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syms pi000 pi001 pi002 pi003 pi010 pi011 pi012 pi013 pi020 pi021 pi022 pi023 pi100 pi101 pi102 pi103 pi110 pi111 pi112 pi113 pi120 pi121 pi122 pi123 a1 a2 a3 b11 b21 b22 b31 b32 b33
eq1=(a1+a2+a3)*pi000-b11*pi100-b21*pi010-b31*pi001-b22*pi020-b32*pi002-b33*pi003;
eq2=(a1+a2+b31)*pi001-b11*pi101-b21*pi011-b22*pi021;
eq3=(a1+a2+b32)*pi002-b11*pi102-b21*pi012-b22*pi022;
eq4=(a1+a2+b33)*pi003-b11*pi103-b21*pi013-b22*pi023-a3*pi000;
eq5=(a1+a2+a3+b21)*pi010-b11*pi110-b31*pi011-b32*pi012-b33*pi013;
eq6=(a1+b21+b31)*pi011-b11*pi111;
eq7=(a1+b21+b32)*pi012-b11*pi112-a2*pi010;
eq8=(a1+b21+b33)*pi013-b11*pi113-a3*pi010;
eq9=(a1+a2+a3+b22)*pi020-b11*pi120-b31*pi021-b32*pi022-b33*pi023-a2*pi000;
eq10=(a1+b31+b22)*pi021-b11*pi121-a2*pi001;
eq11=(a1+b22+b32)*pi022-b11*pi122-a2*(pi002+pi020);
eq12=(a1+b22+b33)*pi023-b11*pi123-a2*pi003-a3*pi020;
eq13=(a1+a2+a3+b11)*pi100-b21*pi110-b31*pi101-b32*pi102-b22*pi120-b33*pi103-a1*pi000;
eq14=(a1+a2+b11+b31)*pi101-b21*pi111-b22*pi121-a1*pi001;
eq15=(a1+a2+b11+b32)*pi102-b11*pi112-b22*pi122-a1*pi002;
eq16=(a1+a2+b11+b33)*pi103-b21*pi113-b22*pi123-a1*pi003-a3*pi100;
eq17=(a1+a2+a3+b11+b21)*pi110-b31*pi111-b32*pi112-b33*pi113-a1*(pi100+pi010);
eq18=(b11+b21+b31)*pi111-a1*(pi101+pi110+pi011);
eq19=(b11+b21+b32)*pi112-a1*(pi012+pi102)-a2*pi110;
eq20=(b11+b21+b33)*pi113-a1*(pi103+pi013)-a3*pi110;
eq21=(a1+a2+a3+b11+b22)*pi120-b31*pi121-b32*pi122-b33*pi123-a1*pi020-a2*pi100;
eq22=(b11+b31+b22)*pi121-a1*(pi021+pi120)+a2*pi101;
eq23=(b11+b22+b32)*pi122-a1*pi022-a2*(pi102+pi120);
eq24=pi000+pi001+pi002+pi003+pi010+pi011+pi012+pi013+pi020+pi021+pi022+pi023+pi100+pi101+pi102+pi103+pi110+pi111+pi112+pi113+pi120+pi121+pi122+pi123-1;
[pi000,pi001,pi002,pi003,pi010,pi011,pi012,pi013,pi020,pi021,pi022,pi023,pi100,pi101,pi102,pi103,pi110,pi111,pi112,pi113,pi120,pi121,pi122,pi123]=solve(eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9,eq10,eq11,eq12,eq13,eq14,eq15,eq16,eq17,eq18,eq19,eq20,eq21,eq22,eq23,eq24,'pi000','pi001','pi002','pi003','pi010','pi011','pi012','pi013','pi020','pi021','pi022','pi023','pi100','pi101','pi102','pi103','pi110','pi111','pi112','pi113','pi120','pi121','pi122','pi123')
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