135:
136: function One_General_Quantum_Pieri_Homotopy
137: ( n,ind : natural; nd : Node; s_mode : natural;
138: bs : Bracket_System;
139: start,target : Standard_Complex_Matrices.Matrix;
140: xpm : Standard_Complex_Poly_Matrices.Matrix;
141: planes : VecMat; s : Vector ) return Link_to_Poly_Sys;
142:
143: -- DESCRIPTION :
144: -- Returns the quantum Pieri homotopy to satisfy one general linear
145: -- subspace intersection, when the type is either top or bottom.
146:
147: -- ON ENTRY :
148: -- n dimension of the working space, equals m+p;
149: -- ind indicates the plane planes(ind) that is folded in;
150: -- nd node in the localization poset, must be top or bottom;
151: -- s_mode = 0 : s goes from 0 to 1,
152: -- = 1 : s remains constant at 1,
153: -- = 2 : s goes from 1 to target value s(ind);
154: -- bs collects the structure of the equations;
155: -- start specialized plane that is met at the start of the homotopy;
156: -- target plane that has to be met at the end of the homotopy;
157: -- xpm localization pattern corresponding to the pivots in nd;
158: -- planes the planes that form the intersection conditions;
159: -- s interpolation points where the planes are sampled.
160:
161: function Two_General_Quantum_Pieri_Homotopy
162: ( n,ind : natural; nd : Node; top_bs,bot_bs : Bracket_System;
163: top_start,top_target,bot_start,bot_target
164: : Standard_Complex_Matrices.Matrix;
165: xpm : Standard_Complex_Poly_Matrices.Matrix;
166: planes : VecMat; s : Vector ) return Link_to_Poly_Sys;
167:
168: -- DESCRIPTION :
169: -- Returns the quantum Pieri homotopy to satisfy two general linear
170: -- subspace intersections, when the type of the node is mixed.
171:
172: -- ON ENTRY :
173: -- n dimension of the working space, equals m+p;
174: -- ind indicates the plane planes(ind) that is folded in;
175: -- nd node in the localization poset, must be mixed;
176: -- top_bs the structure of the equations for top pivots;
177: -- bot_bs the structure of the equations for bottom pivots;
178: -- top_start special plane met at the start for top pivots;
179: -- top_target plane to be met at the end for top pivots;
180: -- bot_start special plane met at the start for bottom pivots;
181: -- bot_target plane to be met at the end for bottom pivots;
182: -- xpm localization pattern corresponding to the pivots in nd;
183: -- planes the planes that form the intersection conditions;
184: -- s interpolation points where the planes are sampled.
185:
186: end Pieri_Homotopies;
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