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