Return to orbits_of_solutions.ads CVS log

Up to [local] / OpenXM_contrib / PHC / Ada / Root_Counts / Symmetry

Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Symmetry/orbits_of_solutions.ads, Revision 1.1

1.1     ! maekawa     1: with text_io;                            use text_io;
        !             2: with Standard_Floating_Numbers;          use Standard_Floating_Numbers;
        !             3: with Generic_Lists;
        !             4: with Standard_Complex_Solutions;         use Standard_Complex_Solutions;
        !             5: with Permutations,Symmetry_Group;        use Permutations,Symmetry_Group;
        !             6:
        !             7: package Orbits_of_Solutions is
        !             8:
        !             9: -- DESCRIPTION :
        !            10: --   This package contains routines for manipulating the
        !            11: --   solutions set of a symmetric polynomial system.
        !            12:
        !            13: -- DATA STRUCTURES :
        !            14:
        !            15:   type Orbit ( n : natural ) is record
        !            16:     orb : Permutation(1..n);  -- data representing the orbit
        !            17:      -- e.g.: orb = [ 1 1 2 2 ] => solution is like (a,a,b,b) or (a,b,a,b)
        !            18:     nbdiff : natural;         -- number of different values
        !            19:     nbgen  : natural;         -- number of generating solutions
        !            20:     nbsols : natural;         -- number of solutions in the orbit
        !            21:   end record;
        !            22:
        !            23:   type Link_to_Orbit is access Orbit;
        !            24:
        !            25:   package Lists_of_Orbits is new Generic_Lists(Link_to_Orbit);
        !            26:   type List_of_Orbits is new Lists_of_Orbits.List;
        !            27:
        !            28: -- CONSTRUCTORS :
        !            29:
        !            30:   function Generating ( sols : Solution_List; sign : boolean;
        !            31:                         tol : double_float ) return Solution_List;
        !            32:
        !            33:   -- DESCRIPTION :
        !            34:   --   Returns a list of generating solutions, by permutations, all
        !            35:   --   other solutions in sols can be derived from the resulting list.
        !            36:   --   If sign is true, then also permutations who alter the sign of
        !            37:   --   the components are tried.
        !            38:
        !            39:   procedure Analyze ( l : in List_of_Permutations; sign : in boolean;
        !            40:                       tol : in double_float; sols : in out Solution_List );
        !            41:
        !            42:   -- DESCRIPTION :
        !            43:   --   the solution list sols will be checked upon symmetry, according
        !            44:   --   to the list of permutations l
        !            45:
        !            46:   -- ON ENTRY :
        !            47:   --   l              a list of permutations;
        !            48:   --   sign           if true then sign symmetry has to be taken into account;
        !            49:   --   tol            tolerance to decide wether two solutions are equal;
        !            50:   --   sols           a list of solutions.
        !            51:
        !            52:   -- ON RETURN :
        !            53:   --   sols           a list of solutions, where only one element per orbit
        !            54:   --                  is in the list;
        !            55:   --                  the multiplicity field is used to indicate the number
        !            56:   --                  of elements in the orbit.
        !            57:
        !            58:   procedure Orbit_Structure
        !            59:                     ( s : in Solution; tol : in double_float;
        !            60:                       orbit : in out Permutation; nbdiff : out natural);
        !            61:
        !            62:   -- DESCRIPTION :
        !            63:   --   This procedure returns the structure of the orbit of the solution.
        !            64:
        !            65:   -- ON ENTRY :
        !            66:   --   s              a solution;
        !            67:   --   tol            tolerance to decide wether two solutions are equal.
        !            68:
        !            69:   -- ON RETURN :
        !            70:   --   orbit          orbit(i) = j means that x_i has the same value as x_j;
        !            71:   --   nbdiff         the number of different values in the orbit.
        !            72:
        !            73:   function Orbits ( sols : Solution_List; tol : double_float )
        !            74:                   return Permutation;
        !            75:
        !            76:   -- DESCRIPTION :
        !            77:   --   Let orb := Orbits(sols,tol),
        !            78:   --   then orb(i) gives the number of solutions belonging to an orbit
        !            79:   --   with i different values.
        !            80:
        !            81:   -- ON ENTRY :
        !            82:   --   sols         a list of solutions;
        !            83:   --   tol          tolerance to decide wether two solutions are equal.
        !            84:
        !            85:   procedure Orbits ( grp : in List_of_Permutations; tol : in double_float;
        !            86:                      sols : in out Solution_List;
        !            87:                      lorb : in out List_of_Orbits );
        !            88:
        !            89:   -- DESCRIPTION :
        !            90:   --   The list of solutions will be analyzed according to the
        !            91:   --   symmetry group.  Together with the information on the orbits,
        !            92:   --   the list of generating solutions will be produced.
        !            93:
        !            94:   -- ON ENTRY :
        !            95:   --   grp           a list of permutations representing the symmetry group;
        !            96:   --   tol           used to compare two solutions;
        !            97:   --   sols          the list of solutions.
        !            98:
        !            99:   -- ON RETURN :
        !           100:   --   sols          the generating list of solutions;
        !           101:   --   lorb          the list containing the information of the orbits.
        !           102:
        !           103: -- SELECTOR :
        !           104:
        !           105:   function Same_Orbit ( orb1,orb2 : Permutation ) return boolean;
        !           106:
        !           107:   -- DESCRIPTION :
        !           108:   --   Returns true when the structures of the orbits are the same.
        !           109:   --   For example : 1 1 1 2 = 1 2 1 1, but 1 1 2 2 /= 2 2 1 2.
        !           110:
        !           111: -- DESTRUCTOR :
        !           112:
        !           113:   procedure Clear ( lorb : in out List_of_Orbits );
        !           114:
        !           115:   -- DESCRIPTION :
        !           116:   --   All memory space allocated for lorb will be freed.
        !           117:
        !           118: end Orbits_of_Solutions;