On the Resolution of Index Form Equations in Quartic Number Fields

@article{Gal1993OnTR,
  title={On the Resolution of Index Form Equations in Quartic Number Fields},
  author={Istv{\'a}n Ga{\'a}l and Attila Peth{\"o} and Michael E. Pohst},
  journal={J. Symb. Comput.},
  year={1993},
  volume={16},
  pages={563-584}
}
In this paper we develop a method for computing all small solutions (i.e. with coordinates of absolute value < 10’) of index form equations in totally real biquadratic number fields. If the index form equation is not solvable, this will also be recognized by our algorithm in most cases, As an application we present all such solutions in quadratic extensions K of Q(d) of discriminant D,, < 63000 and of Q(d) of discriminant D,,,. < 39ooO. c. 1991 Academic Press, Inc.