CALCULATING RELATIVE POWER INTEGRAL BASES IN TOTALLY COMPLEX QUARTIC EXTENSIONS OF TOTALLY REAL FIELDS

DOI10.17654/NT044020129zbMath1490.11121arXiv2004.05393OpenAlexW3104927871MaRDI QIDQ5075019

István Gaál

Publication date: 10 May 2022

Published in: JP Journal of Algebra, Number Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.05393

zbMATH Keywords

power integral basisThue equationunit equationcalculating solutions of index form equationsrelative quartic extensions

Mathematics Subject Classification ID

Thue-Mahler equations (11D59) Computer solution of Diophantine equations (11Y50) Algebraic numbers; rings of algebraic integers (11R04) Multiplicative and norm form equations (11D57)

Uses Software

• KANT/KASH
• Magma
• Maple

Cites Work

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• Factoring polynomials with rational coefficients
• The Magma algebra system. I: The user language
• KANT V4
• Calculating power integral bases by using relative power integral bases
• On the resolution of relative Thue equations
• Relative power integral bases in infinite families of quartic extensions of quadratic fields
• Logarithmic forms and group varieties.
• The Simplest Cubic Fields
• Simplest quartic and simplest sextic Thue equations over imaginary quadratic fields
• Totally real Thue inequalities over imaginary quadratic fields
• Computing power integral bases in quartic relative extensions

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