Annotation of OpenXM_contrib/PHC/Ada/Schubert/pieri_homotopies.ads, Revision 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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