---
title: "Bibliography"
canonical: "https://docs.magma-maths.org/GlobalFields/AlgebraicFunctionFields/bibliography.html"
source: "https://docs.magma-maths.org/GlobalFields/AlgebraicFunctionFields/bibliography.md"
part: "Global Fields"
chapter: "Algebraic Function Fields"
breadcrumbs:
  - {"title": "Magma Handbook", "source": "../../index.md"}
  - {"title": "Global Fields", "source": "../index-global-fields.md"}
  - {"title": "Algebraic Function Fields", "source": "index-algebraic-function-fields.md"}
prev: {"title": "Divisors in OM representation", "source": "divisors-in-om-representation.md"}
next: {"title": "Class Field Theory for Global Function Fields", "source": "../ClassFieldTheoryForGlobalFunctionFields/index-class-field-theory-for-global-function-fields.md"}
---

# Bibliography

<a id="cite-bauch-thesis"></a>
- **[Bau14]** Jens–Dietrich Bauch. *Lattices over Polynomial Rings and Applications to Function Fields*. PhD thesis, Universitat Autònoma de Barcelona, 2014.
<a id="cite-bauch2016382"></a>
- **[Bau16a]** Jens-Dietrich Bauch. Computation of integral bases. *Journal of Number Theory*, 165:382–407, 2016. URL: [https://www.sciencedirect.com/science/article/pii/S0022314X16000743](https://www.sciencedirect.com/science/article/pii/S0022314X16000743), [doi:https://doi.org/10.1016/j.jnt.2016.01.011](https://doi.org/https://doi.org/10.1016/j.jnt.2016.01.011).
<a id="cite-bauch2016lattices"></a>
- **[Bau16b]** Jens-Dietrich Bauch. Lattices over Polynomial Rings and Applications to Function Fields. https://arxiv.org/abs/1601.01361, 2016. [arXiv:1601.01361](https://arxiv.org/abs/1601.01361).
<a id="cite-ad-ecc"></a>
- **[Bla05]** I. Blake, G. Serrousi and N. Smart, editor. *Advances in Elliptic Curve Cryptography*. Volume 317 of LMS LNS. Cambridge University Press, Cambridge, 2005.
<a id="cite-buchman-lenstra"></a>
- **[BL94c]** Johannes A. Buchmann and Hendrik W. Lenstra jr. Approximating rings of integers in number fields. *J. Théor. Nombres Bordx.*, 6(2):221–260, 1994.
<a id="cite-conwayhulpkemckay"></a>
- **[CHM98]** John H. Conway, Alexander Hulpke, and John McKay. On transitive permutation groups. *LMS Journal of Computation and Mathematics*, 1:1–8, 1998.
<a id="cite-elsenhans-short"></a>
- **[Els14]** A.-S. Elsenhans. A Note on Short Cosets. *Experimental Mathematics*, 23:411–413, 2014. [doi:10.1080/10586458.2014.922908](https://doi.org/10.1080/10586458.2014.922908).
<a id="cite-fieker-galois"></a>
- **[FK14]** C. Fieker and J. Klüners. Computation of Galois Groups of Rational Polynomials. *London Mathematical Society Journal of Computation and Mathematics*, 17(1):141 – 158, 2014. http://arxiv.org/abs/1211.3588.
<a id="cite-geissler"></a>
- **[Gei03]** Katharina Geißler. *Berechnung von Galoisgruppen über Zahl- und Funktionenkörpern*. PhD Thesis, TU-Berlin, 2003. available at http://www.math.tu-berlin.de/ kant/publications/diss/geissler.pdf.
<a id="cite-gk1"></a>
- **[GK00]** Katharina Geißler and Jürgen Klüners. Galois Group computation for Rational Polynomials. *J. Symbolic Comp.*, 30(6):653–674, 2000.
<a id="cite-montes-new-approach"></a>
- **[GMN13]** Jordi Guàrdia, Jesús Montes, and Enric Nart. A New Computational Approach to Ideal Theory in Number Fields. *Foundations of Computational Mathematics*, 13(5):729–762, Oct 2013. URL: [https://doi.org/10.1007/s10208-012-9137-5](https://doi.org/10.1007/s10208-012-9137-5), [doi:10.1007/s10208-012-9137-5](https://doi.org/10.1007/s10208-012-9137-5).
<a id="cite-guardia20121318"></a>
- **[GNP12]** Jordi Guàrdia, Enric Nart, and Sebastian Pauli. Single-factor lifting and factorization of polynomials over local fields. *Journal of Symbolic Computation*, 47(11):1318 – 1346, 2012. URL: [http://www.sciencedirect.com/science/article/pii/S0747717112000363](http://www.sciencedirect.com/science/article/pii/S0747717112000363), [doi:https://doi.org/10.1016/j.jsc.2012.03.001](https://doi.org/https://doi.org/10.1016/j.jsc.2012.03.001).
<a id="cite-antshessautiso"></a>
- **[Hes]** F. Heß. “An algorithm for computing isomorphisms of algebraic function fields.” 263–271.
<a id="cite-he2"></a>
- **[Hes99]** Florian Heß. *Zur Divisorenklassengruppenberechnung in globalen Funktionenkörpern*. Dissertation, Technische Universität Berlin, 1999. http://www.staff.uni-oldenburg.de/florian.hess/publications/diss_FH.pdf.
<a id="cite-kl4"></a>
- **[Klu02]** Jürgen Klüners. Algorithms for Function Fields. *Exp. Math.*, pages 171–181, 2002.
<a id="cite-krumm-sutherland"></a>
- **[KS21]** David Krumm and Nicole Sutherland. Galois groups over rational function fields and Explicit Hilbert Irreducibility. *Journal of Symbolic Computation*, 103:108 – 126, 2021. URL: [http://www.sciencedirect.com/science/article/pii/S0747717119301476](http://www.sciencedirect.com/science/article/pii/S0747717119301476), [doi:https://doi.org/10.1016/j.jsc.2019.11.003](https://doi.org/https://doi.org/10.1016/j.jsc.2019.11.003).
<a id="cite-ghs"></a>
- **[PGS00]** F. Heß P. Gaudry and N. P. Smart. Constructive and destructive facets of Weil descent on elliptic curves. *J. Cryptology*, 15(1):19–46, 2000.
<a id="cite-mk2"></a>
- **[SM85]** Leonhard H. Soicher and John McKay. Computing Galois Groups over the rationals. *J. Number Th.*, 20:273–281, 1985.
<a id="cite-2015arxiv150601904s"></a>
- **[Sta18]** Hayden D. Stainsby. Triangular bases of integral closures. *J. Symbolic Comput.*, 87:140–175, 2018. URL: [https://doi.org/10.1016/j.jsc.2017.07.012](https://doi.org/10.1016/j.jsc.2017.07.012), [doi:10.1016/j.jsc.2017.07.012](https://doi.org/10.1016/j.jsc.2017.07.012).
<a id="cite-stau"></a>
- **[Sta73]** Richard P. Stauduhar. The determination of Galois Groups. *Math. Comp.*, 27:981–996, 1973.
<a id="cite-stichtenoth"></a>
- **[Sti93]** Henning Stichtenoth. *Algebraic function fields and codes*. Springer-Verlag, Berlin, 1993. ISBN 3-540-56489-6.
<a id="cite-suth-max-kummer"></a>
- **[Sut12]** Nicole Sutherland. Efficient Computation of Maximal Orders of Radical (including Kummer) Extensions. *Journal of Symbolic Computation*, 47(5):552–567, 2012. [doi:10.1016/j.jsc.2011.12.053](https://doi.org/10.1016/j.jsc.2011.12.053).
<a id="cite-suth-artin"></a>
- **[Sut13]** Nicole Sutherland. Efficient Computation of Maximal Orders of Artin–Schreier Extensions. *Journal of Symbolic Computation*, 53(1):26–39, 2013. URL: [http://dx.doi.org/10.1016/j.jsc.2012.11.001](http://dx.doi.org/10.1016/j.jsc.2012.11.001), [doi:10.1016/j.jsc.2012.11.001](https://doi.org/10.1016/j.jsc.2012.11.001).
<a id="cite-suth-galois"></a>
- **[Sut15]** Nicole Sutherland. Computing Galois Groups of Polynomials (especially over Function Fields of Prime Characteristic). *Journal of Symbolic Computation*, 71:73–97, 2015. [doi:10.1016/j.jsc.2014.09.043](https://doi.org/10.1016/j.jsc.2014.09.043).
<a id="cite-suth-car"></a>
- **[Sut18]** Nicole Sutherland. Galois Groups in Magma. *Computeralgebra Rundbrief*, 62:, 2018.
<a id="cite-vanhoeijklueners"></a>
- **[vHKN11]** M. van Hoeij, J. Klüners, and A. Novocin. Generating Subfields. In Anton Leykin, editor, *Proceedings ISSAC 2011*. 2011.