File: [local] / OpenXM_contrib / PHC / Ada / Schubert / numeric_minor_equations.ads (download)
Revision 1.1.1.1 (vendor branch), Sun Oct 29 17:45:33 2000 UTC (23 years, 10 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_Numbers; use Standard_Complex_Numbers;
with Standard_Complex_Vectors;
with Standard_Floating_Matrices;
with Standard_Complex_Matrices;
with Standard_Complex_Poly_Matrices;
with Standard_Complex_Polynomials; use Standard_Complex_Polynomials;
with Standard_Complex_Poly_Systems; use Standard_Complex_Poly_Systems;
with Bracket_Monomials; use Bracket_Monomials;
with Bracket_Polynomials; use Bracket_Polynomials;
with Bracket_Systems; use Bracket_Systems;
package Numeric_Minor_Equations is
-- DESCRIPTION :
-- This package evaluates the symbolic equations in the Pieri homotopies.
-- EXPANDING ACCORDING A BRACKET MONOMIAL :
function Expanded_Minors
( cffmat : Standard_Floating_Matrices.Matrix;
polmat : Standard_Complex_Poly_Matrices.Matrix;
bm : Bracket_Monomial ) return Poly;
function Expanded_Minors
( cffmat : Standard_Complex_Matrices.Matrix;
polmat : Standard_Complex_Poly_Matrices.Matrix;
bm : Bracket_Monomial ) return Poly;
function Expanded_Minors
( cntmat,polmat : Standard_Complex_Poly_Matrices.Matrix;
bm : Bracket_Monomial ) return Poly;
function Lifted_Expanded_Minors
( cntmat,polmat : Standard_Complex_Poly_Matrices.Matrix;
bm : Bracket_Monomial ) return Poly;
-- DESCRIPTION :
-- Expansion of coefficient and polynomial minors along the Laplace
-- expansion formula in bm creates a polynomial equation.
-- With the prefix Lifted_, the polynomials in polmat are extended
-- with a zero lifting.
-- ON ENTRY :
-- cffmat coefficient matrix, represents m-plane;
-- cntmat polynomial matrix, represents moving m-plane,
-- the continuation parameter is the last variable;
-- polmat polynomial matrix, contains the pattern of the p-plane;
-- bm quadratic bracket monomial, the first bracket is a coefficient
-- minor and has zero as its first entry, the second bracket is
-- a polynomial minor.
-- EXPANDING ACCORDING A BRACKET POLYNOMIAL :
function Expanded_Minors
( cffmat : Standard_Floating_Matrices.Matrix;
polmat : Standard_Complex_Poly_Matrices.Matrix;
bp : Bracket_Polynomial ) return Poly;
function Expanded_Minors
( cffmat : Standard_Complex_Matrices.Matrix;
polmat : Standard_Complex_Poly_Matrices.Matrix;
bp : Bracket_Polynomial ) return Poly;
function Expanded_Minors
( cntmat,polmat : Standard_Complex_Poly_Matrices.Matrix;
bp : Bracket_Polynomial ) return Poly;
function Lifted_Expanded_Minors
( cntmat,polmat : Standard_Complex_Poly_Matrices.Matrix;
bp : Bracket_Polynomial ) return Poly;
-- DESCRIPTION :
-- Expansion of coefficient and polynomial minors along the Laplace
-- expansion formula in bp creates a polynomial equation.
-- With the prefix Lifted_, the polynomials in polmat are extended
-- with a zero lifting.
-- ON ENTRY :
-- cffmat coefficient matrix, represents m-plane, m = n-p;
-- cntmat polynomial matrix, represents moving m-plane, m = n-p,
-- the continuation parameter is the last variable;
-- polmat polynomial matrix, contains the pattern of the p-plane;
-- bp Laplace expansion of one minor, the coefficient minors come
-- first and have a zero as first element.
-- EXPANDING TO CONSTRUCT POLYNOMIAL SYSTEMS :
function Expanded_Minors
( cffmat : Standard_Floating_Matrices.Matrix;
polmat : Standard_Complex_Poly_Matrices.Matrix;
bs : Bracket_System ) return Poly_Sys;
function Expanded_Minors
( cffmat : Standard_Complex_Matrices.Matrix;
polmat : Standard_Complex_Poly_Matrices.Matrix;
bs : Bracket_System ) return Poly_Sys;
function Expanded_Minors
( cntmat,polmat : Standard_Complex_Poly_Matrices.Matrix;
bs : Bracket_System ) return Poly_Sys;
function Lifted_Expanded_Minors
( cntmat,polmat : Standard_Complex_Poly_Matrices.Matrix;
bs : Bracket_System ) return Poly_Sys;
-- DESCRIPTION :
-- Expansion of coefficient and polynomial minors along the Laplace
-- expansion formulas in bs creates a polynomial system.
-- With the prefix Lifted_, the polynomials in polmat are extended
-- with zero lifting.
-- ON ENTRY :
-- cffmat coefficient matrix, represents m-plane;
-- cntmat polynomial matrix, represents moving m-plane,
-- the continuation parameter is the last variable;
-- polmat polynomial matrix, contains the pattern of the p-plane;
-- bs Laplace expansion of all minors, the first equation is
-- the generic one and should not count in the range of
-- the resulting polynomial system.
function Evaluate ( p : Poly; x : Standard_Complex_Matrices.Matrix )
return Complex_Number;
-- DESCRIPTION :
-- Evaluates the polynomial p at the matrix x, where x is a value
-- for the polynomial matrix used above to define p.
function Evaluate ( p : Poly_Sys; x : Standard_Complex_Matrices.Matrix )
return Standard_Complex_Vectors.Vector;
-- DESCRIPTION :
-- Evaluates the polynomial system p at the matrix x, where x is a value
-- for the polynomial matrix used above to define p.
procedure Embed ( t : in out Term );
procedure Embed ( p : in out Poly );
procedure Embed ( p : in out Poly_Sys );
procedure Embed ( m : in out Standard_Complex_Poly_Matrices.Matrix );
-- DESCRIPTION :
-- Augments the number of variables with one, as is required to embed
-- the polynomials in a homotopy.
function Linear_Homotopy ( target,start : Poly ) return Poly;
-- DESCRIPTION :
-- Returns (1-t)*start + t*target, with t an additional last variable.
function Linear_Interpolation
( target,start : Poly; k : natural ) return Poly;
-- DESCRIPTION :
-- Returns (1-t)*start + t*target, with t the k-th variable.
procedure Divide_Common_Factor ( p : in out Poly; k : in natural );
-- DESCRIPTION :
-- If the k-th variable occurs everywhere in p with a positive power,
-- then it will be divided out.
end Numeric_Minor_Equations;