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Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Symmetry/equivariant_polynomial_systems.ads, Revision 1.1.1.1

1.1       maekawa     1: with Standard_Complex_Poly_Systems;      use Standard_Complex_Poly_Systems;
                      2: with Symmetry_Group;                     use Symmetry_Group;
                      3:
                      4: package Equivariant_Polynomial_Systems is
                      5:
                      6: -- DESCRIPTION :
                      7: --   This package contains procedures for, given a group representation V,
                      8: --   to compute the associated representation W, of a (G,V,W)-symmetric
                      9: --   polynomial system.
                     10:
                     11:   procedure Act ( v : in List_of_Permutations; s : in Poly_Sys;
                     12:                   w : in out List_of_Permutations;
                     13:                   fail,inva,equi : out boolean );
                     14:
                     15:   -- DESCRIPTION :
                     16:   --   Each permutation of the list v will be applied on the system s;
                     17:   --   the list w contains the results of each permutation.
                     18:
                     19:   -- ON ENTRY :
                     20:   --   v          a list of permutations;
                     21:   --   s          a polynomial system.
                     22:
                     23:   -- ON RETURN :
                     24:   --   w          a list of Natural_Vectors x
                     25:   --               x(i) = j, where j indicates the index of the
                     26:   --               resulting polynomial of s, after permutation,
                     27:   --              if j = n+1, then the permuted polynomial did not belong to s
                     28:   --              and fail will be true on return;
                     29:   --   fail       true if the system is not (G,V,W)-symmetric, false otherwise;
                     30:   --   inva       true, if every polynomial in the system remains invariant,
                     31:   --              i.e.: Permute(s(i),p) = s(i), with i in s'range,
                     32:   --              for every permutation p, false otherwise;
                     33:   --   equi       true, if v = w, false otherwise.
                     34:
                     35:   function Symmetric ( s : Poly_Sys; v,w : List_of_Permutations )
                     36:                      return boolean;
                     37:
                     38:   -- DESCRIPTION :
                     39:   --   This routine returns true if s is (G,V,W)-symmetric,
                     40:   --   it returns false when s is (G,V,W)-symmetric.
                     41:
                     42:   -- ON ENTRY :
                     43:   --   s          a polynomial system;
                     44:   --   v,w        representations of the group.
                     45:
                     46: end Equivariant_Polynomial_Systems;