Is there any implementation available of an algorithm which solves in full generality the $S$-unit equation $x+y=1$ in a number field? It seems that Magma solves $ax+by=c$ but only in the algebraic integers, while Sage solves $x+y=1$ with $x,y$ $S$-integers, but only for $S$ the set of primes over a fixed rational primes. Is that true? Is there any other implementation available?