File: [local] / OpenXM_contrib / PHC / Ada / Root_Counts / Symmetry / equivariant_polynomial_systems.ads (download)
Revision 1.1.1.1 (vendor branch), Sun Oct 29 17:45:31 2000 UTC (23 years, 10 months ago) by maekawa
Branch: PHC, MAIN
CVS Tags: v2, maekawa-ipv6, RELEASE_1_2_3, RELEASE_1_2_2_KNOPPIX_b, RELEASE_1_2_2_KNOPPIX, RELEASE_1_2_2, RELEASE_1_2_1, HEAD Changes since 1.1: +0 -0
lines
Import the second public release of PHCpack.
OKed by Jan Verschelde.
|
with Standard_Complex_Poly_Systems; use Standard_Complex_Poly_Systems;
with Symmetry_Group; use Symmetry_Group;
package Equivariant_Polynomial_Systems is
-- DESCRIPTION :
-- This package contains procedures for, given a group representation V,
-- to compute the associated representation W, of a (G,V,W)-symmetric
-- polynomial system.
procedure Act ( v : in List_of_Permutations; s : in Poly_Sys;
w : in out List_of_Permutations;
fail,inva,equi : out boolean );
-- DESCRIPTION :
-- Each permutation of the list v will be applied on the system s;
-- the list w contains the results of each permutation.
-- ON ENTRY :
-- v a list of permutations;
-- s a polynomial system.
-- ON RETURN :
-- w a list of Natural_Vectors x
-- x(i) = j, where j indicates the index of the
-- resulting polynomial of s, after permutation,
-- if j = n+1, then the permuted polynomial did not belong to s
-- and fail will be true on return;
-- fail true if the system is not (G,V,W)-symmetric, false otherwise;
-- inva true, if every polynomial in the system remains invariant,
-- i.e.: Permute(s(i),p) = s(i), with i in s'range,
-- for every permutation p, false otherwise;
-- equi true, if v = w, false otherwise.
function Symmetric ( s : Poly_Sys; v,w : List_of_Permutations )
return boolean;
-- DESCRIPTION :
-- This routine returns true if s is (G,V,W)-symmetric,
-- it returns false when s is (G,V,W)-symmetric.
-- ON ENTRY :
-- s a polynomial system;
-- v,w representations of the group.
end Equivariant_Polynomial_Systems;