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Annotation of OpenXM_contrib/PHC/Ada/Schubert/brackets.ads, Revision 1.1.1.1

1.1       maekawa     1: with Standard_Natural_Vectors;
                      2:
                      3: package Brackets is
                      4:
                      5: -- DESCRIPTION :
                      6: --   A bracket is a selection of rows and represents a maximal minor
                      7: --   which is use in the Pluecker embedding of the Grassmannian.
                      8:
                      9: -- DATA STRUCTURES :
                     10:
                     11:   type Bracket is new Standard_Natural_Vectors.Vector;
                     12:                                                  -- typically of range 1..d
                     13:   type Link_to_Bracket is access Bracket;
                     14:
                     15: -- CONSTRUCTORS : puts the bracket in "normal form" with all entries sorted.
                     16:
                     17:   procedure Create ( v : in Standard_Natural_Vectors.Vector;
                     18:                      b : out Bracket; sign : out integer );
                     19:
                     20:   -- DESCRIPTION :
                     21:   --   Sorts the entries in the rows in ascending order.
                     22:   --   Eventually the sign of the bracket coefficient changes,
                     23:   --   when the number of transpositions is odd.
                     24:
                     25:   procedure Create ( v : in Standard_Natural_Vectors.Vector;
                     26:                      perm : out Standard_Natural_Vectors.Vector;
                     27:                      b : out Bracket; sign : out integer );
                     28:
                     29:   -- DESCRIPTION :
                     30:   --   Returns also the permutation "perm" that is used in the sorting.
                     31:
                     32:   function Modulo ( b : Bracket; n : natural ) return Bracket;
                     33:
                     34:   -- DESCRIPTION :
                     35:   --   Returns the modular form of the bracket: every entry mod n.
                     36:
                     37:   procedure Modulo ( b : in Bracket; n : in natural;
                     38:                      perm : out Standard_Natural_Vectors.Vector;
                     39:                      mb : out Bracket );
                     40:
                     41:   -- DESCRIPTION :
                     42:   --   mb = Modulo(b,n) and perm is the permutation used to sort mb.
                     43:
                     44: -- SELECTORS : all require that the brackets are sorted.
                     45:
                     46:   function Is_Zero ( b : Bracket ) return boolean;
                     47:
                     48:   -- DESCRIPTION :
                     49:   --   The bracket is zero when it has repeated entries.
                     50:
                     51:   function Is_Equal ( b1,b2 : Bracket ) return boolean;
                     52:
                     53:   -- DESCRIPTION :
                     54:   --   Returns true if both brackets are the same.
                     55:
                     56:   function "<" ( b1,b2 : Bracket ) return boolean;
                     57:
                     58:   -- DESCRIPTION :
                     59:   --   Returns true if b1 precedes b2 lexicographically.
                     60:
                     61:   function ">" ( b1,b2 : Bracket ) return boolean;
                     62:
                     63:   -- DESCRIPTION :
                     64:   --   Returns true if b1 is larger than b2, lexicographically.
                     65:
                     66:   function Is_Standard ( b1,b2 : Bracket ) return natural;
                     67:
                     68:   -- DESCRIPTION :
                     69:   --   Let s = Is_Standard(b1,b2).  If s = 0, then the pair b1*b2 constitutes
                     70:   --   a Standard bracket monomial, otherwise, s indicates the first entry
                     71:   --   where b1(s) > b2(s).
                     72:
                     73:   -- REQUIRED : b1 < b2, b1 precedes b2 lexicographically.
                     74:
                     75: -- DESTRUCTOR :
                     76:
                     77:   procedure Clear ( lb : in out Link_to_Bracket );
                     78:
                     79:   -- DESCRIPTION :
                     80:   --   Destroys the allocate space.
                     81:
                     82: end Brackets;