![]() ![]() | ![]() |
File: [local] / OpenXM_contrib / PHC / Ada / Schubert / determinantal_systems.ads (download)
Revision 1.1.1.1 (vendor branch), Sun Oct 29 17:45:33 2000 UTC (23 years, 10 months ago) by maekawa
Import the second public release of PHCpack. OKed by Jan Verschelde. |
with Standard_Complex_Numbers; use Standard_Complex_Numbers; with Standard_Complex_Vectors; use Standard_Complex_Vectors; with Standard_Natural_Matrices; with Standard_Complex_Matrices; with Standard_Complex_Poly_Matrices; with Standard_Complex_VecMats; with Standard_Complex_Poly_Systems; use Standard_Complex_Poly_Systems; package Determinantal_Systems is -- DESCRIPTION : -- This package constitutes the bridge between linear subspace intersections -- expressed by determinantal equations and polynomial systems. -- LOCALIZATION MAPS : function Standard_Coordinate_Frame ( x : Standard_Complex_Poly_Matrices.Matrix; plane : Standard_Complex_Matrices.Matrix ) return Standard_Natural_Matrices.Matrix; -- DESCRIPTION : -- Returns a coordinate frame that corresponds to the polynomial matrix x. -- To determine the position of the one, the first nonzero element in the -- columns of the plane is taken. function Maximal_Coordinate_Frame ( x : Standard_Complex_Poly_Matrices.Matrix; plane : Standard_Complex_Matrices.Matrix ) return Standard_Natural_Matrices.Matrix; -- DESCRIPTION : -- Returns a coordinate frame that corresponds to the polynomial matrix x. -- To determine the position of the one, the maximal element in every -- column is taken. function Localize ( locmap : Standard_Natural_Matrices.Matrix; p : Poly_Sys ) return Poly_Sys; -- DESCRIPTION : -- Applies the localization map to the polynomial system p, -- assuming a rowwise lexicographical order on the variables. -- CONSTRUCT POLYNOMIAL SYSTEMS : procedure Concat ( l : in out Link_to_Poly_Sys; p : Poly_Sys ); -- DESCRIPTION : -- Concatenates the nonzero polynomials in p to those in l. -- There is sharing. function Polynomial_Equations ( l : Standard_Complex_Matrices.Matrix; x : Standard_Complex_Poly_Matrices.Matrix ) return Poly_Sys; -- DESCRIPTION : -- Returns the polynomial equations that express the intersection of -- the subspace spanned by the columns of l with the indeterminates -- in the variable matrix x. function Polynomial_Equations ( l : Standard_Complex_VecMats.VecMat; x : Standard_Complex_Poly_Matrices.Matrix ) return Poly_Sys; -- DESCRIPTION : -- Returns the polynomial system generated from expanding the -- determinants that represent the intersections of x with the -- planes in l, with equations of the form det(l|x) = 0. -- EVALUATORS AND DIFFERENTIATORS : function Eval ( l,x : Standard_Complex_Matrices.Matrix ) return Complex_Number; -- DESCRIPTION : -- Returns the result of the evaluation of the determinant which -- has in its columns the columns of l and x. -- REQUIRED : x'length(1) = x'length(2) + l'length(2) = l'length(1). function Eval ( l,x : Standard_Complex_Matrices.Matrix ) return Vector; -- DESCRIPTION : -- Returns the vector of all maximal minors of the matrix that has -- in its columns the columns of l and x. -- REQUIRED : x'length(1) = l'length(1) >= x'length(2) + l'length(2). function Diff ( l,x : Standard_Complex_Matrices.Matrix; i : natural ) return Complex_Number; function Diff ( l,x : Standard_Complex_Matrices.Matrix; locmap : Standard_Natural_Matrices.Matrix; i : natural ) return Complex_Number; -- DESCRIPTION : -- Returns the value of the derivative of the i-th variable in the -- vector representation of the matrix x of unknowns, with coefficients -- obtained from the determinantal equation det(l|x) = 0. -- The same requirements as in Eval on the dimensions hold. -- The i-th variable is w.r.t. the localization map. function Eval ( l : Standard_Complex_VecMats.VecMat; x : Standard_Complex_Matrices.Matrix ) return Vector; -- DESCRIPTION : -- Returns the vector that has in its components the determinant -- of l(i) with x, for i in l'range. function Diff ( l : Standard_Complex_VecMats.VecMat; x : Standard_Complex_Matrices.Matrix ) return Standard_Complex_Matrices.Matrix; function Diff ( l : Standard_Complex_VecMats.VecMat; x : Standard_Complex_Matrices.Matrix; nvars : natural; locmap : Standard_Natural_Matrices.Matrix ) return Standard_Complex_Matrices.Matrix; -- DESCRIPTION : -- Returns the Jacobian matrix of the system det(l(i)|x) = 0. -- If the localization map is specificied, then nvars equals the -- number of free variables. end Determinantal_Systems;