A hybrid Gröbner bases approach to computing power integral bases

DOI10.1007/s10474-015-0544-3zbMath1374.11085OpenAlexW1104643905MaRDI QIDQ519989

Yong-Cai Geng, Sumit K. Garg

Publication date: 31 March 2017

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10474-015-0544-3

zbMATH Keywords

Gröbner basispower integral basiscyclotomic integer

Mathematics Subject Classification ID

Cyclotomic extensions (11R18) Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33) Multiplicative and norm form equations (11D57)

Related Items (1)

On Multiplicative Independent Bases for Canonical Number Systems in Cyclotomic Number Fields

Uses Software

• SageMath

Cites Work

• On the resolution of index form equations in sextic fields with an imaginary quadratic subfield
• Power bases for cyclotomic integer rings
• On the resolution of index form equations in biquadratic number fields. III: The bicyclic biquadratic case
• Simultaneous representation of integers by a pair of ternary quadratic forms -- with an application to index form equations in quartic number fields
• Power integral bases in prime-power cyclotomic fields
• A survey on monogenic orders
• An attack on disguised elliptic curves
• Computing All Power Integral Bases of Cubic Fields
• Index form equations in sextic fields: a hard computation
• Computing all power integral bases in orders of totally real cyclic sextic number fields
• On finite solvable groups in which normality is a transitive relation
• Mean value theorems for polyharmonic functions: A conjecture by Picone
• Power bases for 2-power cyclotomic fields
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