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:

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!

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