with Standard_Complex_Vectors;
with Standard_Natural_Matrices;
with Standard_Floating_Matrices;
with Standard_Complex_Matrices;
with Standard_Complex_Polynomials; use Standard_Complex_Polynomials;
package SAGBI_Homotopies is
-- DESCRIPTION :
-- Provides basic routines to set up the polynomials in the SAGBI homotopy.
-- Due to hexadecimal expansions, n and d are both limited to 16.
-- In practice, since the #roots grow so rapidly, this is no limitation.
function Lifted_Localized_Laplace_Expansion ( n,d : natural ) return Poly;
-- DESCRIPTION :
-- Constructs the generic equation in the SAGBI homotopy.
-- The coefficients are brackets in hexadecimal expansion.
-- These brackets represents the selected rows for the maximal minors.
-- The localization chooses the lower-right upper block of the d-plane
-- as the identity matrix.
function Lifted_Localized_Laplace_Expansion
( locmap : Standard_Natural_Matrices.Matrix ) return Poly;
-- DESCRIPTION :
-- The generic equation in the SAGBI homotopy is constructed using
-- the localizaton map in locmap. Zeros and ones indicate the
-- position of the identity matrix, while free elements are twos.
function Intersection_Coefficients
( m : Standard_Floating_Matrices.Matrix;
c : Standard_Complex_Vectors.Vector )
return Standard_Complex_Vectors.Vector;
function Intersection_Coefficients
( m : Standard_Complex_Matrices.Matrix;
c : Standard_Complex_Vectors.Vector )
return Standard_Complex_Vectors.Vector;
-- DESCRIPTION :
-- Given a matrix m and the hexadecimal expansion of the coefficients
-- in c, the vector of maximal minors of m is returned.
function Intersection_Condition
( m : Standard_Floating_Matrices.Matrix; p : Poly ) return Poly;
function Intersection_Condition
( m : Standard_Complex_Matrices.Matrix; p : Poly ) return Poly;
-- DESCRIPTION :
-- Generates the particular equations in the SAGBI homotopy, with
-- as input a matrix m and the lifted localized Laplace expansion p.
-- The matrix contains in its columns the generating points of the
-- plane of intersection.
-- REQUIRED : The dimensions of the matrix m are n times n-d.
end SAGBI_Homotopies;