with Standard_Complex_Polynomials; use Standard_Complex_Polynomials;
with Standard_Complex_Poly_Matrices;
with Brackets; use Brackets;
with Bracket_Monomials; use Bracket_Monomials;
with Bracket_Systems; use Bracket_Systems;
package Symbolic_Minor_Equations is
-- DESCRIPTION :
-- This package generates the equations that arise from the intersection
-- conditions along the deformations determined by the Pieri trees.
-- The equations are symbolic: the coefficients are brackets.
-- LOCALIZATION PATTERNS :
function Schubert_Pattern ( n : natural; b1,b2 : Bracket )
return Standard_Complex_Poly_Matrices.Matrix;
-- DESCRIPTON :
-- Returns the representation of the pattern of the p-plane that satisfies
-- the Schubert conditions as a polynomial matrix.
-- This definition is used in the original Pieri implementation.
function Localization_Pattern ( n : natural; top,bottom : Bracket )
return Standard_Complex_Poly_Matrices.Matrix;
-- DESCRIPTION :
-- Returns the matrix of indeterminates for the top and bottom pivots.
-- The dimension of the working space equals n.
-- This definition is used in the second Pieri implementation.
-- SYMBOLIC REPRESENTATIONS OF THE EQUATIONS :
function Maximal_Minors ( n,m : natural ) return Bracket_Monomial;
-- DESCRIPTION :
-- Generates all maximal minors of an n-by-m matrix, n >= m.
-- The collection of all these m-by-m minors is represented as the
-- product of m-brackets. Every bracket determines a selection of
-- m rows from the n-by-m matrix.
function Minor_Equations
( m,d : natural; bm : Bracket_Monomial ) return Bracket_System;
-- DESCRIPTION :
-- Returns the bracket polynomials that arise from expanding the
-- above maximal m-minors into blocks of respective sizes m-d and d.
-- Equation 0 in the result is the generic bracket representation of
-- the Laplace expansion.
function Expanded_Minor ( m : Standard_Complex_Poly_Matrices.Matrix;
b : Bracket ) return Poly;
-- DESCRIPTION :
-- The minor that selects rows from m, according to b is expanded.
function Extend_Zero_Lifting ( p : Poly ) return Poly;
-- DESCRIPTION :
-- Extends every term with a new variable t^0.
end Symbolic_Minor_Equations;