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Revision 1.1.1.1 (vendor branch), Sun Oct 29 17:45:32 2000 UTC (23 years, 8 months ago) by maekawa
Branch: PHC, MAIN
CVS Tags: v2, maekawa-ipv6, RELEASE_1_2_3, RELEASE_1_2_2_KNOPPIX_b, RELEASE_1_2_2_KNOPPIX, RELEASE_1_2_2, RELEASE_1_2_1, HEAD Changes since 1.1: +0 -0
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Import the second public release of PHCpack.
OKed by Jan Verschelde.
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with Standard_Complex_Vectors; use Standard_Complex_Vectors;
with Standard_Complex_Matrices;
with Standard_Complex_VecMats; use Standard_Complex_VecMats;
with Standard_Complex_Poly_Matrices;
with Standard_Complex_Poly_Systems; use Standard_Complex_Poly_Systems;
with Brackets; use Brackets;
with Bracket_Polynomials; use Bracket_Polynomials;
with Bracket_Systems; use Bracket_Systems;
with Localization_Posets; use Localization_Posets;
package Pieri_Homotopies is
-- DESCRIPTION :
-- This package provides the homotopy constructors for the poset-oriented
-- Pieri homotopy algorithm for four cases of increasing complexity :
-- 1) hypersurface intersection conditions
-- 2) general co-dimension intersections
-- 3) q-curves satisfying interpolation-intersection conditions
-- 4) q-curves the meet general planes of varying dimensions
-- at specified interpolation points.
-- The prefixes One_ and Two_ refer to the cases of respectively one
-- and two moving equations in the homotopy.
function One_Hypersurface_Pieri_Homotopy
( n : natural; nd : Node; expbp : Bracket_Polynomial;
xpm : Standard_Complex_Poly_Matrices.Matrix;
planes : VecMat ) return Poly_Sys;
-- DESCRIPTION :
-- Returns the Pieri homotopy for the hypersurface case,
-- when the type of the node is either top or bottom,
-- which means that only one intersection condition is folded in.
-- ON ENTRY :
-- n dimension of the working space, equals m+p;
-- nd node in the localization poset, must be top or bottom;
-- expbp general format of the intersection condition;
-- xpm localization pattern corresponding to the pivots in nd;
-- planes the planes that form the intersection conditions.
function Two_Hypersurface_Pieri_Homotopy
( n : natural; nd : Node; expbp : Bracket_Polynomial;
xpm : Standard_Complex_Poly_Matrices.Matrix;
planes : VecMat ) return Poly_Sys;
-- DESCRIPTION :
-- Returns the Pieri homotopy for the hypersurface case,
-- when the type of the node is mixed,
-- which means that two intersection conditions are folded in.
-- ON ENTRY :
-- n dimension of the working space, equals m+p;
-- nd node in the localization poset, must be mixed;
-- expbp general format of the intersection condition;
-- xpm localization pattern corresponding to the pivots in nd;
-- planes the planes that form the intersection conditions.
function One_General_Pieri_Homotopy
( n,ind : natural; nd : Node; bs : Bracket_System;
start,target : Standard_Complex_Matrices.Matrix;
xpm : Standard_Complex_Poly_Matrices.Matrix;
planes : VecMat ) return Link_to_Poly_Sys;
-- DESCRIPTION :
-- Returns the Pieri homotopy to satisfy one general linear subspace
-- intersection, when the type of the node is either top or bottom.
-- ON ENTRY :
-- n dimension of the working space, equals m+p;
-- ind indicates the plane planes(ind) that is folded in;
-- nd node in the localization poset, must be top or bottom;
-- bs collects the structure of the equations;
-- start specialized plane that is met at the start of the homotopy;
-- target plane that has to be met at the end of the homotopy;
-- xpm localization pattern corresponding to the pivots in nd;
-- planes the planes that form the intersection conditions.
function Two_General_Pieri_Homotopy
( n,ind : natural; nd : Node; top_bs,bot_bs : Bracket_System;
top_start,top_target,bot_start,bot_target
: Standard_Complex_Matrices.Matrix;
xpm : Standard_Complex_Poly_Matrices.Matrix;
planes : VecMat ) return Link_to_Poly_Sys;
-- DESCRIPTION :
-- Returns the Pieri homotopy to satisfy two general linear subspace
-- intersections, when the type of the node is mixed.
-- ON ENTRY :
-- n dimension of the working space, equals m+p;
-- ind indicates the plane planes(ind) that is folded in;
-- nd node in the localization poset, must be mixed;
-- top_bs the structure of the equations for top pivots;
-- bot_bs the structure of the equations for bottom pivots;
-- top_start special plane met at the start for top pivots;
-- top_target plane to be met at the end for top pivots;
-- bot_start special plane met at the start for bottom pivots;
-- bot_target plane to be met at the end for bottom pivots;
-- xpm localization pattern corresponding to the pivots in nd;
-- planes the planes that form the intersection conditions.
function One_Quantum_Pieri_Homotopy
( n : natural; nd : Node; expbp : Bracket_Polynomial;
xpm : Standard_Complex_Poly_Matrices.Matrix;
planes : VecMat; s : Vector ) return Poly_Sys;
-- DESCRIPTION :
-- Returns the Pieri homotopy to compute q-curves for one interpolation-
-- intersection condition, when the node is either top or bottom.
-- ON ENTRY :
-- n dimension of the working space, equals m+p;
-- nd node in the localization poset, must be top or bottom;
-- expbp general format of the intersection condition;
-- xpm localization pattern corresponding to the pivots in nd;
-- planes the planes that form the intersection conditions;
-- s interpolation points where the planes are sampled.
function Two_Quantum_Pieri_Homotopy
( n : natural; nd : Node; expbp : Bracket_Polynomial;
xpm : Standard_Complex_Poly_Matrices.Matrix;
planes : VecMat; s : Vector ) return Poly_Sys;
-- DESCRIPTION :
-- Returns the Pieri homotopy to compute q-curves for one interpolation-
-- intersection condition, when the node is either top or bottom.
-- ON ENTRY :
-- n dimension of the working space, equals m+p;
-- nd node in the localization poset, must be mixed;
-- expbp general format of the intersection condition;
-- xpm localization pattern corresponding to the pivots in nd;
-- planes the planes that form the intersection conditions;
-- s interpolation points where the planes are sampled.
function One_General_Quantum_Pieri_Homotopy
( n,ind : natural; nd : Node; s_mode : natural;
bs : Bracket_System;
start,target : Standard_Complex_Matrices.Matrix;
xpm : Standard_Complex_Poly_Matrices.Matrix;
planes : VecMat; s : Vector ) return Link_to_Poly_Sys;
-- DESCRIPTION :
-- Returns the quantum Pieri homotopy to satisfy one general linear
-- subspace intersection, when the type is either top or bottom.
-- ON ENTRY :
-- n dimension of the working space, equals m+p;
-- ind indicates the plane planes(ind) that is folded in;
-- nd node in the localization poset, must be top or bottom;
-- s_mode = 0 : s goes from 0 to 1,
-- = 1 : s remains constant at 1,
-- = 2 : s goes from 1 to target value s(ind);
-- bs collects the structure of the equations;
-- start specialized plane that is met at the start of the homotopy;
-- target plane that has to be met at the end of the homotopy;
-- xpm localization pattern corresponding to the pivots in nd;
-- planes the planes that form the intersection conditions;
-- s interpolation points where the planes are sampled.
function Two_General_Quantum_Pieri_Homotopy
( n,ind : natural; nd : Node; top_bs,bot_bs : Bracket_System;
top_start,top_target,bot_start,bot_target
: Standard_Complex_Matrices.Matrix;
xpm : Standard_Complex_Poly_Matrices.Matrix;
planes : VecMat; s : Vector ) return Link_to_Poly_Sys;
-- DESCRIPTION :
-- Returns the quantum Pieri homotopy to satisfy two general linear
-- subspace intersections, when the type of the node is mixed.
-- ON ENTRY :
-- n dimension of the working space, equals m+p;
-- ind indicates the plane planes(ind) that is folded in;
-- nd node in the localization poset, must be mixed;
-- top_bs the structure of the equations for top pivots;
-- bot_bs the structure of the equations for bottom pivots;
-- top_start special plane met at the start for top pivots;
-- top_target plane to be met at the end for top pivots;
-- bot_start special plane met at the start for bottom pivots;
-- bot_target plane to be met at the end for bottom pivots;
-- xpm localization pattern corresponding to the pivots in nd;
-- planes the planes that form the intersection conditions;
-- s interpolation points where the planes are sampled.
end Pieri_Homotopies;