LOAD("c1998.mth") bt:=[b1,b2,b3,b4,b5,b6,b7,b8,b9] dt:=[[0,d12,d13,d14,d15,d16,d17,d18,d19],[-d12,0,d23,d24,d25,d26,d27,d28,d29]~ ,[-d13,-d23,0,d34,d35,d36,d37,d38,d39],[-d14,-d24,-d34,0,d45,d46,d47,d48,d49]~ ,[-d15,-d25,-d35,-d45,0,d56,d57,d58,d59],[-d16,-d26,-d36,-d46,-d56,0,d67,d68,~ d69],[-d17,-d27,-d37,-d47,-d57,-d67,0,d78,d79],[-d18,-d28,-d38,-d48,-d58,-d68~ ,-d78,0,d89],[-d19,-d29,-d39,-d49,-d59,-d69,-d79,-d89,0]] e1:= et:=[e1,e2,e3,e4,e5,e6,e7,e8,e9] DFA(i,j):=dt SUB i SUB j DAA(i,m,n):=PRODUCT(IF(i/=j_,DFA(j_,i)^m SUB j_,1),j_,1,n) mu_AA(s,i,m,n):=-1/ABS(s)*SUM(IF(i/=j_,m SUB j_*(DFA(i,j_)/bt SUB j_)^s,0),j_~ ,1,n) "CS10(n) function is from Johann Wiesenbauer :" CS10(n,k_,n_:=2,s_:=[[[1]]],t_,u_):=PROG(LOOP(IF(n=1,exit),k_:=n_,t_:=[[n_]],~ LOOP(k_:-1,IF(k_=0,exit),u_:=s_ SUB (k_-n_),LOOP(IF(FIRST(FIRST(u_))<=k_,exit~ ),u_:=REST(u_)),t_:=APPEND(t_,VECTOR(APPEND([k_],v_),v_,u_))),s_:=ADJOIN(t_,s~ _),n_:+1,n:-1),u_:=FIRST(s_),s_:=0,LOOP(IF(u_=[],RETURN(s_)),t_:=PRODUCT(x SU~ B l_,l_,FIRST(u_)),t_:=t_/PRODUCT(l_!,l_,(FACTORS(t_)) COL 2),s_:+t_,u_:=REST~ (u_))) CS11(s,i,m,n):=SUBST(CS10(ABS(s)),x,VECTOR(mu_AA(r_*SIGN(s),i,m,n),r_,1,ABS(s~ ))) CAA(s,i,m,n):=IF(s=0,1,CS11(s,i,m,n)) EPA(p,j,s,h):=IF(p=0,1,SUM(DFA(i_,j)/bt SUB i_*EPA(p-1,j,i_+1,h),i_,s,h)) sigma0A(h):=PRODUCT(bt SUB i_,i_,1,h) åPA(p,j,h):=sigma0A(h)*EPA(p,j,1,h) R35A(q,j,h):=-bt SUB j^(h-1)*AA((q+1)*et SUB j+SUM(et SUB i_,i_,1,h))+SUM((q+~ r_/2+1)*åPA(h-r_,j,h)*IA((q+r_)*et SUB j),r_,0,h) R35B(p,j,h):=IF(p>0,R35A(p-h,j,h),IF(j>h,R35A(p,j,h),R35A(p-1,j,h))) R35F(i,p,j,h):= R35C(i,q,j,h):=(bt SUB j^(h-1)*AA((q+1)*et SUB j+SUM(et SUB i_,i_,1,h))-SUM((~ q+r_/2+1)*åPA(h-r_,j,h)*R35F(i,q+r_,j,h),r_,0,h-1))/((q+h/2+1)*åPA(0,j,h)) R35D(i,q,j,h):=(bt SUB j^(h-1)*AA((q+1)*et SUB j+SUM(et SUB i_,i_,1,h))-SUM((~ q+r_/2+1)*åPA(h-r_,j,h)*R35F(i,q+r_,j,h),r_,1,h))/((q+1)*åPA(h,j,h)) R35E(i,q,j,h):=(bt SUB j^(h-1)*AA((q+1)*et SUB j+SUM(et SUB i_,i_,1,h))-SUM((~ q+r_/2+1)*åPA(h-r_,j,h)*R35F(i,q+r_,j,h),r_,2,h))/((q+1/2+1)*åPA(h-1,j,h)) R311A(i,q,j,h):=SUM(COMB(q,r_)*bt SUB j^r_*DFA(j,i)^(q-r_)*R35F(i,r_,i,h),r_,~ 0,q)/bt SUB i^q R35F(i,p,j,h):=IF(p>0,IF(i/=j,R311A(i,p,j,h),IF(p=1 AND h=4,IA(et SUB j),R35C~ (i,p-h,j,h))),IF(p>-2,IA(p*et SUB j),IF(j>h,R35D(i,p,j,h),R35E(i,p-1,j,h)))) D219A_AUX(i,m,ma_,n,h):=IF(ma_>-1,BA(m,n,bt)*bt SUB i^(-ma_)*SUM(CAA(ma_-q_,i~ ,m,n)*R35F(i,q_,i,h),q_,0,ma_),0)+SUM(IF(-m SUB i_>0,DAA(i_,m,n)*bt SUB i_^(m~ SUB i_-ma_)*SUM(CAA(m SUB i_+q_,i_,m,n)*R35F(i,-q_,i_,h),q_,1,-m SUB i_),0),~ i_,1,n) D219A(i,m,n,h):=D219A_AUX(i,m,MA(m,n),n,h) D219B(v,b):=SUBST(v,[b1,b2,b3,b4,b5,b6,b7,b8,b9],[b SUB 1,b SUB 2,b SUB 3,b S~ UB 4,b SUB 5,b SUB 6,b SUB 7,b SUB 8,b SUB 9]) D219D(v,a,b):=SUBST(v,[d12,d13,d14,d15,d16,d17,d18,d19,d23,d24,d25,d26,d27,d2~ 8,d29,d34,d35,d36,d37,d38,d39,d45,d46,d47,d48,d49,d56,d57,d58,d59,d67,d68,d69~ ,d78,d79,d89],[DF(1,2,a,b),DF(1,3,a,b),DF(1,4,a,b),DF(1,5,a,b),DF(1,6,a,b),DF~ (1,7,a,b),DF(1,8,a,b),DF(1,8,a,b),DF(2,3,a,b),DF(2,4,a,b),DF(2,5,a,b),DF(2,6,~ a,b),DF(2,7,a,b),DF(2,8,a,b),DF(2,8,a,b),DF(3,4,a,b),DF(3,5,a,b),DF(3,6,a,b),~ DF(3,7,a,b),DF(3,8,a,b),DF(3,9,a,b),DF(4,5,a,b),DF(4,6,a,b),DF(4,7,a,b),DF(4,~ 8,a,b),DF(4,9,a,b),DF(5,6,a,b),DF(5,7,a,b),DF(5,8,a,b),DF(5,9,a,b),DF(6,7,a,b~ ),DF(6,8,a,b),DF(6,9,a,b),DF(7,8,a,b),DF(7,9,a,b),DF(8,9,a,b)]) D219C(v,a,b):=D219D(D219B(v,b),a,b) [RFT(x,y,z):=,RJT(x,y,z,p):=,RCT(x,y):=,RDT(x,y,z):=] i414t:=2*RFT(u12t^2,u13t^2,u23t^2) i427t:=2*b5*RCT(s15t^2,q15t^2)/d15-2*b1*RFT(u12t^2,u13t^2,u23t^2)/d15+2*b5*d1~ 2*d13*d14*RJT(u12t^2,u13t^2,u23t^2,u15t^2)/(3*d15^2) i428t:=-2*b1*d23*d24*RDT(u13t^2,u23t^2,u12t^2)/(3*d12)+2*b2*RFT(u12t^2,u13t^2~ ,u23t^2)/d12-2*b1*x2t*y2t/(d12*u12t*x1t*y1t) i429t:=2*RCT(s10t^2,q10t^2)-2*d12*d13*d14*RJT(u12t^2,u13t^2,u23t^2,u10t^2)/(3~ *b1)