id: 05817695
dt: j
an: 05817695
au: Alvanos, Paraskevas; Poulakis, Dimitrios
ti: Solving genus zero Diophantine equations over number fields.
so: J. Symb. Comput. 46, No. 1, 54-69 (2011).
py: 2011
pu: Elsevier Science (Academic Press), London
la: EN
cc: 
ut: genus zero Diophantine equations; rational curves; parameterization
ci: Zbl 0985.11051; Zbl 0998.11014
li: doi:10.1016/j.jsc.2010.09.002
ab: Let $K$ be an algebraic number field and $F(X,Y)$ an absolutely irreducible
    polynomial with coefficients in $K$ such that the curve defined by the
    equation $F(X,Y)=0$ is rational. Continuing the works of {\it D.
    Poulakis} and {\it E. Voskos} [J. Symb. Comput. 30, No. 5, 573—582
    (2000; Zbl 0985.11051), J. Symb. Comput. 33, No. 4, 479‒491 (2002;
    Zbl 0998.11014)] the authors of the present paper give an algorithm to
    determine all solutions of $F(X,Y)=0$ in algebraic integers of $K$. The
    paper is illustrated by interesting examples. The algebraic number
    theory procedures necessary for these calculations are available in the
    well known packages.
rv: István Gaál (Debrecen)