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- István Gaál, Nico Schulte
- 1989

Applying Baker's effective method and the reduction procedure of Baker and Davenport, we present several lists of solutions of index form equations in (totally real and complex) cubic algebraic… (More)

LetQ1, Q2∈Z[X, Y, Z] be two ternary quadratic forms andu1, u2∈Z. In this paper we consider the problem of solving the system of equations[formula]According to Mordell [12] the coprime solutions… (More)

- István Gaál
- J. Symb. Comput.
- 1995

In the present paper we show, that the problem of determining elements of given index in totally complex cyclic sextic fields (or in general, in sextic fields containing an imaginary quadratic and a… (More)

In this paper we develop a method for computing all small solutions (i.e. with coordinates of absolute value <107) of index form equations in totally real biquadratic number fields. If the index form… (More)

- István Gaál
- 2002

- István Gaál, Attila Pethö, Michael E. Pohst
- J. Symb. Comput.
- 1993

Abstract In this paper we reduce the problem of solving index form equations in quartic number fields K to the resolution of a cubic equation F ( u, v ) = i and a corresponding system of quadratic… (More)

- István Gaál, Attila Pethö, Michael E. Pohst
- ISSAC
- 1991

is soluble and to compute all solutions of (2) to find all integral elements with least index. The problem of solving (1) was worked out by Gad and Schulte [3] for cubic number fields and by Gad,… (More)

- István Gaál, Michael E. Pohst
- Math. Comput.
- 1997

We consider the totally real cyclic quintic fields K n = Q(v n ), generated by a root v n of the polynomial f n (x) = x 5 + n 2 x 4 - (2n 3 + 6n 2 + 10n + 10)x 3 + (n 4 + 5n 3 + 11n 2 + 15n + 5)x 2 +… (More)

- István Gaál
- 1998

In the present paper we consider the problem of finding power integral bases in number fields which are composits of two subfields with coprime discriminants. Especially, we consider imaginary… (More)

- István Gaál, Michael E. Pohst
- Math. Comput.
- 2002

An efficient algorithm is given for the resolution of relative Thue equations. The essential improvement is the application of an appropriate version of Wildanger's enumeration procedure based on the… (More)