Explicit construction of integral bases of radical function fields

DOI10.5802/jtnb.714zbMath1236.11089OpenAlexW2329847744MaRDI QIDQ614490

Qingquan Wu

Publication date: 3 January 2011

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_2010__22_1_259_0

zbMATH Keywords

integral basesradical function fields

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Algebraic number theory computations (11Y40) Algebraic numbers; rings of algebraic integers (11R04)

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On computing integral points of a Mordell curve over rational function fields in characteristic \(>3\)

Uses Software

• Magma

Cites Work

• Integral basis of the field \(\mathbb Q(\root n\of a)\)
• Algebraic function fields and codes
• The integers of a cyclic quartic field
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• Prime ideal decomposition in \(F({\root m\of\mu})\)
• Prime ideal decomposition in \(F(\mu^{1/p})\)
• The Magma algebra system. I: The user language
• Integral bases for quartic fields with quadratic subfields
• Approximating rings of integers in number fields
• An algorithm for computing an integral basis in an algebraic function field
• On Integral Bases
• Structure theorems for radical extensions of fields
• A polynomial-time complexity bound for the computation of the singular part of a Puiseux expansion of an algebraic function
• Voronoi's algorithm in purely cubic congruence function fields of unit rank 1
• Integral Bases in Kummer Extensions of Dedekind Fields
• Number fields
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