---
title: "Bibliography"
canonical: "https://docs.magma-maths.org/BasicRings/UnivariatePolynomialRings/bibliography.html"
source: "https://docs.magma-maths.org/BasicRings/UnivariatePolynomialRings/bibliography.md"
part: "Basic Rings"
chapter: "Univariate Polynomial Rings"
breadcrumbs:
  - {"title": "Magma Handbook", "source": "../../index.md"}
  - {"title": "Basic Rings", "source": "../index-basic-rings.md"}
  - {"title": "Univariate Polynomial Rings", "source": "index-univariate-polynomial-rings.md"}
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next: {"title": "Multivariate Polynomial Rings", "source": "../MultivariatePolynomialRings/index-multivariate-polynomial-rings.md"}
---

# Bibliography

<a id="cite-szutkoski"></a>
- **[ACvHS17]** Emilio Allem, Juliane Capaverde, Mark van Hoeij, and Jonas Szutkoski. Functional Decomposition using Principal Subfields. In *ISSAC '17, July 25-28, 2017, Kaiserslautern, Germany*. ACM, 2017. accepted. [doi:doi.org/10.1145/3087604.3087608](https://doi.org/doi.org/10.1145/3087604.3087608).
<a id="cite-gcdheu"></a>
- **[CGG89]** Bruce W. Char, Keith O. Geddes, and Gaston H. Gonnet. GCDHEU: Heuristic Polynomial GCD Algorithm Based on Integer GCD Computation. *J. Symbolic Comp.*, 7(1):31–48, 1989.
<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-coppersmith96"></a>
- **[Cop96]** Don Coppersmith. Finding a small root of a univariate modular equation. In *Advances in Cryptology—EuroCrypt 1996*, volume 1070 of LNCS, pages 155–165. Springer, 1996.
<a id="cite-gcl"></a>
- **[GCL92]** Keith O. Geddes, Stephen R. Czapor, and George Labahn. *Algorithms for Computer Algebra*. Kluwer, Boston/Dordrecht/London, 1992.
<a id="cite-ks-factorization"></a>
- **[KS95]** Erich Kaltofen and Victor Shoup. Subquadratic-time factoring of polynomials over finite fields. In *Proceedings of the Twenty-Seventh Annual ACM Symposium on Theory of Computing*, 398–406. ACM, 1995.
<a id="cite-knuth2"></a>
- **[Knu97]** Donald E. Knuth. *The Art of Computer Programming*. Volume 2. Addison Wesley, Reading, Massachusetts, 3rd edition, 1997.
<a id="cite-lll"></a>
- **[LLL82]** Arjen K. Lenstra, Hendrik W. Lenstra, and László Lovász. Factoring polynomials with rational coefficients. *Mathematische Annalen*, 261:515–534, 1982.
<a id="cite-may03"></a>
- **[May03]** Alexander May. *New RSA Vulnerabilities Using Lattice Reduction Methods*. Dissertation, University of Paderborn, 2003.
<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-shoup-factorization"></a>
- **[Sho95b]** Victor Shoup. A New Polynomial Factorization Algorithm and its Implementation. *J. Symbolic Comp.*, 20(4):363–397, 1995.
<a id="cite-steelinsep"></a>
- **[Ste05]** Allan Steel. Conquering Inseparability: Primary Decomposition and Multivariate Factorization over Algebraic Function Fields of Positive Characteristic. *J. Symbolic Comp.*, 40(3):1053–1075, 2005.
<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-vhoeij2"></a>
- **[vH01]** Mark van Hoeij. Factoring Polynomials and 0-1 vectors. In *Proceedings of the Cryptography and Lattices Conference (CaLC 2001), Brown University, Providence, RI, USA, March 29-30, 2001*, 142–146. Springer, 2001.
<a id="cite-vhoeij1"></a>
- **[vH02]** Mark van Hoeij. Factoring Polynomials and the knapsack problem. *J. Number Th.*, 95(2):167–189, 2002. http://www.math.fsu.edu/$\sim$hoeij/paper/knapsack.ps.
<a id="cite-gathengerhard"></a>
- **[vzGG99]** Joachim von zur Gathen and Jürgen Gerhard. *Modern Computer Algebra*. Cambridge University Press, Cambridge, 1999.
<a id="cite-gs-frobenius"></a>
- **[vzGS92]** Joachim von zur Gathen and Victor Shoup. Computing Frobenius Maps And Factoring Polynomials. *Computational Complexity*, 2:187–224, 1992.