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CALCULATING GENERATORS OF POWER INTEGRAL BASES IN SEXTIC FIELDS WITH A REAL QUADRATIC SUBFIELD
Keywords:
monogenity, power integral basis, sextic fields, relative cubic extension, quadratic subfield, relative Thue equations, sievingDOI:
https://doi.org/10.17654/0972555525016Abstract
We discuss the problem of calculating generators of power integral bases in sextic fields, especially focusing on the case of sextic fields with real quadratic subfields. Our main purpose is to describe an efficient algorithm for calculating generators of power integral bases. We show that appropriately using integer arithmetics speeds up the calculations considerably. Our experiences lead to some interesting general statements on generators of power integral bases in number fields generated by a unit.
Received: March 12, 2025
Revised: March 28, 2025
Accepted: April 8, 2025
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