%off nat;
%on rounded;


matrix RM(2,2);


for tt:=1:2 do Rm(tt,tt):=r(tt);


*** R declared operator 



matrix NM(2,2);


for tt:=1:2 do for pp:=1:2 do nm(tt,pp):=n(tt,pp);


*** N declared operator 



matrix RnM(2,2);


for tt:=1:2 do for pp:=1:2 do Rnm(tt,pp):=rn(tt,pp);


*** RN declared operator 



matrix sM(2,2);


for tt:=1:2 do sm(tt,tt):=s(tt);


*** S declared operator 



rm;


[R(1)   0  ]
[          ]
[ 0    R(2)]


nm;


[N(1,1)  N(1,2)]
[              ]
[N(2,1)  N(2,2)]


rnm;


[RN(1,1)  RN(1,2)]
[                ]
[RN(2,1)  RN(2,2)]


sm;


[S(1)   0  ]
[          ]
[ 0    S(2)]


%-----------------
sm*rm*sm**-1;


[R(1)   0  ]
[          ]
[ 0    R(2)]


sm*rnm*sm**-1;


[                 S(1)*RN(1,2) ]
[   RN(1,1)      --------------]
[                     S(2)     ]
[                              ]
[ S(2)*RN(2,1)                 ]
[--------------     RN(2,2)    ]
[     S(1)                     ]



sm*rnm*sm**-1 - rnm;


[                          RN(1,2)*( - S(2) + S(1)) ]
[           0             --------------------------]
[                                    S(2)           ]
[                                                   ]
[ RN(2,1)*(S(2) - S(1))                             ]
[-----------------------              0             ]
[         S(1)                                      ]


sm*rnm;


[S(1)*RN(1,1)  S(1)*RN(1,2)]
[                          ]
[S(2)*RN(2,1)  S(2)*RN(2,2)]


%-----------------

eqq:=rnm - rm - nm;


       [ - N(1,1) - R(1) + RN(1,1)      - N(1,2) + RN(1,2)    ]
EQQ := [                                                      ]
       [    - N(2,1) + RN(2,1)       - N(2,2) - R(2) + RN(2,2)]


eqqs:=sm*(eqq)*sm**-1;


        [                               S(1)*( - N(1,2) + RN(1,2)) ]
        [  - N(1,1) - R(1) + RN(1,1)   ----------------------------]
        [                                          S(2)            ]
EQQS := [                                                          ]
        [ S(2)*( - N(2,1) + RN(2,1))                               ]
        [----------------------------    - N(2,2) - R(2) + RN(2,2) ]
        [            S(1)                                          ]



eqqs - eqq;


        N(1,2)*S(2) - N(1,2)*S(1) - S(2)*RN(1,2) + S(1)*RN(1,2)
MAT((0,---------------------------------------------------------),
                                 S(2)

       - N(2,1)*S(2) + N(2,1)*S(1) + S(2)*RN(2,1) - S(1)*RN(2,1)
    (------------------------------------------------------------,0))
                                 S(1)


shut aa98;