Annotation of OpenXM_contrib/PHC/Ada/Schubert/numeric_minor_equations.ads, Revision 1.1
1.1 ! maekawa 1: with Standard_Complex_Numbers; use Standard_Complex_Numbers;
! 2: with Standard_Complex_Vectors;
! 3: with Standard_Floating_Matrices;
! 4: with Standard_Complex_Matrices;
! 5: with Standard_Complex_Poly_Matrices;
! 6: with Standard_Complex_Polynomials; use Standard_Complex_Polynomials;
! 7: with Standard_Complex_Poly_Systems; use Standard_Complex_Poly_Systems;
! 8: with Bracket_Monomials; use Bracket_Monomials;
! 9: with Bracket_Polynomials; use Bracket_Polynomials;
! 10: with Bracket_Systems; use Bracket_Systems;
! 11:
! 12: package Numeric_Minor_Equations is
! 13:
! 14: -- DESCRIPTION :
! 15: -- This package evaluates the symbolic equations in the Pieri homotopies.
! 16:
! 17: -- EXPANDING ACCORDING A BRACKET MONOMIAL :
! 18:
! 19: function Expanded_Minors
! 20: ( cffmat : Standard_Floating_Matrices.Matrix;
! 21: polmat : Standard_Complex_Poly_Matrices.Matrix;
! 22: bm : Bracket_Monomial ) return Poly;
! 23:
! 24: function Expanded_Minors
! 25: ( cffmat : Standard_Complex_Matrices.Matrix;
! 26: polmat : Standard_Complex_Poly_Matrices.Matrix;
! 27: bm : Bracket_Monomial ) return Poly;
! 28:
! 29: function Expanded_Minors
! 30: ( cntmat,polmat : Standard_Complex_Poly_Matrices.Matrix;
! 31: bm : Bracket_Monomial ) return Poly;
! 32:
! 33: function Lifted_Expanded_Minors
! 34: ( cntmat,polmat : Standard_Complex_Poly_Matrices.Matrix;
! 35: bm : Bracket_Monomial ) return Poly;
! 36:
! 37: -- DESCRIPTION :
! 38: -- Expansion of coefficient and polynomial minors along the Laplace
! 39: -- expansion formula in bm creates a polynomial equation.
! 40: -- With the prefix Lifted_, the polynomials in polmat are extended
! 41: -- with a zero lifting.
! 42:
! 43: -- ON ENTRY :
! 44: -- cffmat coefficient matrix, represents m-plane;
! 45: -- cntmat polynomial matrix, represents moving m-plane,
! 46: -- the continuation parameter is the last variable;
! 47: -- polmat polynomial matrix, contains the pattern of the p-plane;
! 48: -- bm quadratic bracket monomial, the first bracket is a coefficient
! 49: -- minor and has zero as its first entry, the second bracket is
! 50: -- a polynomial minor.
! 51:
! 52: -- EXPANDING ACCORDING A BRACKET POLYNOMIAL :
! 53:
! 54: function Expanded_Minors
! 55: ( cffmat : Standard_Floating_Matrices.Matrix;
! 56: polmat : Standard_Complex_Poly_Matrices.Matrix;
! 57: bp : Bracket_Polynomial ) return Poly;
! 58:
! 59: function Expanded_Minors
! 60: ( cffmat : Standard_Complex_Matrices.Matrix;
! 61: polmat : Standard_Complex_Poly_Matrices.Matrix;
! 62: bp : Bracket_Polynomial ) return Poly;
! 63:
! 64: function Expanded_Minors
! 65: ( cntmat,polmat : Standard_Complex_Poly_Matrices.Matrix;
! 66: bp : Bracket_Polynomial ) return Poly;
! 67:
! 68: function Lifted_Expanded_Minors
! 69: ( cntmat,polmat : Standard_Complex_Poly_Matrices.Matrix;
! 70: bp : Bracket_Polynomial ) return Poly;
! 71:
! 72: -- DESCRIPTION :
! 73: -- Expansion of coefficient and polynomial minors along the Laplace
! 74: -- expansion formula in bp creates a polynomial equation.
! 75: -- With the prefix Lifted_, the polynomials in polmat are extended
! 76: -- with a zero lifting.
! 77:
! 78: -- ON ENTRY :
! 79: -- cffmat coefficient matrix, represents m-plane, m = n-p;
! 80: -- cntmat polynomial matrix, represents moving m-plane, m = n-p,
! 81: -- the continuation parameter is the last variable;
! 82: -- polmat polynomial matrix, contains the pattern of the p-plane;
! 83: -- bp Laplace expansion of one minor, the coefficient minors come
! 84: -- first and have a zero as first element.
! 85:
! 86: -- EXPANDING TO CONSTRUCT POLYNOMIAL SYSTEMS :
! 87:
! 88: function Expanded_Minors
! 89: ( cffmat : Standard_Floating_Matrices.Matrix;
! 90: polmat : Standard_Complex_Poly_Matrices.Matrix;
! 91: bs : Bracket_System ) return Poly_Sys;
! 92:
! 93: function Expanded_Minors
! 94: ( cffmat : Standard_Complex_Matrices.Matrix;
! 95: polmat : Standard_Complex_Poly_Matrices.Matrix;
! 96: bs : Bracket_System ) return Poly_Sys;
! 97:
! 98: function Expanded_Minors
! 99: ( cntmat,polmat : Standard_Complex_Poly_Matrices.Matrix;
! 100: bs : Bracket_System ) return Poly_Sys;
! 101:
! 102: function Lifted_Expanded_Minors
! 103: ( cntmat,polmat : Standard_Complex_Poly_Matrices.Matrix;
! 104: bs : Bracket_System ) return Poly_Sys;
! 105:
! 106: -- DESCRIPTION :
! 107: -- Expansion of coefficient and polynomial minors along the Laplace
! 108: -- expansion formulas in bs creates a polynomial system.
! 109: -- With the prefix Lifted_, the polynomials in polmat are extended
! 110: -- with zero lifting.
! 111:
! 112: -- ON ENTRY :
! 113: -- cffmat coefficient matrix, represents m-plane;
! 114: -- cntmat polynomial matrix, represents moving m-plane,
! 115: -- the continuation parameter is the last variable;
! 116: -- polmat polynomial matrix, contains the pattern of the p-plane;
! 117: -- bs Laplace expansion of all minors, the first equation is
! 118: -- the generic one and should not count in the range of
! 119: -- the resulting polynomial system.
! 120:
! 121: function Evaluate ( p : Poly; x : Standard_Complex_Matrices.Matrix )
! 122: return Complex_Number;
! 123:
! 124: -- DESCRIPTION :
! 125: -- Evaluates the polynomial p at the matrix x, where x is a value
! 126: -- for the polynomial matrix used above to define p.
! 127:
! 128: function Evaluate ( p : Poly_Sys; x : Standard_Complex_Matrices.Matrix )
! 129: return Standard_Complex_Vectors.Vector;
! 130:
! 131: -- DESCRIPTION :
! 132: -- Evaluates the polynomial system p at the matrix x, where x is a value
! 133: -- for the polynomial matrix used above to define p.
! 134:
! 135: procedure Embed ( t : in out Term );
! 136: procedure Embed ( p : in out Poly );
! 137: procedure Embed ( p : in out Poly_Sys );
! 138: procedure Embed ( m : in out Standard_Complex_Poly_Matrices.Matrix );
! 139:
! 140: -- DESCRIPTION :
! 141: -- Augments the number of variables with one, as is required to embed
! 142: -- the polynomials in a homotopy.
! 143:
! 144: function Linear_Homotopy ( target,start : Poly ) return Poly;
! 145:
! 146: -- DESCRIPTION :
! 147: -- Returns (1-t)*start + t*target, with t an additional last variable.
! 148:
! 149: function Linear_Interpolation
! 150: ( target,start : Poly; k : natural ) return Poly;
! 151:
! 152: -- DESCRIPTION :
! 153: -- Returns (1-t)*start + t*target, with t the k-th variable.
! 154:
! 155: procedure Divide_Common_Factor ( p : in out Poly; k : in natural );
! 156:
! 157: -- DESCRIPTION :
! 158: -- If the k-th variable occurs everywhere in p with a positive power,
! 159: -- then it will be divided out.
! 160:
! 161: end Numeric_Minor_Equations;
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