Annotation of OpenXM_contrib/PHC/Ada/Schubert/symbolic_minor_equations.ads, Revision 1.1.1.1
1.1 maekawa 1: with Standard_Complex_Polynomials; use Standard_Complex_Polynomials;
2: with Standard_Complex_Poly_Matrices;
3: with Brackets; use Brackets;
4: with Bracket_Monomials; use Bracket_Monomials;
5: with Bracket_Systems; use Bracket_Systems;
6:
7: package Symbolic_Minor_Equations is
8:
9: -- DESCRIPTION :
10: -- This package generates the equations that arise from the intersection
11: -- conditions along the deformations determined by the Pieri trees.
12: -- The equations are symbolic: the coefficients are brackets.
13:
14: -- LOCALIZATION PATTERNS :
15:
16: function Schubert_Pattern ( n : natural; b1,b2 : Bracket )
17: return Standard_Complex_Poly_Matrices.Matrix;
18:
19: -- DESCRIPTON :
20: -- Returns the representation of the pattern of the p-plane that satisfies
21: -- the Schubert conditions as a polynomial matrix.
22: -- This definition is used in the original Pieri implementation.
23:
24: function Localization_Pattern ( n : natural; top,bottom : Bracket )
25: return Standard_Complex_Poly_Matrices.Matrix;
26:
27: -- DESCRIPTION :
28: -- Returns the matrix of indeterminates for the top and bottom pivots.
29: -- The dimension of the working space equals n.
30: -- This definition is used in the second Pieri implementation.
31:
32: -- SYMBOLIC REPRESENTATIONS OF THE EQUATIONS :
33:
34: function Maximal_Minors ( n,m : natural ) return Bracket_Monomial;
35:
36: -- DESCRIPTION :
37: -- Generates all maximal minors of an n-by-m matrix, n >= m.
38: -- The collection of all these m-by-m minors is represented as the
39: -- product of m-brackets. Every bracket determines a selection of
40: -- m rows from the n-by-m matrix.
41:
42: function Minor_Equations
43: ( m,d : natural; bm : Bracket_Monomial ) return Bracket_System;
44:
45: -- DESCRIPTION :
46: -- Returns the bracket polynomials that arise from expanding the
47: -- above maximal m-minors into blocks of respective sizes m-d and d.
48: -- Equation 0 in the result is the generic bracket representation of
49: -- the Laplace expansion.
50:
51: function Expanded_Minor ( m : Standard_Complex_Poly_Matrices.Matrix;
52: b : Bracket ) return Poly;
53:
54: -- DESCRIPTION :
55: -- The minor that selects rows from m, according to b is expanded.
56:
57: function Extend_Zero_Lifting ( p : Poly ) return Poly;
58:
59: -- DESCRIPTION :
60: -- Extends every term with a new variable t^0.
61:
62: end Symbolic_Minor_Equations;
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