In: Tatra Mountains Mathematical Publications, vol. 59, no. 2
László Remete - Tímea Szabó - István Gaál
Detaily:
Rok, strany: 2014, 79 - 92
Kľúčové slová:
relative Thue equation, LLL reduction, relative cubic extension, relative quartic extension,
power integral bases, supercomputers
O článku:
In our recent paper
I. Gaál: \textit{Calculating ``small" solutions of relative Thue equations},
J. Experiment. Math. (to appear)
we gave an efficient algorithm to calculate ``small"
solutions of relative Thue equations (where ``small" means an upper bound of type $10^{500}$
for the sizes of solutions). Here we apply this algorithm to calculating power integral bases
in sextic fields with an imaginary quadratic subfield and to calculating relative
power integral bases in pure quartic extensions of imaginary quadratic fields.
In both cases the crucial point of the calculation is the resolution of a relative
Thue equation. We produce numerical data that were not known before.
Ako citovať:
ISO 690:
Remete, L., Szabó, T., Gaál, I. 2014. Calculating power integral bases by solving relative Thue equations. In Tatra Mountains Mathematical Publications, vol. 59, no.2, pp. 79-92. 1210-3195.
APA:
Remete, L., Szabó, T., Gaál, I. (2014). Calculating power integral bases by solving relative Thue equations. Tatra Mountains Mathematical Publications, 59(2), 79-92. 1210-3195.