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Question: How do replacing some special character to get another function ?

Question:How do replacing some special character to get another function ?

SSMB 90 Maple 2024
substitution duplicate-question duplicate-account
March 03 2025
4

i want to to get the eq(14) but i need to do some Hard replacing which i am unfamiliar with it any one can help ?

> 

restart;
> 

 

> 

f :=  1 + exp(eta[1]) + b[1, 2]*exp(eta[1] + eta[2]) + exp(eta[2]) + b[2, 3]*exp(eta[2] + eta[3]) + b[1, 2]*b[1, 3]*b[2, 3]*exp(eta[1] + eta[2] + eta[3]) + b[1, 3]*exp(eta[1] + eta[3]) + exp(eta[3])

1+exp(eta[1])+b[1, 2]*exp(eta[1]+eta[2])+exp(eta[2])+b[2, 3]*exp(eta[2]+eta[3])+b[1, 2]*b[1, 3]*b[2, 3]*exp(eta[1]+eta[2]+eta[3])+b[1, 3]*exp(eta[1]+eta[3])+exp(eta[3])

 (1)
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NULL
> 

C :=(i,j)->6*l[j]*l[i]*(l[i] + l[j])/((l[i] - l[j])^2*beta)

proc (i, j) options operator, arrow; 6*l[j]*l[i]*(l[i]+l[j])/((l[i]-l[j])^2*beta) end proc

 (2)
> 

NULL
> 

etai := k[i]*(t*w[i]+y*l[i]+x)+eta[i]

k[i]*(t*w[i]+y*l[i]+x)+eta[i]

 (3)
> 

theta[i] := t*w[i]+y*l[i]+x

t*w[i]+y*l[i]+x

 (4)
> 

eqw := w[i] = -(alpha*l[i]+beta)/l[i]

w[i] = -(alpha*l[i]+beta)/l[i]

 (5)
> 

theta[1] := normal(eval(eval(theta[i], eqw), i = 1)); theta[2] := normal(eval(eval(theta[i], eqw), i = 2))

-(alpha*t*l[1]-y*l[1]^2+beta*t-x*l[1])/l[1]

  

-(alpha*t*l[2]-y*l[2]^2+beta*t-x*l[2])/l[2]

 (6)
> 

fix:=proc(F)
   local i,j;
   i:=op(1,F); j:=op(2,F);
   if i<j then
      C(i,j);
   else
      F;
   fi;
end proc:
> 

evalindets(f,b[anything,anything],F->fix(F));

1+exp(eta[1])+6*l[2]*l[1]*(l[1]+l[2])*exp(eta[1]+eta[2])/((l[1]-l[2])^2*beta)+exp(eta[2])+6*l[3]*l[2]*(l[2]+l[3])*exp(eta[2]+eta[3])/((l[2]-l[3])^2*beta)+216*l[2]^2*l[1]^2*(l[1]+l[2])*l[3]^2*(l[1]+l[3])*(l[2]+l[3])*exp(eta[1]+eta[2]+eta[3])/((l[1]-l[2])^2*beta^3*(l[1]-l[3])^2*(l[2]-l[3])^2)+6*l[3]*l[1]*(l[1]+l[3])*exp(eta[1]+eta[3])/((l[1]-l[3])^2*beta)+exp(eta[3])

 (7)
> 

simplify(%);

1+exp(eta[1])+b[1, 2]*exp(eta[1]+eta[2])+exp(eta[2])+b[2, 3]*exp(eta[2]+eta[3])+b[1, 2]*b[1, 3]*b[2, 3]*exp(eta[1]+eta[2]+eta[3])+b[1, 3]*exp(eta[1]+eta[3])+exp(eta[3])

 (8)
 

 

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