module symmetry;
%
% ----------------------------------------------------------
% Symmetry Package
% ----------------------------------------------------------
%
% Author : Karin Gatermann
% Konrad-Zuse-Zentrum fuer
% Informationstechnik Berlin
% Heilbronner Str. 10
% W-1000 Berlin 31
% Germany
% Email: Gatermann@sc.ZIB-Berlin.de
%
% Version 1.0 9. December 1991
%
% Abstract:
% ---------
% This program is an implementation of the algorithm
% for computation of symmetry adapted bases from the
% theory of linear representations of finite grous.
% Projections for the computation of block diagonal form
% of matrices are computed having the symmetry of a group.
%
%
% REDUCE 3.4 is required.
%
% References:
% -----------
% J.-P. Serre, Linear Representations of Finite Groups.
% Springer, New York (1977).
% E. Stiefel, A. F{\"a}ssler, Gruppentheoretische
% Methoden und ihre Anwendung. Teubner, Stuttgart (1979).
% (English translation to appear by Birkh\"auser (1992)).
%
% Keywords:
% --------
% linear representations, symmetry adapted bases,
% matrix with the symmetry of a group,
% block diagonalization
%
% symmetry.red
% definition of available algebraic operators
% To build a fast loading version of this package, the following
% sequence of commands should be used:
create!-package('(symmetry symdata1 symdata2),'(contrib symmetry));
load!-package 'symaux;
endmodule;
module symdata1; % Data for symmetry package, part 1.
% Author: Karin Gatermann <Gatermann@sc.ZIB-Berlin.de>.
set!*elems!*group('z2,'(id sz2))$
set!*generators('z2,'(sz2))$
set!*relations('z2,'(((sz2 sz2) (id))))$
set!*grouptable('z2,'((grouptable id sz2) (id id sz2) (sz2 sz2 id)))$
set!*inverse('z2,'((id sz2) (id sz2)))$
set!*elemasgen('z2,'(((sz2) (sz2))))$
set!*group('z2,'((id) (sz2)))$
set!*representation('z2,'((id (((1 . 1)))) (sz2 (((1 . 1))))),'complex)$
set!*representation('z2,
'((id (((1 . 1)))) (sz2 (((-1 . 1))))),'complex)$
set!*representation('z2,
'(realtype (id (((1 . 1)))) (sz2 (((1 . 1))))),'real)$
set!*representation('z2,
'(realtype (id (((1 . 1)))) (sz2 (((-1 . 1))))),'real)$
set!*available 'z2$
set!*elems!*group('k4,'(id s1k4 s2k4 rk4))$
set!*generators('k4,'(s1k4 s2k4))$
set!*relations('k4,
'(((s1k4 s1k4) (id))
((s2k4 s2k4) (id))
((s1k4 s2k4) (s2k4 s1k4))))$
set!*grouptable('k4,
'((grouptable id s1k4 s2k4 rk4)
(id id s1k4 s2k4 rk4)
(s1k4 s1k4 id rk4 s2k4)
(s2k4 s2k4 rk4 id s1k4)
(rk4 rk4 s2k4 s1k4 id)))$
set!*inverse('k4,'((id s1k4 s2k4 rk4) (id s1k4 s2k4 rk4)))$
set!*elemasgen('k4,
'(((s1k4) (s1k4)) ((s2k4) (s2k4)) ((rk4) (s1k4 s2k4))))$
set!*group('k4,'((id) (s1k4) (s2k4) (rk4)))$
set!*representation('k4,
'((id (((1 . 1))))
(s1k4 (((1 . 1))))
(s2k4 (((1 . 1))))
(rk4 (((1 . 1))))),'complex)$
set!*representation('k4,
'((id (((1 . 1))))
(s1k4 (((-1 . 1))))
(s2k4 (((1 . 1))))
(rk4 (((-1 . 1))))),'complex)$
set!*representation('k4,
'((id (((1 . 1))))
(s1k4 (((1 . 1))))
(s2k4 (((-1 . 1))))
(rk4 (((-1 . 1))))),'complex)$
set!*representation('k4,
'((id (((1 . 1))))
(s1k4 (((-1 . 1))))
(s2k4 (((-1 . 1))))
(rk4 (((1 . 1))))),'complex)$
set!*representation('k4,
'(realtype
(id (((1 . 1))))
(s1k4 (((1 . 1))))
(s2k4 (((1 . 1))))
(rk4 (((1 . 1))))),'real)$
set!*representation('k4,
'(realtype
(id (((1 . 1))))
(s1k4 (((-1 . 1))))
(s2k4 (((1 . 1))))
(rk4 (((-1 . 1))))),'real)$
set!*representation('k4,
'(realtype
(id (((1 . 1))))
(s1k4 (((1 . 1))))
(s2k4 (((-1 . 1))))
(rk4 (((-1 . 1))))),'real)$
set!*representation('k4,
'(realtype
(id (((1 . 1))))
(s1k4 (((-1 . 1))))
(s2k4 (((-1 . 1))))
(rk4 (((1 . 1))))),'real)$
set!*available 'k4$
set!*elems!*group('d3,'(id rd3 rot2d3 sd3 srd3 sr2d3))$
set!*generators('d3,'(rd3 sd3))$
set!*relations('d3,
'(((sd3 sd3) (id))
((rd3 rd3 rd3) (id))
((sd3 rd3 sd3) (rd3 rd3))))$
set!*grouptable('d3,
'((grouptable id rd3 rot2d3 sd3 srd3 sr2d3)
(id id rd3 rot2d3 sd3 srd3 sr2d3)
(rd3 rd3 rot2d3 id sr2d3 sd3 srd3)
(rot2d3 rot2d3 id rd3 srd3 sr2d3 sd3)
(sd3 sd3 srd3 sr2d3 id rd3 rot2d3)
(srd3 srd3 sr2d3 sd3 rot2d3 id rd3)
(sr2d3 sr2d3 sd3 srd3 rd3 rot2d3 id)))$
set!*inverse('d3,
'((id rd3 rot2d3 sd3 srd3 sr2d3) (id rot2d3 rd3 sd3 srd3 sr2d3)))$
set!*elemasgen('d3,
'(((rd3) (rd3))
((rot2d3) (rd3 rd3))
((sd3) (sd3))
((srd3) (sd3 rd3))
((sr2d3) (sd3 rd3 rd3))))$
set!*group('d3,'((id) (rd3 rot2d3) (sr2d3 sd3 srd3)))$
set!*representation('d3,
'((id (((1 . 1))))
(rd3 (((1 . 1))))
(rot2d3 (((1 . 1))))
(sd3 (((1 . 1))))
(srd3 (((1 . 1))))
(sr2d3 (((1 . 1))))),'complex)$
set!*representation('d3,
'((id (((1 . 1))))
(rd3 (((1 . 1))))
(rot2d3 (((1 . 1))))
(sd3 (((-1 . 1))))
(srd3 (((-1 . 1))))
(sr2d3 (((-1 . 1))))),'complex)$
set!*representation('d3,
'((id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(rd3
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(rot2d3
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(sd3 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(srd3
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
(sr2d3
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(1 . 2))))),'complex)$
set!*representation('d3,
'(realtype
(id (((1 . 1))))
(rd3 (((1 . 1))))
(rot2d3 (((1 . 1))))
(sd3 (((1 . 1))))
(srd3 (((1 . 1))))
(sr2d3 (((1 . 1))))),'real)$
set!*representation('d3,
'(realtype
(id (((1 . 1))))
(rd3 (((1 . 1))))
(rot2d3 (((1 . 1))))
(sd3 (((-1 . 1))))
(srd3 (((-1 . 1))))
(sr2d3 (((-1 . 1))))),'real)$
set!*representation('d3,
'(realtype
(id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(rd3
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(rot2d3
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(sd3 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(srd3
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
(sr2d3
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(1 . 2))))),'real)$
set!*available 'd3$
set!*elems!*group('d4,'(id rd4 rot2d4 rot3d4 sd4 srd4 sr2d4 sr3d4))$
set!*generators('d4,'(rd4 sd4))$
set!*relations('d4,
'(((sd4 sd4) (id))
((rd4 rd4 rd4 rd4) (id))
((sd4 rd4 sd4) (rd4 rd4 rd4))))$
set!*grouptable('d4,
'((grouptable id rd4 rot2d4 rot3d4 sd4 srd4 sr2d4 sr3d4)
(id id rd4 rot2d4 rot3d4 sd4 srd4 sr2d4 sr3d4)
(rd4 rd4 rot2d4 rot3d4 id sr3d4 sd4 srd4 sr2d4)
(rot2d4 rot2d4 rot3d4 id rd4 sr2d4 sr3d4 sd4 srd4)
(rot3d4 rot3d4 id rd4 rot2d4 srd4 sr2d4 sr3d4 sd4)
(sd4 sd4 srd4 sr2d4 sr3d4 id rd4 rot2d4 rot3d4)
(srd4 srd4 sr2d4 sr3d4 sd4 rot3d4 id rd4 rot2d4)
(sr2d4 sr2d4 sr3d4 sd4 srd4 rot2d4 rot3d4 id rd4)
(sr3d4 sr3d4 sd4 srd4 sr2d4 rd4 rot2d4 rot3d4 id)))$
set!*inverse('d4,
'((id rd4 rot2d4 rot3d4 sd4 srd4 sr2d4 sr3d4)
(id rot3d4 rot2d4 rd4 sd4 srd4 sr2d4 sr3d4)))$
set!*elemasgen('d4,
'(((rd4) (rd4))
((rot2d4) (rd4 rd4))
((rot3d4) (rd4 rd4 rd4))
((sd4) (sd4))
((srd4) (sd4 rd4))
((sr2d4) (sd4 rd4 rd4))
((sr3d4) (sd4 rd4 rd4 rd4))))$
set!*group('d4,'((id) (rd4 rot3d4) (rot2d4) (sd4 sr2d4) (sr3d4 srd4)))$
set!*representation('d4,
'((id (((1 . 1))))
(rd4 (((1 . 1))))
(rot2d4 (((1 . 1))))
(rot3d4 (((1 . 1))))
(sd4 (((1 . 1))))
(srd4 (((1 . 1))))
(sr2d4 (((1 . 1))))
(sr3d4 (((1 . 1))))),'complex)$
set!*representation('d4,
'((id (((1 . 1))))
(rd4 (((1 . 1))))
(rot2d4 (((1 . 1))))
(rot3d4 (((1 . 1))))
(sd4 (((-1 . 1))))
(srd4 (((-1 . 1))))
(sr2d4 (((-1 . 1))))
(sr3d4 (((-1 . 1))))),'complex)$
set!*representation('d4,
'((id (((1 . 1))))
(rd4 (((-1 . 1))))
(rot2d4 (((1 . 1))))
(rot3d4 (((-1 . 1))))
(sd4 (((1 . 1))))
(srd4 (((-1 . 1))))
(sr2d4 (((1 . 1))))
(sr3d4 (((-1 . 1))))),'complex)$
set!*representation('d4,
'((id (((1 . 1))))
(rd4 (((-1 . 1))))
(rot2d4 (((1 . 1))))
(rot3d4 (((-1 . 1))))
(sd4 (((-1 . 1))))
(srd4 (((1 . 1))))
(sr2d4 (((-1 . 1))))
(sr3d4 (((1 . 1))))),'complex)$
set!*representation('d4,
'((id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(rd4 (((nil . 1) (1 . 1)) ((-1 . 1) (nil . 1))))
(rot2d4 (((-1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(rot3d4 (((nil . 1) (-1 . 1)) ((1 . 1) (nil . 1))))
(sd4 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(srd4 (((nil . 1) (1 . 1)) ((1 . 1) (nil . 1))))
(sr2d4 (((-1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(sr3d4 (((nil . 1) (-1 . 1)) ((-1 . 1) (nil . 1))))),
'complex)$
set!*representation('d4,
'(realtype
(id (((1 . 1))))
(rd4 (((1 . 1))))
(rot2d4 (((1 . 1))))
(rot3d4 (((1 . 1))))
(sd4 (((1 . 1))))
(srd4 (((1 . 1))))
(sr2d4 (((1 . 1))))
(sr3d4 (((1 . 1))))),'real)$
set!*representation('d4,
'(realtype
(id (((1 . 1))))
(rd4 (((1 . 1))))
(rot2d4 (((1 . 1))))
(rot3d4 (((1 . 1))))
(sd4 (((-1 . 1))))
(srd4 (((-1 . 1))))
(sr2d4 (((-1 . 1))))
(sr3d4 (((-1 . 1))))),'real)$
set!*representation('d4,
'(realtype
(id (((1 . 1))))
(rd4 (((-1 . 1))))
(rot2d4 (((1 . 1))))
(rot3d4 (((-1 . 1))))
(sd4 (((1 . 1))))
(srd4 (((-1 . 1))))
(sr2d4 (((1 . 1))))
(sr3d4 (((-1 . 1))))),'real)$
set!*representation('d4,
'(realtype
(id (((1 . 1))))
(rd4 (((-1 . 1))))
(rot2d4 (((1 . 1))))
(rot3d4 (((-1 . 1))))
(sd4 (((-1 . 1))))
(srd4 (((1 . 1))))
(sr2d4 (((-1 . 1))))
(sr3d4 (((1 . 1))))),'real)$
set!*representation('d4,
'(realtype
(id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(rd4 (((nil . 1) (1 . 1)) ((-1 . 1) (nil . 1))))
(rot2d4 (((-1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(rot3d4 (((nil . 1) (-1 . 1)) ((1 . 1) (nil . 1))))
(sd4 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(srd4 (((nil . 1) (1 . 1)) ((1 . 1) (nil . 1))))
(sr2d4 (((-1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(sr3d4 (((nil . 1) (-1 . 1)) ((-1 . 1) (nil . 1))))),
'real)$
set!*available 'd4$
set!*elems!*group('d5,
'(id rd5 r2d5 r3d5 r4d5 sd5 srd5 sr2d5 sr3d5 sr4d5))$
set!*generators('d5,'(rd5 sd5))$
set!*relations('d5,
'(((sd5 sd5) (id))
((rd5 rd5 rd5 rd5 rd5) (id))
((sd5 rd5 sd5) (rd5 rd5 rd5 rd5))))$
set!*grouptable('d5,
'((grouptable id rd5 r2d5 r3d5 r4d5 sd5 srd5 sr2d5 sr3d5 sr4d5)
(id id rd5 r2d5 r3d5 r4d5 sd5 srd5 sr2d5 sr3d5 sr4d5)
(rd5 rd5 r2d5 r3d5 r4d5 id sr4d5 sd5 srd5 sr2d5 sr3d5)
(r2d5 r2d5 r3d5 r4d5 id rd5 sr3d5 sr4d5 sd5 srd5 sr2d5)
(r3d5 r3d5 r4d5 id rd5 r2d5 sr2d5 sr3d5 sr4d5 sd5 srd5)
(r4d5 r4d5 id rd5 r2d5 r3d5 srd5 sr2d5 sr3d5 sr4d5 sd5)
(sd5 sd5 srd5 sr2d5 sr3d5 sr4d5 id rd5 r2d5 r3d5 r4d5)
(srd5 srd5 sr2d5 sr3d5 sr4d5 sd5 r4d5 id rd5 r2d5 r3d5)
(sr2d5 sr2d5 sr3d5 sr4d5 sd5 srd5 r3d5 r4d5 id rd5 r2d5)
(sr3d5 sr3d5 sr4d5 sd5 srd5 sr2d5 r2d5 r3d5 r4d5 id rd5)
(sr4d5 sr4d5 sd5 srd5 sr2d5 sr3d5 rd5 r2d5 r3d5 r4d5 id)))$
set!*inverse('d5,
'((id rd5 r2d5 r3d5 r4d5 sd5 srd5 sr2d5 sr3d5 sr4d5)
(id r4d5 r3d5 r2d5 rd5 sd5 srd5 sr2d5 sr3d5 sr4d5)))$
set!*elemasgen('d5,
'(((rd5) (rd5))
((r2d5) (rd5 rd5))
((r3d5) (rd5 rd5 rd5))
((r4d5) (rd5 rd5 rd5 rd5))
((sd5) (sd5))
((srd5) (sd5 rd5))
((sr2d5) (sd5 rd5 rd5))
((sr3d5) (sd5 rd5 rd5 rd5))
((sr4d5) (sd5 rd5 rd5 rd5 rd5))))$
set!*group('d5,
'((id) (rd5 r4d5) (r2d5 r3d5) (srd5 sr2d5 sd5 sr4d5 sr3d5)))$
set!*representation('d5,
'((id (((1 . 1))))
(rd5 (((1 . 1))))
(r2d5 (((1 . 1))))
(r3d5 (((1 . 1))))
(r4d5 (((1 . 1))))
(sd5 (((1 . 1))))
(srd5 (((1 . 1))))
(sr2d5 (((1 . 1))))
(sr3d5 (((1 . 1))))
(sr4d5 (((1 . 1))))),'complex)$
set!*representation('d5,
'((id (((1 . 1))))
(rd5 (((1 . 1))))
(r2d5 (((1 . 1))))
(r3d5 (((1 . 1))))
(r4d5 (((1 . 1))))
(sd5 (((-1 . 1))))
(srd5 (((-1 . 1))))
(sr2d5 (((-1 . 1))))
(sr3d5 (((-1 . 1))))
(sr4d5 (((-1 . 1))))),'complex)$
set!*representation('d5,
'((id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(rd5
(((((((cos (quotient (times 2 pi) 5)) . 1) . 1)) . 1)
(((((sin (quotient (times 2 pi) 5)) . 1) . -1)) . 1))
((((((sin (quotient (times 2 pi) 5)) . 1) . 1)) . 1)
(((((cos (quotient (times 2 pi) 5)) . 1) . 1)) . 1))))
(r2d5
(((((((sin (quotient (times 2 pi) 5)) . 2) . -1)
(((cos (quotient (times 2 pi) 5)) . 2) . 1))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 1) . -2)))
. 1))
((((((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 1) . 2)))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 2) . -1)
(((cos (quotient (times 2 pi) 5)) . 2) . 1))
. 1))))
(r3d5
(((((((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 1) . -3))
(((cos (quotient (times 2 pi) 5)) . 3) . 1))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 3) . 1)
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 2) . -3)))
. 1))
((((((sin (quotient (times 2 pi) 5)) . 3) . -1)
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 2) . 3)))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 1) . -3))
(((cos (quotient (times 2 pi) 5)) . 3) . 1))
. 1))))
(r4d5
(((((((sin (quotient (times 2 pi) 5)) . 4) . 1)
(((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 2) . -6))
(((cos (quotient (times 2 pi) 5)) . 4) . 1))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 3)
(((cos (quotient (times 2 pi) 5)) . 1) . 4))
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 3) . -4)))
. 1))
((((((sin (quotient (times 2 pi) 5)) . 3)
(((cos (quotient (times 2 pi) 5)) . 1) . -4))
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 3) . 4)))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 4) . 1)
(((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 2) . -6))
(((cos (quotient (times 2 pi) 5)) . 4) . 1))
. 1))))
(sd5 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(srd5
(((((((cos (quotient (times 2 pi) 5)) . 1) . 1)) . 1)
(((((sin (quotient (times 2 pi) 5)) . 1) . -1)) . 1))
((((((sin (quotient (times 2 pi) 5)) . 1) . -1)) . 1)
(((((cos (quotient (times 2 pi) 5)) . 1) . -1)) . 1))))
(sr2d5
(((((((sin (quotient (times 2 pi) 5)) . 2) . -1)
(((cos (quotient (times 2 pi) 5)) . 2) . 1))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 1) . -2)))
. 1))
((((((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 1) . -2)))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 2) . 1)
(((cos (quotient (times 2 pi) 5)) . 2) . -1))
. 1))))
(sr3d5
(((((((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 1) . -3))
(((cos (quotient (times 2 pi) 5)) . 3) . 1))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 3) . 1)
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 2) . -3)))
. 1))
((((((sin (quotient (times 2 pi) 5)) . 3) . 1)
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 2) . -3)))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 1) . 3))
(((cos (quotient (times 2 pi) 5)) . 3) . -1))
. 1))))
(sr4d5
(((((((sin (quotient (times 2 pi) 5)) . 4) . 1)
(((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 2) . -6))
(((cos (quotient (times 2 pi) 5)) . 4) . 1))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 3)
(((cos (quotient (times 2 pi) 5)) . 1) . 4))
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 3) . -4)))
. 1))
((((((sin (quotient (times 2 pi) 5)) . 3)
(((cos (quotient (times 2 pi) 5)) . 1) . 4))
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 3) . -4)))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 4) . -1)
(((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 2) . 6))
(((cos (quotient (times 2 pi) 5)) . 4) . -1))
. 1))))),'complex)$
set!*representation('d5,
'((id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(rd5
(((((((cos (quotient (times 4 pi) 5)) . 1) . 1)) . 1)
(((((sin (quotient (times 4 pi) 5)) . 1) . -1)) . 1))
((((((sin (quotient (times 4 pi) 5)) . 1) . 1)) . 1)
(((((cos (quotient (times 4 pi) 5)) . 1) . 1)) . 1))))
(r2d5
(((((((sin (quotient (times 4 pi) 5)) . 2) . -1)
(((cos (quotient (times 4 pi) 5)) . 2) . 1))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 1) . -2)))
. 1))
((((((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 1) . 2)))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 2) . -1)
(((cos (quotient (times 4 pi) 5)) . 2) . 1))
. 1))))
(r3d5
(((((((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 1) . -3))
(((cos (quotient (times 4 pi) 5)) . 3) . 1))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 3) . 1)
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 2) . -3)))
. 1))
((((((sin (quotient (times 4 pi) 5)) . 3) . -1)
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 2) . 3)))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 1) . -3))
(((cos (quotient (times 4 pi) 5)) . 3) . 1))
. 1))))
(r4d5
(((((((sin (quotient (times 4 pi) 5)) . 4) . 1)
(((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 2) . -6))
(((cos (quotient (times 4 pi) 5)) . 4) . 1))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 3)
(((cos (quotient (times 4 pi) 5)) . 1) . 4))
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 3) . -4)))
. 1))
((((((sin (quotient (times 4 pi) 5)) . 3)
(((cos (quotient (times 4 pi) 5)) . 1) . -4))
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 3) . 4)))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 4) . 1)
(((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 2) . -6))
(((cos (quotient (times 4 pi) 5)) . 4) . 1))
. 1))))
(sd5 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(srd5
(((((((cos (quotient (times 4 pi) 5)) . 1) . 1)) . 1)
(((((sin (quotient (times 4 pi) 5)) . 1) . -1)) . 1))
((((((sin (quotient (times 4 pi) 5)) . 1) . -1)) . 1)
(((((cos (quotient (times 4 pi) 5)) . 1) . -1)) . 1))))
(sr2d5
(((((((sin (quotient (times 4 pi) 5)) . 2) . -1)
(((cos (quotient (times 4 pi) 5)) . 2) . 1))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 1) . -2)))
. 1))
((((((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 1) . -2)))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 2) . 1)
(((cos (quotient (times 4 pi) 5)) . 2) . -1))
. 1))))
(sr3d5
(((((((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 1) . -3))
(((cos (quotient (times 4 pi) 5)) . 3) . 1))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 3) . 1)
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 2) . -3)))
. 1))
((((((sin (quotient (times 4 pi) 5)) . 3) . 1)
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 2) . -3)))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 1) . 3))
(((cos (quotient (times 4 pi) 5)) . 3) . -1))
. 1))))
(sr4d5
(((((((sin (quotient (times 4 pi) 5)) . 4) . 1)
(((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 2) . -6))
(((cos (quotient (times 4 pi) 5)) . 4) . 1))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 3)
(((cos (quotient (times 4 pi) 5)) . 1) . 4))
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 3) . -4)))
. 1))
((((((sin (quotient (times 4 pi) 5)) . 3)
(((cos (quotient (times 4 pi) 5)) . 1) . 4))
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 3) . -4)))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 4) . -1)
(((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 2) . 6))
(((cos (quotient (times 4 pi) 5)) . 4) . -1))
. 1))))),'complex)$
set!*representation('d5,
'(realtype
(id (((1 . 1))))
(rd5 (((1 . 1))))
(r2d5 (((1 . 1))))
(r3d5 (((1 . 1))))
(r4d5 (((1 . 1))))
(sd5 (((1 . 1))))
(srd5 (((1 . 1))))
(sr2d5 (((1 . 1))))
(sr3d5 (((1 . 1))))
(sr4d5 (((1 . 1))))),'real)$
set!*representation('d5,
'(realtype
(id (((1 . 1))))
(rd5 (((1 . 1))))
(r2d5 (((1 . 1))))
(r3d5 (((1 . 1))))
(r4d5 (((1 . 1))))
(sd5 (((-1 . 1))))
(srd5 (((-1 . 1))))
(sr2d5 (((-1 . 1))))
(sr3d5 (((-1 . 1))))
(sr4d5 (((-1 . 1))))),'real)$
set!*representation('d5,
'(realtype
(id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(rd5
(((((((cos (quotient (times 2 pi) 5)) . 1) . 1)) . 1)
(((((sin (quotient (times 2 pi) 5)) . 1) . -1)) . 1))
((((((sin (quotient (times 2 pi) 5)) . 1) . 1)) . 1)
(((((cos (quotient (times 2 pi) 5)) . 1) . 1)) . 1))))
(r2d5
(((((((sin (quotient (times 2 pi) 5)) . 2) . -1)
(((cos (quotient (times 2 pi) 5)) . 2) . 1))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 1) . -2)))
. 1))
((((((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 1) . 2)))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 2) . -1)
(((cos (quotient (times 2 pi) 5)) . 2) . 1))
. 1))))
(r3d5
(((((((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 1) . -3))
(((cos (quotient (times 2 pi) 5)) . 3) . 1))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 3) . 1)
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 2) . -3)))
. 1))
((((((sin (quotient (times 2 pi) 5)) . 3) . -1)
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 2) . 3)))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 1) . -3))
(((cos (quotient (times 2 pi) 5)) . 3) . 1))
. 1))))
(r4d5
(((((((sin (quotient (times 2 pi) 5)) . 4) . 1)
(((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 2) . -6))
(((cos (quotient (times 2 pi) 5)) . 4) . 1))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 3)
(((cos (quotient (times 2 pi) 5)) . 1) . 4))
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 3) . -4)))
. 1))
((((((sin (quotient (times 2 pi) 5)) . 3)
(((cos (quotient (times 2 pi) 5)) . 1) . -4))
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 3) . 4)))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 4) . 1)
(((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 2) . -6))
(((cos (quotient (times 2 pi) 5)) . 4) . 1))
. 1))))
(sd5 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(srd5
(((((((cos (quotient (times 2 pi) 5)) . 1) . 1)) . 1)
(((((sin (quotient (times 2 pi) 5)) . 1) . -1)) . 1))
((((((sin (quotient (times 2 pi) 5)) . 1) . -1)) . 1)
(((((cos (quotient (times 2 pi) 5)) . 1) . -1)) . 1))))
(sr2d5
(((((((sin (quotient (times 2 pi) 5)) . 2) . -1)
(((cos (quotient (times 2 pi) 5)) . 2) . 1))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 1) . -2)))
. 1))
((((((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 1) . -2)))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 2) . 1)
(((cos (quotient (times 2 pi) 5)) . 2) . -1))
. 1))))
(sr3d5
(((((((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 1) . -3))
(((cos (quotient (times 2 pi) 5)) . 3) . 1))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 3) . 1)
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 2) . -3)))
. 1))
((((((sin (quotient (times 2 pi) 5)) . 3) . 1)
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 2) . -3)))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 1) . 3))
(((cos (quotient (times 2 pi) 5)) . 3) . -1))
. 1))))
(sr4d5
(((((((sin (quotient (times 2 pi) 5)) . 4) . 1)
(((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 2) . -6))
(((cos (quotient (times 2 pi) 5)) . 4) . 1))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 3)
(((cos (quotient (times 2 pi) 5)) . 1) . 4))
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 3) . -4)))
. 1))
((((((sin (quotient (times 2 pi) 5)) . 3)
(((cos (quotient (times 2 pi) 5)) . 1) . 4))
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 3) . -4)))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 4) . -1)
(((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 2) . 6))
(((cos (quotient (times 2 pi) 5)) . 4) . -1))
. 1))))),'real)$
set!*representation('d5,
'(realtype
(id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(rd5
(((((((cos (quotient (times 4 pi) 5)) . 1) . 1)) . 1)
(((((sin (quotient (times 4 pi) 5)) . 1) . -1)) . 1))
((((((sin (quotient (times 4 pi) 5)) . 1) . 1)) . 1)
(((((cos (quotient (times 4 pi) 5)) . 1) . 1)) . 1))))
(r2d5
(((((((sin (quotient (times 4 pi) 5)) . 2) . -1)
(((cos (quotient (times 4 pi) 5)) . 2) . 1))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 1) . -2)))
. 1))
((((((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 1) . 2)))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 2) . -1)
(((cos (quotient (times 4 pi) 5)) . 2) . 1))
. 1))))
(r3d5
(((((((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 1) . -3))
(((cos (quotient (times 4 pi) 5)) . 3) . 1))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 3) . 1)
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 2) . -3)))
. 1))
((((((sin (quotient (times 4 pi) 5)) . 3) . -1)
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 2) . 3)))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 1) . -3))
(((cos (quotient (times 4 pi) 5)) . 3) . 1))
. 1))))
(r4d5
(((((((sin (quotient (times 4 pi) 5)) . 4) . 1)
(((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 2) . -6))
(((cos (quotient (times 4 pi) 5)) . 4) . 1))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 3)
(((cos (quotient (times 4 pi) 5)) . 1) . 4))
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 3) . -4)))
. 1))
((((((sin (quotient (times 4 pi) 5)) . 3)
(((cos (quotient (times 4 pi) 5)) . 1) . -4))
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 3) . 4)))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 4) . 1)
(((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 2) . -6))
(((cos (quotient (times 4 pi) 5)) . 4) . 1))
. 1))))
(sd5 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(srd5
(((((((cos (quotient (times 4 pi) 5)) . 1) . 1)) . 1)
(((((sin (quotient (times 4 pi) 5)) . 1) . -1)) . 1))
((((((sin (quotient (times 4 pi) 5)) . 1) . -1)) . 1)
(((((cos (quotient (times 4 pi) 5)) . 1) . -1)) . 1))))
(sr2d5
(((((((sin (quotient (times 4 pi) 5)) . 2) . -1)
(((cos (quotient (times 4 pi) 5)) . 2) . 1))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 1) . -2)))
. 1))
((((((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 1) . -2)))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 2) . 1)
(((cos (quotient (times 4 pi) 5)) . 2) . -1))
. 1))))
(sr3d5
(((((((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 1) . -3))
(((cos (quotient (times 4 pi) 5)) . 3) . 1))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 3) . 1)
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 2) . -3)))
. 1))
((((((sin (quotient (times 4 pi) 5)) . 3) . 1)
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 2) . -3)))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 1) . 3))
(((cos (quotient (times 4 pi) 5)) . 3) . -1))
. 1))))
(sr4d5
(((((((sin (quotient (times 4 pi) 5)) . 4) . 1)
(((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 2) . -6))
(((cos (quotient (times 4 pi) 5)) . 4) . 1))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 3)
(((cos (quotient (times 4 pi) 5)) . 1) . 4))
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 3) . -4)))
. 1))
((((((sin (quotient (times 4 pi) 5)) . 3)
(((cos (quotient (times 4 pi) 5)) . 1) . 4))
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 3) . -4)))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 4) . -1)
(((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 2) . 6))
(((cos (quotient (times 4 pi) 5)) . 4) . -1))
. 1))))),'real)$
set!*available 'd5$
set!*elems!*group('d6,
'(id
rd6
r2d6
r3d6
r4d6
r5d6
sd6
srd6
sr2d6
sr3d6
sr4d6
sr5d6))$
set!*generators('d6,'(rd6 sd6))$
set!*relations('d6,
'(((sd6 sd6) (id))
((rd6 rd6 rd6 rd6 rd6 rd6) (id))
((sd6 rd6 sd6) (rd6 rd6 rd6 rd6 rd6))))$
set!*grouptable('d6,
'((grouptable
id
rd6
r2d6
r3d6
r4d6
r5d6
sd6
srd6
sr2d6
sr3d6
sr4d6
sr5d6)
(id
id
rd6
r2d6
r3d6
r4d6
r5d6
sd6
srd6
sr2d6
sr3d6
sr4d6
sr5d6)
(rd6
rd6
r2d6
r3d6
r4d6
r5d6
id
sr5d6
sd6
srd6
sr2d6
sr3d6
sr4d6)
(r2d6
r2d6
r3d6
r4d6
r5d6
id
rd6
sr4d6
sr5d6
sd6
srd6
sr2d6
sr3d6)
(r3d6
r3d6
r4d6
r5d6
id
rd6
r2d6
sr3d6
sr4d6
sr5d6
sd6
srd6
sr2d6)
(r4d6
r4d6
r5d6
id
rd6
r2d6
r3d6
sr2d6
sr3d6
sr4d6
sr5d6
sd6
srd6)
(r5d6
r5d6
id
rd6
r2d6
r3d6
r4d6
srd6
sr2d6
sr3d6
sr4d6
sr5d6
sd6)
(sd6
sd6
srd6
sr2d6
sr3d6
sr4d6
sr5d6
id
rd6
r2d6
r3d6
r4d6
r5d6)
(srd6
srd6
sr2d6
sr3d6
sr4d6
sr5d6
sd6
r5d6
id
rd6
r2d6
r3d6
r4d6)
(sr2d6
sr2d6
sr3d6
sr4d6
sr5d6
sd6
srd6
r4d6
r5d6
id
rd6
r2d6
r3d6)
(sr3d6
sr3d6
sr4d6
sr5d6
sd6
srd6
sr2d6
r3d6
r4d6
r5d6
id
rd6
r2d6)
(sr4d6
sr4d6
sr5d6
sd6
srd6
sr2d6
sr3d6
r2d6
r3d6
r4d6
r5d6
id
rd6)
(sr5d6
sr5d6
sd6
srd6
sr2d6
sr3d6
sr4d6
rd6
r2d6
r3d6
r4d6
r5d6
id)))$
set!*inverse('d6,
'((id rd6 r2d6 r3d6 r4d6 r5d6 sd6 srd6 sr2d6 sr3d6 sr4d6 sr5d6)
(id r5d6 r4d6 r3d6 r2d6 rd6 sd6 srd6 sr2d6 sr3d6 sr4d6 sr5d6)))$
set!*elemasgen('d6,
'(((rd6) (rd6))
((r2d6) (rd6 rd6))
((r3d6) (rd6 rd6 rd6))
((r4d6) (rd6 rd6 rd6 rd6))
((r5d6) (rd6 rd6 rd6 rd6 rd6))
((sd6) (sd6))
((srd6) (sd6 rd6))
((sr2d6) (sd6 rd6 rd6))
((sr3d6) (sd6 rd6 rd6 rd6))
((sr4d6) (sd6 rd6 rd6 rd6 rd6))
((sr5d6) (sd6 rd6 rd6 rd6 rd6 rd6))))$
set!*group('d6,
'((id)
(rd6 r5d6)
(r2d6 r4d6)
(r3d6)
(sr2d6 sd6 sr4d6)
(srd6 sr5d6 sr3d6)))$
set!*representation('d6,
'((id (((1 . 1))))
(rd6 (((1 . 1))))
(r2d6 (((1 . 1))))
(r3d6 (((1 . 1))))
(r4d6 (((1 . 1))))
(r5d6 (((1 . 1))))
(sd6 (((1 . 1))))
(srd6 (((1 . 1))))
(sr2d6 (((1 . 1))))
(sr3d6 (((1 . 1))))
(sr4d6 (((1 . 1))))
(sr5d6 (((1 . 1))))),'complex)$
set!*representation('d6,
'((id (((1 . 1))))
(rd6 (((1 . 1))))
(r2d6 (((1 . 1))))
(r3d6 (((1 . 1))))
(r4d6 (((1 . 1))))
(r5d6 (((1 . 1))))
(sd6 (((-1 . 1))))
(srd6 (((-1 . 1))))
(sr2d6 (((-1 . 1))))
(sr3d6 (((-1 . 1))))
(sr4d6 (((-1 . 1))))
(sr5d6 (((-1 . 1))))),'complex)$
set!*representation('d6,
'((id (((1 . 1))))
(rd6 (((-1 . 1))))
(r2d6 (((1 . 1))))
(r3d6 (((-1 . 1))))
(r4d6 (((1 . 1))))
(r5d6 (((-1 . 1))))
(sd6 (((1 . 1))))
(srd6 (((-1 . 1))))
(sr2d6 (((1 . 1))))
(sr3d6 (((-1 . 1))))
(sr4d6 (((1 . 1))))
(sr5d6 (((-1 . 1))))),'complex)$
set!*representation('d6,
'((id (((1 . 1))))
(rd6 (((-1 . 1))))
(r2d6 (((1 . 1))))
(r3d6 (((-1 . 1))))
(r4d6 (((1 . 1))))
(r5d6 (((-1 . 1))))
(sd6 (((-1 . 1))))
(srd6 (((1 . 1))))
(sr2d6 (((-1 . 1))))
(sr3d6 (((1 . 1))))
(sr4d6 (((-1 . 1))))
(sr5d6 (((1 . 1))))),'complex)$
set!*representation('d6,
'((id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(rd6
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2) (1 . 2))))
(r2d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(r3d6 (((-1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(r4d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(r5d6
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
(sd6 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(srd6
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(sr2d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
(sr3d6 (((-1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(sr4d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2) (1 . 2))))
(sr5d6
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))),'complex)$
set!*representation('d6,
'((id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(rd6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(r2d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(r3d6 (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(r4d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(r5d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(sd6 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(srd6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
(sr2d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2) (1 . 2))))
(sr3d6 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(sr4d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
(sr5d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(1 . 2))))),'complex)$
set!*representation('d6,
'(realtype
(id (((1 . 1))))
(rd6 (((1 . 1))))
(r2d6 (((1 . 1))))
(r3d6 (((1 . 1))))
(r4d6 (((1 . 1))))
(r5d6 (((1 . 1))))
(sd6 (((1 . 1))))
(srd6 (((1 . 1))))
(sr2d6 (((1 . 1))))
(sr3d6 (((1 . 1))))
(sr4d6 (((1 . 1))))
(sr5d6 (((1 . 1))))),'real)$
set!*representation('d6,
'(realtype
(id (((1 . 1))))
(rd6 (((1 . 1))))
(r2d6 (((1 . 1))))
(r3d6 (((1 . 1))))
(r4d6 (((1 . 1))))
(r5d6 (((1 . 1))))
(sd6 (((-1 . 1))))
(srd6 (((-1 . 1))))
(sr2d6 (((-1 . 1))))
(sr3d6 (((-1 . 1))))
(sr4d6 (((-1 . 1))))
(sr5d6 (((-1 . 1))))),'real)$
set!*representation('d6,
'(realtype
(id (((1 . 1))))
(rd6 (((-1 . 1))))
(r2d6 (((1 . 1))))
(r3d6 (((-1 . 1))))
(r4d6 (((1 . 1))))
(r5d6 (((-1 . 1))))
(sd6 (((1 . 1))))
(srd6 (((-1 . 1))))
(sr2d6 (((1 . 1))))
(sr3d6 (((-1 . 1))))
(sr4d6 (((1 . 1))))
(sr5d6 (((-1 . 1))))),'real)$
set!*representation('d6,
'(realtype
(id (((1 . 1))))
(rd6 (((-1 . 1))))
(r2d6 (((1 . 1))))
(r3d6 (((-1 . 1))))
(r4d6 (((1 . 1))))
(r5d6 (((-1 . 1))))
(sd6 (((-1 . 1))))
(srd6 (((1 . 1))))
(sr2d6 (((-1 . 1))))
(sr3d6 (((1 . 1))))
(sr4d6 (((-1 . 1))))
(sr5d6 (((1 . 1))))),'real)$
set!*representation('d6,
'(realtype
(id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(rd6
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2) (1 . 2))))
(r2d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(r3d6 (((-1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(r4d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(r5d6
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
(sd6 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(srd6
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(sr2d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
(sr3d6 (((-1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(sr4d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2) (1 . 2))))
(sr5d6
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))),'real)$
set!*representation('d6,
'(realtype
(id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(rd6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(r2d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(r3d6 (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(r4d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(r5d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(sd6 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(srd6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
(sr2d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2) (1 . 2))))
(sr3d6 (((1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(sr4d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
(sr5d6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(1 . 2))))),'real)$
set!*available 'd6$
set!*elems!*group('c3,'(id rc3 r2c3))$
set!*generators('c3,'(rc3))$
set!*relations('c3,'(((rc3 rc3 rc3) (id))))$
set!*grouptable('c3,
'((grouptable id rc3 r2c3)
(id id rc3 r2c3)
(rc3 rc3 r2c3 id)
(r2c3 r2c3 id rc3)))$
set!*inverse('c3,'((id rc3 r2c3) (id r2c3 rc3)))$
set!*elemasgen('c3,'(((rc3) (rc3)) ((r2c3) (rc3 rc3))))$
set!*group('c3,'((id) (rc3) (r2c3)))$
set!*representation('c3,
'((id (((1 . 1)))) (rc3 (((1 . 1)))) (r2c3 (((1 . 1))))),
'complex)$
set!*representation('c3,
'((id (((1 . 1))))
(rc3
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1)) . -1)
. 2))))
(r2c3
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . -1)) . -1)
. 2))))),'complex)$
set!*representation('c3,
'((id (((1 . 1))))
(rc3
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . -1)) . -1)
. 2))))
(r2c3
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1)) . -1)
. 2))))),'complex)$
set!*representation('c3,
'(realtype
(id (((1 . 1))))
(rc3 (((1 . 1))))
(r2c3 (((1 . 1))))),'real)$
set!*representation('c3,
'(complextype
(id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(rc3
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(r2c3
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))),'real)$
set!*available 'c3$
set!*elems!*group('c4,'(id rc4 r2c4 r3c4))$
set!*generators('c4,'(rc4))$
set!*relations('c4,'(((rc4 rc4 rc4 rc4) (id))))$
set!*grouptable('c4,
'((grouptable id rc4 r2c4 r3c4)
(id id rc4 r2c4 r3c4)
(rc4 rc4 r2c4 r3c4 id)
(r2c4 r2c4 r3c4 id rc4)
(r3c4 r3c4 id rc4 r2c4)))$
set!*inverse('c4,'((id rc4 r2c4 r3c4) (id r3c4 r2c4 rc4)))$
set!*elemasgen('c4,
'(((rc4) (rc4)) ((r2c4) (rc4 rc4)) ((r3c4) (rc4 rc4 rc4))))$
set!*group('c4,'((id) (rc4) (r2c4) (r3c4)))$
set!*representation('c4,
'((id (((1 . 1))))
(rc4 (((1 . 1))))
(r2c4 (((1 . 1))))
(r3c4 (((1 . 1))))),'complex)$
set!*representation('c4,
'((id (((1 . 1))))
(rc4 (((-1 . 1))))
(r2c4 (((1 . 1))))
(r3c4 (((-1 . 1))))),'complex)$
set!*representation('c4,
'((id (((1 . 1))))
(rc4 ((((((i . 1) . 1)) . 1))))
(r2c4 (((-1 . 1))))
(r3c4 ((((((i . 1) . -1)) . 1))))),'complex)$
set!*representation('c4,
'((id (((1 . 1))))
(rc4 ((((((i . 1) . -1)) . 1))))
(r2c4 (((-1 . 1))))
(r3c4 ((((((i . 1) . 1)) . 1))))),'complex)$
set!*representation('c4,
'(realtype
(id (((1 . 1))))
(rc4 (((1 . 1))))
(r2c4 (((1 . 1))))
(r3c4 (((1 . 1))))),'real)$
set!*representation('c4,
'(realtype
(id (((1 . 1))))
(rc4 (((-1 . 1))))
(r2c4 (((1 . 1))))
(r3c4 (((-1 . 1))))),'real)$
set!*representation('c4,
'(complextype
(id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(rc4 (((nil . 1) (-1 . 1)) ((1 . 1) (nil . 1))))
(r2c4 (((-1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(r3c4 (((nil . 1) (1 . 1)) ((-1 . 1) (nil . 1))))),'real)$
set!*available 'c4$
set!*elems!*group('c5,'(id rc5 r2c5 r3c5 r4c5))$
set!*generators('c5,'(rc5))$
set!*relations('c5,'(((rc5 rc5 rc5 rc5 rc5) (id))))$
set!*grouptable('c5,
'((grouptable id rc5 r2c5 r3c5 r4c5)
(id id rc5 r2c5 r3c5 r4c5)
(rc5 rc5 r2c5 r3c5 r4c5 id)
(r2c5 r2c5 r3c5 r4c5 id rc5)
(r3c5 r3c5 r4c5 id rc5 r2c5)
(r4c5 r4c5 id rc5 r2c5 r3c5)))$
set!*inverse('c5,'((id rc5 r2c5 r3c5 r4c5) (id r4c5 r3c5 r2c5 rc5)))$
set!*elemasgen('c5,
'(((rc5) (rc5))
((r2c5) (rc5 rc5))
((r3c5) (rc5 rc5 rc5))
((r4c5) (rc5 rc5 rc5 rc5))))$
set!*group('c5,'((id) (rc5) (r2c5) (r3c5) (r4c5)))$
set!*representation('c5,
'((id (((1 . 1))))
(rc5 (((1 . 1))))
(r2c5 (((1 . 1))))
(r3c5 (((1 . 1))))
(r4c5 (((1 . 1))))),'complex)$
set!*representation('c5,
'((id (((1 . 1))))
(rc5
(((((((sin (quotient (times 2 pi) 5)) . 1) ((i . 1) . 1))
(((cos (quotient (times 2 pi) 5)) . 1) . 1))
. 1))))
(r2c5
(((((((sin (quotient (times 2 pi) 5)) . 2) . -1)
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 1)
((i . 1) . 2)))
(((cos (quotient (times 2 pi) 5)) . 2) . 1))
. 1))))
(r3c5
(((((((sin (quotient (times 2 pi) 5)) . 3)
((i . 1) . -1))
(((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 1) . -3))
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 2)
((i . 1) . 3)))
(((cos (quotient (times 2 pi) 5)) . 3) . 1))
. 1))))
(r4c5
(((((((sin (quotient (times 2 pi) 5)) . 4) . 1)
(((sin (quotient (times 2 pi) 5)) . 3)
(((cos (quotient (times 2 pi) 5)) . 1)
((i . 1) . -4)))
(((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 2) . -6))
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 3)
((i . 1) . 4)))
(((cos (quotient (times 2 pi) 5)) . 4) . 1))
. 1))))),'complex)$
set!*representation('c5,
'((id (((1 . 1))))
(rc5
(((((((sin (quotient (times 4 pi) 5)) . 1) ((i . 1) . 1))
(((cos (quotient (times 4 pi) 5)) . 1) . 1))
. 1))))
(r2c5
(((((((sin (quotient (times 4 pi) 5)) . 2) . -1)
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 1)
((i . 1) . 2)))
(((cos (quotient (times 4 pi) 5)) . 2) . 1))
. 1))))
(r3c5
(((((((sin (quotient (times 4 pi) 5)) . 3)
((i . 1) . -1))
(((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 1) . -3))
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 2)
((i . 1) . 3)))
(((cos (quotient (times 4 pi) 5)) . 3) . 1))
. 1))))
(r4c5
(((((((sin (quotient (times 4 pi) 5)) . 4) . 1)
(((sin (quotient (times 4 pi) 5)) . 3)
(((cos (quotient (times 4 pi) 5)) . 1)
((i . 1) . -4)))
(((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 2) . -6))
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 3)
((i . 1) . 4)))
(((cos (quotient (times 4 pi) 5)) . 4) . 1))
. 1))))),'complex)$
set!*representation('c5,
'((id (((1 . 1))))
(rc5
(((((((sin (quotient (times 4 pi) 5)) . 1)
((i . 1) . -1))
(((cos (quotient (times 4 pi) 5)) . 1) . 1))
. 1))))
(r2c5
(((((((sin (quotient (times 4 pi) 5)) . 2) . -1)
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 1)
((i . 1) . -2)))
(((cos (quotient (times 4 pi) 5)) . 2) . 1))
. 1))))
(r3c5
(((((((sin (quotient (times 4 pi) 5)) . 3) ((i . 1) . 1))
(((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 1) . -3))
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 2)
((i . 1) . -3)))
(((cos (quotient (times 4 pi) 5)) . 3) . 1))
. 1))))
(r4c5
(((((((sin (quotient (times 4 pi) 5)) . 4) . 1)
(((sin (quotient (times 4 pi) 5)) . 3)
(((cos (quotient (times 4 pi) 5)) . 1)
((i . 1) . 4)))
(((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 2) . -6))
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 3)
((i . 1) . -4)))
(((cos (quotient (times 4 pi) 5)) . 4) . 1))
. 1))))),'complex)$
set!*representation('c5,
'((id (((1 . 1))))
(rc5
(((((((sin (quotient (times 2 pi) 5)) . 1)
((i . 1) . -1))
(((cos (quotient (times 2 pi) 5)) . 1) . 1))
. 1))))
(r2c5
(((((((sin (quotient (times 2 pi) 5)) . 2) . -1)
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 1)
((i . 1) . -2)))
(((cos (quotient (times 2 pi) 5)) . 2) . 1))
. 1))))
(r3c5
(((((((sin (quotient (times 2 pi) 5)) . 3) ((i . 1) . 1))
(((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 1) . -3))
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 2)
((i . 1) . -3)))
(((cos (quotient (times 2 pi) 5)) . 3) . 1))
. 1))))
(r4c5
(((((((sin (quotient (times 2 pi) 5)) . 4) . 1)
(((sin (quotient (times 2 pi) 5)) . 3)
(((cos (quotient (times 2 pi) 5)) . 1)
((i . 1) . 4)))
(((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 2) . -6))
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 3)
((i . 1) . -4)))
(((cos (quotient (times 2 pi) 5)) . 4) . 1))
. 1))))),'complex)$
set!*representation('c5,
'(realtype
(id (((1 . 1))))
(rc5 (((1 . 1))))
(r2c5 (((1 . 1))))
(r3c5 (((1 . 1))))
(r4c5 (((1 . 1))))),'real)$
set!*representation('c5,
'(complextype
(id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(rc5
(((((((cos (quotient (times 2 pi) 5)) . 1) . 1)) . 1)
(((((sin (quotient (times 2 pi) 5)) . 1) . -1)) . 1))
((((((sin (quotient (times 2 pi) 5)) . 1) . 1)) . 1)
(((((cos (quotient (times 2 pi) 5)) . 1) . 1)) . 1))))
(r2c5
(((((((sin (quotient (times 2 pi) 5)) . 2) . -1)
(((cos (quotient (times 2 pi) 5)) . 2) . 1))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 1) . -2)))
. 1))
((((((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 1) . 2)))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 2) . -1)
(((cos (quotient (times 2 pi) 5)) . 2) . 1))
. 1))))
(r3c5
(((((((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 1) . -3))
(((cos (quotient (times 2 pi) 5)) . 3) . 1))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 3) . 1)
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 2) . -3)))
. 1))
((((((sin (quotient (times 2 pi) 5)) . 3) . -1)
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 2) . 3)))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 1) . -3))
(((cos (quotient (times 2 pi) 5)) . 3) . 1))
. 1))))
(r4c5
(((((((sin (quotient (times 2 pi) 5)) . 4) . 1)
(((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 2) . -6))
(((cos (quotient (times 2 pi) 5)) . 4) . 1))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 3)
(((cos (quotient (times 2 pi) 5)) . 1) . 4))
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 3) . -4)))
. 1))
((((((sin (quotient (times 2 pi) 5)) . 3)
(((cos (quotient (times 2 pi) 5)) . 1) . -4))
(((sin (quotient (times 2 pi) 5)) . 1)
(((cos (quotient (times 2 pi) 5)) . 3) . 4)))
. 1)
(((((sin (quotient (times 2 pi) 5)) . 4) . 1)
(((sin (quotient (times 2 pi) 5)) . 2)
(((cos (quotient (times 2 pi) 5)) . 2) . -6))
(((cos (quotient (times 2 pi) 5)) . 4) . 1))
. 1))))),'real)$
set!*representation('c5,
'(complextype
(id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(rc5
(((((((cos (quotient (times 4 pi) 5)) . 1) . 1)) . 1)
(((((sin (quotient (times 4 pi) 5)) . 1) . -1)) . 1))
((((((sin (quotient (times 4 pi) 5)) . 1) . 1)) . 1)
(((((cos (quotient (times 4 pi) 5)) . 1) . 1)) . 1))))
(r2c5
(((((((sin (quotient (times 4 pi) 5)) . 2) . -1)
(((cos (quotient (times 4 pi) 5)) . 2) . 1))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 1) . -2)))
. 1))
((((((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 1) . 2)))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 2) . -1)
(((cos (quotient (times 4 pi) 5)) . 2) . 1))
. 1))))
(r3c5
(((((((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 1) . -3))
(((cos (quotient (times 4 pi) 5)) . 3) . 1))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 3) . 1)
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 2) . -3)))
. 1))
((((((sin (quotient (times 4 pi) 5)) . 3) . -1)
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 2) . 3)))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 1) . -3))
(((cos (quotient (times 4 pi) 5)) . 3) . 1))
. 1))))
(r4c5
(((((((sin (quotient (times 4 pi) 5)) . 4) . 1)
(((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 2) . -6))
(((cos (quotient (times 4 pi) 5)) . 4) . 1))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 3)
(((cos (quotient (times 4 pi) 5)) . 1) . 4))
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 3) . -4)))
. 1))
((((((sin (quotient (times 4 pi) 5)) . 3)
(((cos (quotient (times 4 pi) 5)) . 1) . -4))
(((sin (quotient (times 4 pi) 5)) . 1)
(((cos (quotient (times 4 pi) 5)) . 3) . 4)))
. 1)
(((((sin (quotient (times 4 pi) 5)) . 4) . 1)
(((sin (quotient (times 4 pi) 5)) . 2)
(((cos (quotient (times 4 pi) 5)) . 2) . -6))
(((cos (quotient (times 4 pi) 5)) . 4) . 1))
. 1))))),'real)$
set!*available 'c5$
endmodule;
module symdata2; % Symmetry data, part 2.
% Author: Karin Gatermann <Gatermann@sc.ZIB-Berlin.de>.
set!*elems!*group('c6,'(id rc6 r2c6 r3c6 r4c6 r5c6))$
set!*generators('c6,'(rc6))$
set!*relations('c6,'(((rc6 rc6 rc6 rc6 rc6 rc6) (id))))$
set!*grouptable('c6,
'((grouptable id rc6 r2c6 r3c6 r4c6 r5c6)
(id id rc6 r2c6 r3c6 r4c6 r5c6)
(rc6 rc6 r2c6 r3c6 r4c6 r5c6 id)
(r2c6 r2c6 r3c6 r4c6 r5c6 id rc6)
(r3c6 r3c6 r4c6 r5c6 id rc6 r2c6)
(r4c6 r4c6 r5c6 id rc6 r2c6 r3c6)
(r5c6 r5c6 id rc6 r2c6 r3c6 r4c6)))$
set!*inverse('c6,
'((id rc6 r2c6 r3c6 r4c6 r5c6) (id r5c6 r4c6 r3c6 r2c6 rc6)))$
set!*elemasgen('c6,
'(((rc6) (rc6))
((r2c6) (rc6 rc6))
((r3c6) (rc6 rc6 rc6))
((r4c6) (rc6 rc6 rc6 rc6))
((r5c6) (rc6 rc6 rc6 rc6 rc6))))$
set!*group('c6,'((id) (rc6) (r2c6) (r3c6) (r4c6) (r5c6)))$
set!*representation('c6,
'((id (((1 . 1))))
(rc6 (((1 . 1))))
(r2c6 (((1 . 1))))
(r3c6 (((1 . 1))))
(r4c6 (((1 . 1))))
(r5c6 (((1 . 1))))),'complex)$
set!*representation('c6,
'((id (((1 . 1))))
(rc6 (((-1 . 1))))
(r2c6 (((1 . 1))))
(r3c6 (((-1 . 1))))
(r4c6 (((1 . 1))))
(r5c6 (((-1 . 1))))),'complex)$
set!*representation('c6,
'((id (((1 . 1))))
(rc6
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1)) . 1)
. 2))))
(r2c6
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1)) . -1)
. 2))))
(r3c6 (((-1 . 1))))
(r4c6
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . -1)) . -1)
. 2))))
(r5c6
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . -1)) . 1)
. 2))))),'complex)$
set!*representation('c6,
'((id (((1 . 1))))
(rc6
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1)) . -1)
. 2))))
(r2c6
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . -1)) . -1)
. 2))))
(r3c6 (((1 . 1))))
(r4c6
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1)) . -1)
. 2))))
(r5c6
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . -1)) . -1)
. 2))))),'complex)$
set!*representation('c6,
'((id (((1 . 1))))
(rc6
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . -1)) . -1)
. 2))))
(r2c6
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1)) . -1)
. 2))))
(r3c6 (((1 . 1))))
(r4c6
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . -1)) . -1)
. 2))))
(r5c6
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1)) . -1)
. 2))))),'complex)$
set!*representation('c6,
'((id (((1 . 1))))
(rc6
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . -1)) . 1)
. 2))))
(r2c6
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . -1)) . -1)
. 2))))
(r3c6 (((-1 . 1))))
(r4c6
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1)) . -1)
. 2))))
(r5c6
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1)) . 1)
. 2))))),'complex)$
set!*representation('c6,
'(realtype
(id (((1 . 1))))
(rc6 (((1 . 1))))
(r2c6 (((1 . 1))))
(r3c6 (((1 . 1))))
(r4c6 (((1 . 1))))
(r5c6 (((1 . 1))))),'real)$
set!*representation('c6,
'(realtype
(id (((1 . 1))))
(rc6 (((-1 . 1))))
(r2c6 (((1 . 1))))
(r3c6 (((-1 . 1))))
(r4c6 (((1 . 1))))
(r5c6 (((-1 . 1))))),'real)$
set!*representation('c6,
'(complextype
(id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(rc6
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (1 . 2))))
(r2c6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(r3c6 (((-1 . 1) (nil . 1)) ((nil . 1) (-1 . 1))))
(r4c6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(r5c6
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(1 . 2))))),'real)$
set!*representation('c6,
'(complextype
(id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(rc6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(r2c6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(r3c6 (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(r4c6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(r5c6
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))),'real)$
set!*available 'c6$
set!*elems!*group('s4,
'(id
bacd
acbd
abdc
dbca
cabd
bcad
dacb
bdca
dbac
cbda
adbc
acdb
badc
cdab
dcba
cbad
adcb
bcda
bdac
cadb
dabc
cdba
dcab))$
set!*generators('s4,'(bacd acbd abdc dbca))$
set!*relations('s4,
'(((bacd bacd) (id))
((acbd acbd) (id))
((abdc abdc) (id))
((dbca) (bacd acbd abdc acbd bacd))))$
set!*grouptable('s4,
'((grouptable
dcab
dcba
dbac
dbca
dabc
dacb
cdab
cdba
cbad
cbda
cabd
cadb
bdac
bdca
bcad
bcda
bacd
badc
adbc
adcb
acbd
acdb
id
abdc)
(dcab
badc
abdc
cadb
acdb
cbda
bcda
bacd
id
dacb
adcb
dbca
bdca
cabd
acbd
dabc
adbc
dcba
cdba
cbad
bcad
dbac
bdac
dcab
cdab)
(dcba
bacd
id
cabd
acbd
cbad
bcad
badc
abdc
dabc
adbc
dbac
bdac
cadb
acdb
dacb
adcb
dcab
cdab
cbda
bcda
dbca
bdca
dcba
cdba)
(dbac
bcda
acdb
cbda
abdc
cadb
badc
bdca
adcb
dbca
id
dacb
bacd
cdba
adbc
dcba
acbd
dabc
cabd
cdab
bdac
dcab
bcad
dbac
cbad)
(dbca
bcad
acbd
cbad
id
cabd
bacd
bdac
adbc
dbac
abdc
dabc
badc
cdab
adcb
dcab
acdb
dacb
cadb
cdba
bdca
dcba
bcda
dbca
cbda)
(dabc
bdca
adcb
cdba
adbc
cdab
bdac
bcda
acdb
dcba
acbd
dcab
bcad
cbda
abdc
dbca
id
dbac
cbad
cadb
badc
dacb
bacd
dabc
cabd)
(dacb
bdac
adbc
cdab
adcb
cdba
bdca
bcad
acbd
dcab
acdb
dcba
bcda
cbad
id
dbac
abdc
dbca
cbda
cabd
bacd
dabc
badc
dacb
cadb)
(cdab
abdc
badc
acdb
cadb
bcda
cbda
id
bacd
adcb
dacb
bdca
dbca
acbd
cabd
adbc
dabc
cdba
dcba
bcad
cbad
bdac
dbac
cdab
dcab)
(cdba
id
bacd
acbd
cabd
bcad
cbad
abdc
badc
adbc
dabc
bdac
dbac
acdb
cadb
adcb
dacb
cdab
dcab
bcda
cbda
bdca
dbca
cdba
dcba)
(cbad
acdb
bcda
abdc
cbda
badc
cadb
adcb
bdca
id
dbca
bacd
dacb
adbc
cdba
acbd
dcba
cabd
dabc
bdac
cdab
bcad
dcab
cbad
dbac)
(cbda
acbd
bcad
id
cbad
bacd
cabd
adbc
bdac
abdc
dbac
badc
dabc
adcb
cdab
acdb
dcab
cadb
dacb
bdca
cdba
bcda
dcba
cbda
dbca)
(cabd
adcb
bdca
adbc
cdba
bdac
cdab
acdb
bcda
acbd
dcba
bcad
dcab
abdc
cbda
id
dbca
cbad
dbac
badc
cadb
bacd
dacb
cabd
dabc)
(cadb
adbc
bdac
adcb
cdab
bdca
cdba
acbd
bcad
acdb
dcab
bcda
dcba
id
cbad
abdc
dbac
cbda
dbca
bacd
cabd
badc
dabc
cadb
dacb)
(bdac
cbda
cadb
bcda
badc
acdb
abdc
dbca
dacb
bdca
bacd
adcb
id
dcba
dabc
cdba
cabd
adbc
acbd
dcab
dbac
cdab
cbad
bdac
bcad)
(bdca
cbad
cabd
bcad
bacd
acbd
id
dbac
dabc
bdac
badc
adbc
abdc
dcab
dacb
cdab
cadb
adcb
acdb
dcba
dbca
cdba
cbda
bdca
bcda)
(bcad
cadb
cbda
badc
bcda
abdc
acdb
dacb
dbca
bacd
bdca
id
adcb
dabc
dcba
cabd
cdba
acbd
adbc
dbac
dcab
cbad
cdab
bcad
bdac)
(bcda
cabd
cbad
bacd
bcad
id
acbd
dabc
dbac
badc
bdac
abdc
adbc
dacb
dcab
cadb
cdab
acdb
adcb
dbca
dcba
cbda
cdba
bcda
bdca)
(bacd
cdab
cdba
bdac
bdca
adbc
adcb
dcab
dcba
bcad
bcda
acbd
acdb
dbac
dbca
cbad
cbda
id
abdc
dabc
dacb
cabd
cadb
bacd
badc)
(badc
cdba
cdab
bdca
bdac
adcb
adbc
dcba
dcab
bcda
bcad
acdb
acbd
dbca
dbac
cbda
cbad
abdc
id
dacb
dabc
cadb
cabd
badc
bacd)
(adbc
dbca
dacb
dcba
dabc
dcab
dbac
cbda
cadb
cdba
cabd
cdab
cbad
bcda
badc
bdca
bacd
bdac
bcad
acdb
abdc
adcb
id
adbc
acbd)
(adcb
dbac
dabc
dcab
dacb
dcba
dbca
cbad
cabd
cdab
cadb
cdba
cbda
bcad
bacd
bdac
badc
bdca
bcda
acbd
id
adbc
abdc
adcb
acdb)
(acbd
dacb
dbca
dabc
dcba
dbac
dcab
cadb
cbda
cabd
cdba
cbad
cdab
badc
bcda
bacd
bdca
bcad
bdac
abdc
acdb
id
adcb
acbd
adbc)
(acdb
dabc
dbac
dacb
dcab
dbca
dcba
cabd
cbad
cadb
cdab
cbda
cdba
bacd
bcad
badc
bdac
bcda
bdca
id
acbd
abdc
adbc
acdb
adcb)
(id
dcab
dcba
dbac
dbca
dabc
dacb
cdab
cdba
cbad
cbda
cabd
cadb
bdac
bdca
bcad
bcda
bacd
badc
adbc
adcb
acbd
acdb
id
abdc)
(abdc
dcba
dcab
dbca
dbac
dacb
dabc
cdba
cdab
cbda
cbad
cadb
cabd
bdca
bdac
bcda
bcad
badc
bacd
adcb
adbc
acdb
acbd
abdc
id)))$
set!*inverse('s4,
'((dcab
dcba
dbac
dbca
dabc
dacb
cdab
cdba
cbad
cbda
cabd
cadb
bdac
bdca
bcad
bcda
bacd
badc
adbc
adcb
acbd
acdb
id
abdc)
(cdba
dcba
cbda
dbca
bcda
bdca
cdab
dcab
cbad
dbac
bcad
bdac
cadb
dacb
cabd
dabc
bacd
badc
acdb
adcb
acbd
adbc
id
abdc)))$
set!*elemasgen('s4,
'(((bacd) (bacd))
((acbd) (acbd))
((abdc) (abdc))
((dbca) (dbca))
((cabd) (bacd acbd))
((bcad) (acbd bacd))
((dacb) (dbca bacd))
((bdca) (bacd dbca))
((dbac) (abdc dbca))
((cbda) (dbca abdc))
((adbc) (acbd abdc))
((acdb) (abdc acbd))
((badc) (bacd abdc))
((cdab) (abdc bacd acbd dbca))
((dcba) (acbd dbca))
((cbad) (bacd acbd bacd))
((adcb) (dbca bacd dbca))
((bcda) (abdc acbd bacd))
((bdac) (acbd bacd abdc))
((cadb) (abdc bacd acbd))
((dabc) (bacd acbd abdc))
((cdba) (bacd acbd dbca))
((dcab) (abdc acbd dbca))))$
set!*group('s4,
'((dcab dabc cadb bdac bcda cdba)
(dcba badc cdab)
(dbac dacb cabd adbc acdb bcad bdca cbda)
(dbca adcb abdc acbd bacd cbad)
(id)))$
set!*representation('s4,
'((id (((1 . 1))))
(bacd (((1 . 1))))
(acbd (((1 . 1))))
(abdc (((1 . 1))))
(dbca (((1 . 1))))
(cabd (((1 . 1))))
(bcad (((1 . 1))))
(dacb (((1 . 1))))
(bdca (((1 . 1))))
(dbac (((1 . 1))))
(cbda (((1 . 1))))
(adbc (((1 . 1))))
(acdb (((1 . 1))))
(badc (((1 . 1))))
(cdab (((1 . 1))))
(dcba (((1 . 1))))
(cbad (((1 . 1))))
(adcb (((1 . 1))))
(bcda (((1 . 1))))
(bdac (((1 . 1))))
(cadb (((1 . 1))))
(dabc (((1 . 1))))
(cdba (((1 . 1))))
(dcab (((1 . 1))))),'complex)$
set!*representation('s4,
'((id (((1 . 1))))
(bacd (((-1 . 1))))
(acbd (((-1 . 1))))
(abdc (((-1 . 1))))
(dbca (((-1 . 1))))
(cabd (((1 . 1))))
(bcad (((1 . 1))))
(dacb (((1 . 1))))
(bdca (((1 . 1))))
(dbac (((1 . 1))))
(cbda (((1 . 1))))
(adbc (((1 . 1))))
(acdb (((1 . 1))))
(badc (((1 . 1))))
(cdab (((1 . 1))))
(dcba (((1 . 1))))
(cbad (((-1 . 1))))
(adcb (((-1 . 1))))
(bcda (((-1 . 1))))
(bdac (((-1 . 1))))
(cadb (((-1 . 1))))
(dabc (((-1 . 1))))
(cdba (((-1 . 1))))
(dcab (((-1 . 1))))),'complex)$
set!*representation('s4,
'((id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(bacd
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(acbd
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(abdc
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(dbca
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(cabd
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(bcad
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(dacb
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(bdca
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(dbac
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(cbda
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(adbc
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(acdb
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(badc (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(cdab (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(dcba (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(cbad (((-1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(adcb (((-1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(bcda (((-1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(bdac
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(cadb
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(dabc (((-1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(cdba
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(dcab
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2)
(-1 . 2))))),'complex)$
set!*representation('s4,
'((id
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(bacd
(((nil . 1) (nil . 1) (-1 . 1))
((nil . 1) (1 . 1) (nil . 1))
((-1 . 1) (nil . 1) (nil . 1))))
(acbd
(((nil . 1) (-1 . 1) (nil . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(abdc
(((nil . 1) (nil . 1) (1 . 1))
((nil . 1) (1 . 1) (nil . 1))
((1 . 1) (nil . 1) (nil . 1))))
(dbca
(((nil . 1) (1 . 1) (nil . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(cabd
(((nil . 1) (nil . 1) (-1 . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))))
(bcad
(((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((-1 . 1) (nil . 1) (nil . 1))))
(dacb
(((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((-1 . 1) (nil . 1) (nil . 1))))
(bdca
(((nil . 1) (nil . 1) (-1 . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(dbac
(((nil . 1) (nil . 1) (1 . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))))
(cbda
(((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((1 . 1) (nil . 1) (nil . 1))))
(adbc
(((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((1 . 1) (nil . 1) (nil . 1))))
(acdb
(((nil . 1) (nil . 1) (1 . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(badc
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(cdab
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(dcba
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(cbad
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((nil . 1) (1 . 1) (nil . 1))))
(adcb
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(bcda
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(bdac
(((nil . 1) (-1 . 1) (nil . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(cadb
(((nil . 1) (1 . 1) (nil . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(dabc
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((nil . 1) (1 . 1) (nil . 1))))
(cdba
(((nil . 1) (nil . 1) (-1 . 1))
((nil . 1) (-1 . 1) (nil . 1))
((1 . 1) (nil . 1) (nil . 1))))
(dcab
(((nil . 1) (nil . 1) (1 . 1))
((nil . 1) (-1 . 1) (nil . 1))
((-1 . 1) (nil . 1) (nil . 1))))),'complex)$
set!*representation('s4,
'((id
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(bacd
(((nil . 1) (nil . 1) (1 . 1))
((nil . 1) (-1 . 1) (nil . 1))
((1 . 1) (nil . 1) (nil . 1))))
(acbd
(((nil . 1) (1 . 1) (nil . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(abdc
(((nil . 1) (nil . 1) (-1 . 1))
((nil . 1) (-1 . 1) (nil . 1))
((-1 . 1) (nil . 1) (nil . 1))))
(dbca
(((nil . 1) (-1 . 1) (nil . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(cabd
(((nil . 1) (nil . 1) (-1 . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))))
(bcad
(((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((-1 . 1) (nil . 1) (nil . 1))))
(dacb
(((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((-1 . 1) (nil . 1) (nil . 1))))
(bdca
(((nil . 1) (nil . 1) (-1 . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(dbac
(((nil . 1) (nil . 1) (1 . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))))
(cbda
(((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((1 . 1) (nil . 1) (nil . 1))))
(adbc
(((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((1 . 1) (nil . 1) (nil . 1))))
(acdb
(((nil . 1) (nil . 1) (1 . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(badc
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(cdab
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(dcba
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(cbad
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(adcb
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((nil . 1) (1 . 1) (nil . 1))))
(bcda
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((nil . 1) (1 . 1) (nil . 1))))
(bdac
(((nil . 1) (1 . 1) (nil . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(cadb
(((nil . 1) (-1 . 1) (nil . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(dabc
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(cdba
(((nil . 1) (nil . 1) (1 . 1))
((nil . 1) (1 . 1) (nil . 1))
((-1 . 1) (nil . 1) (nil . 1))))
(dcab
(((nil . 1) (nil . 1) (-1 . 1))
((nil . 1) (1 . 1) (nil . 1))
((1 . 1) (nil . 1) (nil . 1))))),'complex)$
set!*representation('s4,
'(realtype
(id (((1 . 1))))
(bacd (((1 . 1))))
(acbd (((1 . 1))))
(abdc (((1 . 1))))
(dbca (((1 . 1))))
(cabd (((1 . 1))))
(bcad (((1 . 1))))
(dacb (((1 . 1))))
(bdca (((1 . 1))))
(dbac (((1 . 1))))
(cbda (((1 . 1))))
(adbc (((1 . 1))))
(acdb (((1 . 1))))
(badc (((1 . 1))))
(cdab (((1 . 1))))
(dcba (((1 . 1))))
(cbad (((1 . 1))))
(adcb (((1 . 1))))
(bcda (((1 . 1))))
(bdac (((1 . 1))))
(cadb (((1 . 1))))
(dabc (((1 . 1))))
(cdba (((1 . 1))))
(dcab (((1 . 1))))),'real)$
set!*representation('s4,
'(realtype
(id (((1 . 1))))
(bacd (((-1 . 1))))
(acbd (((-1 . 1))))
(abdc (((-1 . 1))))
(dbca (((-1 . 1))))
(cabd (((1 . 1))))
(bcad (((1 . 1))))
(dacb (((1 . 1))))
(bdca (((1 . 1))))
(dbac (((1 . 1))))
(cbda (((1 . 1))))
(adbc (((1 . 1))))
(acdb (((1 . 1))))
(badc (((1 . 1))))
(cdab (((1 . 1))))
(dcba (((1 . 1))))
(cbad (((-1 . 1))))
(adcb (((-1 . 1))))
(bcda (((-1 . 1))))
(bdac (((-1 . 1))))
(cadb (((-1 . 1))))
(dabc (((-1 . 1))))
(cdba (((-1 . 1))))
(dcab (((-1 . 1))))),'real)$
set!*representation('s4,
'(realtype
(id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(bacd
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(acbd
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(abdc
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(dbca
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(cabd
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(bcad
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(dacb
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(bdca
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(dbac
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(cbda
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(adbc
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(acdb
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(badc (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(cdab (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(dcba (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(cbad (((-1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(adcb (((-1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(bcda (((-1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(bdac
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(cadb
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . -1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(dabc (((-1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(cdba
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2) (-1 . 2))))
(dcab
(((1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1)) . 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2)
(-1 . 2))))),'real)$
set!*representation('s4,
'(realtype
(id
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(bacd
(((nil . 1) (nil . 1) (-1 . 1))
((nil . 1) (1 . 1) (nil . 1))
((-1 . 1) (nil . 1) (nil . 1))))
(acbd
(((nil . 1) (-1 . 1) (nil . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(abdc
(((nil . 1) (nil . 1) (1 . 1))
((nil . 1) (1 . 1) (nil . 1))
((1 . 1) (nil . 1) (nil . 1))))
(dbca
(((nil . 1) (1 . 1) (nil . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(cabd
(((nil . 1) (nil . 1) (-1 . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))))
(bcad
(((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((-1 . 1) (nil . 1) (nil . 1))))
(dacb
(((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((-1 . 1) (nil . 1) (nil . 1))))
(bdca
(((nil . 1) (nil . 1) (-1 . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(dbac
(((nil . 1) (nil . 1) (1 . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))))
(cbda
(((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((1 . 1) (nil . 1) (nil . 1))))
(adbc
(((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((1 . 1) (nil . 1) (nil . 1))))
(acdb
(((nil . 1) (nil . 1) (1 . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(badc
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(cdab
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(dcba
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(cbad
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((nil . 1) (1 . 1) (nil . 1))))
(adcb
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(bcda
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(bdac
(((nil . 1) (-1 . 1) (nil . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(cadb
(((nil . 1) (1 . 1) (nil . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(dabc
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((nil . 1) (1 . 1) (nil . 1))))
(cdba
(((nil . 1) (nil . 1) (-1 . 1))
((nil . 1) (-1 . 1) (nil . 1))
((1 . 1) (nil . 1) (nil . 1))))
(dcab
(((nil . 1) (nil . 1) (1 . 1))
((nil . 1) (-1 . 1) (nil . 1))
((-1 . 1) (nil . 1) (nil . 1))))),'real)$
set!*representation('s4,
'(realtype
(id
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(bacd
(((nil . 1) (nil . 1) (1 . 1))
((nil . 1) (-1 . 1) (nil . 1))
((1 . 1) (nil . 1) (nil . 1))))
(acbd
(((nil . 1) (1 . 1) (nil . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(abdc
(((nil . 1) (nil . 1) (-1 . 1))
((nil . 1) (-1 . 1) (nil . 1))
((-1 . 1) (nil . 1) (nil . 1))))
(dbca
(((nil . 1) (-1 . 1) (nil . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(cabd
(((nil . 1) (nil . 1) (-1 . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))))
(bcad
(((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((-1 . 1) (nil . 1) (nil . 1))))
(dacb
(((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((-1 . 1) (nil . 1) (nil . 1))))
(bdca
(((nil . 1) (nil . 1) (-1 . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(dbac
(((nil . 1) (nil . 1) (1 . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))))
(cbda
(((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((1 . 1) (nil . 1) (nil . 1))))
(adbc
(((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((1 . 1) (nil . 1) (nil . 1))))
(acdb
(((nil . 1) (nil . 1) (1 . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(badc
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(cdab
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(dcba
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(cbad
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(adcb
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((nil . 1) (1 . 1) (nil . 1))))
(bcda
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((nil . 1) (1 . 1) (nil . 1))))
(bdac
(((nil . 1) (1 . 1) (nil . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(cadb
(((nil . 1) (-1 . 1) (nil . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(dabc
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(cdba
(((nil . 1) (nil . 1) (1 . 1))
((nil . 1) (1 . 1) (nil . 1))
((-1 . 1) (nil . 1) (nil . 1))))
(dcab
(((nil . 1) (nil . 1) (-1 . 1))
((nil . 1) (1 . 1) (nil . 1))
((1 . 1) (nil . 1) (nil . 1))))),'real)$
set!*available 's4$
set!*elems!*group('a4,
'(id ta4 t2a4 xa4 ya4 za4 txa4 tya4 tza4 t2xa4 t2ya4
t2za4))$
set!*generators('a4,'(ta4 xa4 ya4 za4))$
set!*relations('a4,
'(((za4) (ta4 xa4 ta4 ta4))
((ya4) (ta4 za4 ta4 ta4))
((xa4) (ta4 ya4 ta4 ta4))
((ta4 ta4 ta4) (id))
((xa4 xa4) (id))
((ya4 ya4) (id))
((za4 za4) (id))
((xa4 ya4) (za4))))$
set!*grouptable('a4,
'((grouptable
id
ta4
t2a4
xa4
ya4
za4
txa4
tya4
tza4
t2xa4
t2ya4
t2za4)
(id id ta4 t2a4 xa4 ya4 za4 txa4 tya4 tza4 t2xa4
t2ya4 t2za4)
(ta4 ta4 t2a4 id txa4 tya4 tza4 t2xa4 t2ya4 t2za4 xa4
ya4 za4)
(t2a4
t2a4
id
ta4
t2xa4
t2ya4
t2za4
xa4
ya4
za4
txa4
tya4
tza4)
(xa4 xa4 tya4 t2za4 id za4 ya4 tza4 ta4 txa4 t2ya4
t2xa4 t2a4)
(ya4 ya4 tza4 t2xa4 za4 id xa4 tya4 txa4 ta4 t2a4
t2za4 t2ya4)
(za4 za4 txa4 t2ya4 ya4 xa4 id ta4 tza4 tya4 t2za4
t2a4 t2xa4)
(txa4
txa4
t2ya4
za4
ta4
tza4
tya4
t2za4
t2a4
t2xa4
ya4
xa4
id)
(tya4
tya4
t2za4
xa4
tza4
ta4
txa4
t2ya4
t2xa4
t2a4
id
za4
ya4)
(tza4
tza4
t2xa4
ya4
tya4
txa4
ta4
t2a4
t2za4
t2ya4
za4
id
xa4)
(t2xa4
t2xa4
ya4
tza4
t2a4
t2za4
t2ya4
za4
id
xa4
tya4
txa4
ta4)
(t2ya4
t2ya4
za4
txa4
t2za4
t2a4
t2xa4
ya4
xa4
id
ta4
tza4
tya4)
(t2za4
t2za4
xa4
tya4
t2ya4
t2xa4
t2a4
id
za4
ya4
tza4
ta4
txa4)))$
set!*inverse('a4,
'((id ta4 t2a4 xa4 ya4 za4 txa4 tya4 tza4 t2xa4 t2ya4 t2za4)
(id t2a4 ta4 xa4 ya4 za4 t2za4 t2xa4 t2ya4 tya4 tza4 txa4)
))$
set!*elemasgen('a4,
'(((ta4) (ta4))
((t2a4) (ta4 ta4))
((xa4) (xa4))
((ya4) (ya4))
((za4) (za4))
((txa4) (ta4 xa4))
((tya4) (ta4 ya4))
((tza4) (ta4 za4))
((t2xa4) (ta4 ta4 xa4))
((t2ya4) (ta4 ta4 ya4))
((t2za4) (ta4 ta4 za4))))$
set!*group('a4,
'((id) (txa4 ta4 tza4 tya4) (t2za4 t2a4 t2ya4 t2xa4)
(ya4 xa4 za4)))$
set!*representation('a4,
'((id (((1 . 1))))
(ta4 (((1 . 1))))
(t2a4 (((1 . 1))))
(xa4 (((1 . 1))))
(ya4 (((1 . 1))))
(za4 (((1 . 1))))
(txa4 (((1 . 1))))
(tya4 (((1 . 1))))
(tza4 (((1 . 1))))
(t2xa4 (((1 . 1))))
(t2ya4 (((1 . 1))))
(t2za4 (((1 . 1))))),'complex)$
set!*representation('a4,
'((id (((1 . 1))))
(ta4
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1))
. -1)
. 2))))
(t2a4
(((((((expt 3 (quotient 1 2)) . 1)((i . 1) . -1))
. -1)
. 2))))
(xa4 (((1 . 1))))
(ya4 (((1 . 1))))
(za4 (((1 . 1))))
(txa4
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1))
. -1)
. 2))))
(tya4
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1))
. -1)
. 2))))
(tza4
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1))
. -1)
. 2))))
(t2xa4
(((((((expt 3 (quotient 1 2)) . 1)((i . 1) . -1))
. -1)
. 2))))
(t2ya4
(((((((expt 3 (quotient 1 2)) . 1)((i . 1) . -1))
. -1)
. 2))))
(t2za4
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . -1))
. -1)
. 2))))),'complex)$
set!*representation('a4,
'((id (((1 . 1))))
(ta4
(((((((expt 3 (quotient 1 2)) . 1)((i . 1) . -1))
. -1)
. 2))))
(t2a4
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1))
. -1)
. 2))))
(xa4 (((1 . 1))))
(ya4 (((1 . 1))))
(za4 (((1 . 1))))
(txa4
(((((((expt 3 (quotient 1 2)) . 1)((i . 1) . -1))
. -1)
. 2))))
(tya4
(((((((expt 3 (quotient 1 2)) . 1)((i . 1) . -1))
. -1)
. 2))))
(tza4
(((((((expt 3 (quotient 1 2)) . 1)((i . 1) . -1))
. -1)
. 2))))
(t2xa4
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1))
. -1)
. 2))))
(t2ya4
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1))
. -1)
. 2))))
(t2za4
(((((((expt 3 (quotient 1 2)) . 1) ((i . 1) . 1))
. -1)
. 2))))),'complex)$
set!*representation('a4,
'((id
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(ta4
(((nil . 1) (nil . 1) (-1 . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))))
(t2a4
(((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((-1 . 1) (nil . 1) (nil . 1))))
(xa4
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(ya4
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(za4
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(txa4
(((nil . 1) (nil . 1) (1 . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))))
(tya4
(((nil . 1) (nil . 1) (1 . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(tza4
(((nil . 1) (nil . 1) (-1 . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(t2xa4
(((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((1 . 1) (nil . 1) (nil . 1))))
(t2ya4
(((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((-1 . 1) (nil . 1) (nil . 1))))
(t2za4
(((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((1 . 1) (nil . 1) (nil . 1))))),'complex)$
set!*representation('a4,
'(realtype
(id (((1 . 1))))
(ta4 (((1 . 1))))
(t2a4 (((1 . 1))))
(xa4 (((1 . 1))))
(ya4 (((1 . 1))))
(za4 (((1 . 1))))
(txa4 (((1 . 1))))
(tya4 (((1 . 1))))
(tza4 (((1 . 1))))
(t2xa4 (((1 . 1))))
(t2ya4 (((1 . 1))))
(t2za4 (((1 . 1))))),'real)$
set!*representation('a4,
'(complextype
(id (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(ta4
(((-1 . 2)(((((expt 3 (quotient 1 2)) . 1) . 1))
. 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(t2a4
(((-1 . 2)(((((expt 3 (quotient 1 2)) . 1) . -1))
. 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2)
(-1 . 2))))
(xa4 (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(ya4 (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(za4 (((1 . 1) (nil . 1)) ((nil . 1) (1 . 1))))
(txa4
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1))
. 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(tya4
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1))
. 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(tza4
(((-1 . 2) (((((expt 3 (quotient 1 2)) . 1) . 1))
. 2))
((((((expt 3 (quotient 1 2)) . 1) . -1)) . 2)
(-1 . 2))))
(t2xa4
(((-1 . 2)(((((expt 3 (quotient 1 2)) . 1) . -1))
. 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2)
(-1 . 2))))
(t2ya4
(((-1 . 2)(((((expt 3 (quotient 1 2)) . 1) . -1))
. 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2)
(-1 . 2))))
(t2za4
(((-1 . 2)(((((expt 3 (quotient 1 2)) . 1) . -1))
. 2))
((((((expt 3 (quotient 1 2)) . 1) . 1)) . 2)
(-1 . 2))))),'real)$
set!*representation('a4,
'(realtype
(id
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(ta4
(((nil . 1) (nil . 1) (-1 . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))))
(t2a4
(((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((-1 . 1) (nil . 1) (nil . 1))))
(xa4
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(ya4
(((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))))
(za4
(((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))))
(txa4
(((nil . 1) (nil . 1) (1 . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (1 . 1) (nil . 1))))
(tya4
(((nil . 1) (nil . 1) (1 . 1))
((-1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(tza4
(((nil . 1) (nil . 1) (-1 . 1))
((1 . 1) (nil . 1) (nil . 1))
((nil . 1) (-1 . 1) (nil . 1))))
(t2xa4
(((nil . 1) (-1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((1 . 1) (nil . 1) (nil . 1))))
(t2ya4
(((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (-1 . 1))
((-1 . 1) (nil . 1) (nil . 1))))
(t2za4
(((nil . 1) (1 . 1) (nil . 1))
((nil . 1) (nil . 1) (1 . 1))
((1 . 1) (nil . 1) (nil . 1))))),'real)$
set!*available 'a4$
endmodule;
end;