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 Inverse super-composition Xorter Fellow Posts: 93 Threads: 30 Joined: Aug 2016 05/26/2018, 12:00 AM Hi here, again! I have been thinking about functional logarithm, and I coded it in pari/gp in this way: Code:```D(f,n)={if(n>0,return(D(deriv(f),n-1)),return(f));}; M(f,n)=matrix(n,n,j,k,1/(k-1)!*subst(D(x*0+f^(j-1),k-1),x,0)); T(A,n)=sum(k=1,n,A[2,k]*x^(k-1)); inv(f,n)=T(M(f,n)^-1,n); Ln(A,n)=sum(k=1,n,(-1)^(k+1)*(A-1)^k/k); olog(f,g,n)=T(Ln(M(f,n),n^2)/(0.1^n+Ln(M(g,n),n^2)));``` M is the Carleman-matrix, T is a generated taylor-series from the M matrix. Ln is log of a quadratic matrix. And olog is the functional logarithm: olog(f(x),(f^og(x))(x)) = g(x), but somewhy it is not working. E. g. olog(2x,x*2^(2x),100...) = 2x. Could help me? Thank you very much! Xorter Unizo « Next Oldest | Next Newest »

 Messages In This Thread Inverse super-composition - by Xorter - 11/24/2016, 12:53 PM RE: Inverse super-composition - by JmsNxn - 11/25/2016, 08:55 PM RE: Inverse super-composition - by Xorter - 12/23/2016, 01:33 PM RE: Inverse super-composition - by JmsNxn - 12/23/2016, 08:12 PM RE: Inverse super-composition - by Xorter - 12/24/2016, 09:53 PM RE: Inverse super-composition - by sheldonison - 12/25/2016, 04:16 AM RE: Inverse super-composition - by Xorter - 12/25/2016, 04:38 PM RE: Inverse super-composition - by sheldonison - 12/25/2016, 08:35 PM RE: Inverse super-composition - by Xorter - 12/25/2016, 10:23 PM RE: Inverse super-composition - by sheldonison - 12/26/2016, 07:10 AM RE: Inverse super-composition - by Xorter - 01/12/2017, 04:19 PM RE: Inverse super-composition - by Xorter - 05/26/2018, 12:00 AM

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