4 citations · 4 across the 3 of their papers we have counts for
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Calculating power integral bases by solving relative Thue equations
István Gaál, László Remete, Tí mea Szabó
In our recent paper we gave an efficient algorithm to calculate "small" solutions of relative Thue equations (where "small" means an upper bound of type for the sizes of…
Calculating "small" solutions of relative Thue equations
István Gaál
Diophantine equations can often be reduced to various types of classical Thue equations. These equations usually have only very small solutions, on the other hand to compute all so…
Calculating all elements of minimal index in the infinite parametric family of simplest quartic fields
István Gaál, Gábor Petrányi
It is a classical problem in algebraic number theory to decide if a number field is monogeneous, that is if it admits power integral bases. It is especially interesting to consider…
Power integral bases in a family of sextic fields with quadratic subfields
István Gaál, László Remete
Let be any imaginary quadratic field with a positive square-free . Consider the polynomial \[ f(x)=x^3-ax^2-(a+3)x-1, \] with a parameter . Let …
Integral bases and monogenity of composite fields
István Gaál, László Remete
We consider infinite parametric families of high degree number fields composed of quadratic fields with pure cubic, pure quartic, pure sextic fields and with the so called simplest…