Re: S-Unit questions

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Thu, Mar 12, 2026 at 02:58:16PM +0100, hermann@stamm-wilbrandt.de wrote:
> On error message it explained that linear polynomial has too low degree for
> thueinit.
> And to use a script with "bnfisunit()" — but current GP does not know this
> command.

bnfisunit certainly exist, though it will probably not help you...

? ?bnfisunit()
bnfisunit(bnf,x,{U}): bnf being output by bnfinit, give the column vector of exponents of x on the fundamental units and the roots of
unity if x is a unit, the empty vector otherwise. If U is present, as given by bnfunits, decompose x on the attached S-units generators.

> So how to solve this equation using PARI/GP with its Baker(?) algorithm?
> 
> ±2^{a1}*3^{b1}±2^{a2}*3^{b2}=1

I do not think there is a GP function that can solve this, though this is solvable
in principle using linear forms in logarithms.

Cheers,
Bill.