|Bill Allombert on Sat, 25 Jun 2016 14:21:16 +0200|
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|Re: p-adic logarithm|
On Thu, Jun 23, 2016 at 06:49:07PM +0200, Bill Allombert wrote: > On Thu, Jun 23, 2016 at 02:48:00PM +0000, LECOUTURIER Emmanuel wrote: > > Hello, > > Is there any function which allows us to compute directly Iwasawa > > p-adic logarithm in finite extensions of Q_p ? (like Q_p(zeta_p)) > > GP itself only handles Q_p, however you can factor x as > x = t*(1+u) where t is of torsion and u is in the convergence domain of > log(1+X) and then use the power series for log (or for atanh). Writing this gives me an idea: instead of computing t, if n is the order of the torsion subgroup, then x^n = (1+u)^n = 1+v and log(x^n)= log(x)/n In some case this can be simpler than actually computing t. Cheers, Bill.