---
title: "Bibliography"
canonical: "https://docs.magma-maths.org/GlobalFields/NumberFieldsAndOrders/bibliography.html"
source: "https://docs.magma-maths.org/GlobalFields/NumberFieldsAndOrders/bibliography.md"
part: "Global Fields"
chapter: "Number Fields and Orders"
breadcrumbs:
  - {"title": "Magma Handbook", "source": "../../index.md"}
  - {"title": "Global Fields", "source": "../index-global-fields.md"}
  - {"title": "Number Fields and Orders", "source": "index-number-fields-and-orders.md"}
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---

# Bibliography

<a id="cite-bai1"></a>
- **[Bai96]** Georg Baier. Zum Round 4 Algorithmus. Master's thesis, Technische Universität Berlin, 1996. http://www.math.tu-berlin.de/$\sim$kant/publications/diplom/baier.ps.gz.
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- **[BF15]** Karim Belabas and Eduardo Friedman. Computing the residue of the Dedekind zeta function. *Math. Comp.*, 84(291):357–369, 2015. URL: [https://doi.org/10.1090/S0025-5718-2014-02843-3](https://doi.org/10.1090/S0025-5718-2014-02843-3), [doi:10.1090/S0025-5718-2014-02843-3](https://doi.org/10.1090/S0025-5718-2014-02843-3).
<a id="cite-bernstein2005"></a>
- **[Ber05]** Daniel J. Bernstein. Factoring into coprimes in essentially linear time. *J. of Algorithms*, 54(1):1–30, 2005.
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- **[Bia]** J. Biasse. “Number field sieve to compute Class groups.”
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- **[BH96]** Yuri Bilu and Guillaume Hanrot. Solving Thue Equations of High Degree. *J. Number Th.*, 60:373–392, 1996.
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- **[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-cohen1"></a>
- **[Coh93]** Henri Cohen. *A Course in Computational Algebraic Number Theory*. Volume 138 of Graduate Texts in Mathematics. Springer, Berlin–Heidelberg–New York, 1993.
<a id="cite-cohen2"></a>
- **[Coh00]** Henri Cohen. *Advanced Topics in Computational Number Theory*. Springer, Berlin–Heidelberg–New York, 2000.
<a id="cite-fijupo"></a>
- **[FJP97]** C. Fieker, A. Jurk, and M. Pohst. On solving relative norm equations in algebraic number fields. *Math. Comput.*, 66(217):399–410, 1997.
<a id="cite-fi1"></a>
- **[Fie97]** Claus Fieker. *Über relative Normgleichungen in algebraischen Zahlkörpern*. Dissertation, Technische Universität Berlin, 1997. http://www.math.tu-berlin.de/$\sim$kant/publications/diss/diss_CF.ps.gz.
<a id="cite-fifi2000"></a>
- **[FF]** C. Fieker, C. Friedrichs. “On reconstruction of algebraic numbers.” 285–296.
<a id="cite-fin1"></a>
- **[Fin84]** Ulrich Fincke. *Ein Ellipsoidverfahren zur Lösung von Normgleichungen in algebraischen Zahlkörpern*. Dissertation, Heinrich-Heine-Universität Düsseldorf, 1984.
<a id="cite-fr1"></a>
- **[Fri97]** Carsten Friedrichs. Berechnung relativer Ganzheitsbasen mit dem Round-2-Algorithmus. Master's thesis, Technische Universität Berlin, 1997. http://www.math.tu-berlin.de/$\sim$kant/publications/diplom/friedrichs.ps.gz.
<a id="cite-fr2"></a>
- **[Fri00]** Carsten Friedrichs. *Berechnung von Maximalordnungen über Dedekindringen*. Dissertation, Technische Universität Berlin, 2000. http://www.math.tu-berlin.de/$\sim$kant/publications/diss/diss_fried.pdf.gz.
<a id="cite-gapepo1"></a>
- **[GPP93]** Istvan Gaál, Attila Petho, and Michael E. Pohst. On the resolution of index form equations in quartic number fields. *J. Symbolic Comp.*, 16:563–584, 1993.
<a id="cite-gapepo2"></a>
- **[GPP96]** Istvan Gaál, Attila Petho, and Michael E. Pohst. Simultaneous representation of integers by a pair of ternary quadratic forms – With an application to index form equations in quartic number fields. *J. Number Th.*, 57:90–104, 1996.
<a id="cite-gasch"></a>
- **[GS89]** Istvan Gaál and Nicole Schulte. Computing all power integral bases of cubic fields. *Math. Comp.*, 53:689–696, 1989.
<a id="cite-garbanati"></a>
- **[Gar80]** Dennis A. Garbanati. An Algorithm for finding an algebraic number whose norm is a given rational number. *J. reine angew. Math.*, 316:1–13, 1980.
<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-he1"></a>
- **[Hes96]** Florian Heß. Zur Klassengruppenberechnung in algebraischen Zahlkörpern. Master's thesis, Technische Universität Berlin, 1996. http://www.math.tu-berlin.de/$\sim$kant/publications/diplom/hess.ps.gz.
<a id="cite-jurk"></a>
- **[Jur93]** Andreas Jurk. *Über die Berechnung von Lösungen relativer Normgleichungen in algebraischen Zahlkörpern*. Dissertation, Heinrich-Heine-Universität Düsseldorf, 1993.
<a id="cite-muldersquarefree"></a>
- **[Mul25]** Erik Mulder. Fast square-free decomposition of integers using class groups. *Res. Number Theory*, 11(1):Paper No. 9, 21, 2025. URL: [https://doi.org/10.1007/s40993-024-00585-8](https://doi.org/10.1007/s40993-024-00585-8), [doi:10.1007/s40993-024-00585-8](https://doi.org/10.1007/s40993-024-00585-8).
<a id="cite-kluenerspauli2005"></a>
- **[PK05]** Sebastian Pauli and Jüren Klüners. Computing residue class rings and Picard groups of orders. *J. of Algebra*, 292:47–64, 2005.
<a id="cite-pohst2"></a>
- **[Poh93]** M. Pohst. *Computational Algebraic Number Theory*. DMV Seminar Band 21. Birkhäuser Verlag, Basel - Boston - Berlin, 1993.
<a id="cite-po64"></a>
- **[Poh]** M. E. Pohst. “Computational Aspects of Kummer Theory.” 259–272.
<a id="cite-pohst1"></a>
- **[PZ89]** Michael E. Pohst and Hans Zassenhaus. *Algorithmic Algebraic Number Theory*. Encyclopaedia of mathematics and its applications. Cambridge University Press, Cambridge, 1989.
<a id="cite-simon1"></a>
- **[Sim02]** Denis Simon. Solving norm equations in relative number fields using $S$-units. *Math. Comput.*, 71(239):1287–1305, 2002.
<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-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-trager-factorization"></a>
- **[Tra76]** Barry M. Trager. Algebraic factoring and rational function integration. In R.D. Jenks, editor, *Proc. SYMSAC '76*, 196–208. ACM press, 1976.
<a id="cite-wi2"></a>
- **[Wil97]** Klaus Wildanger. *Über das Lösen von Einheiten- und Indexformgleichungen in algebraischen Zahlkörpern mit einer Anwendung auf die Bestimmung aller ganzen Punkte einer Mordellschen Kurve*. Dissertation, Technische Universität Berlin, 1997. http://www.math.tu-berlin.de/$\sim$kant/publications/diss/KW_diss.ps.gz.
<a id="cite-wi3"></a>
- **[Wil00]** Klaus Wildanger. Über das Lösen von Einheiten- und Indexformgleichungen in algebraischen Zahlkörpern. (On the solution of units and index form equations in algebraic number fields). *J. Number Th.*, 2(82):188–224, 2000.
<a id="cite-kash"></a>
- **[KAN97]** KANT Group. KANT V4. *J. Symbolic Comp.*, 24(3–4):267–383, 1997.
<a id="cite-kant"></a>
- **[KAN00]** KANT Group. The Number Theory Package KANT/KASH. http://www.math.tu-berlin.de/$\sim$kant, 2000.