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Comments on Integration of algebraic functions. (English) Zbl 1511.26007

Raab, Clemens G. (ed.) et al., Integration in finite terms: fundamental sources. Cham: Springer. Texts Monogr. Symb. Comput., 287-295 (2022).
Concerns the author’s thesis [Integration of algebraic functions. Cambridge, MA: Massachusetts Institute of Technology (PhD Thesis) (1984)] reprinted in this volume [in: Integration in finite terms: fundamental sources. Cham: Springer. 230–286 (2022; Zbl 1511.26013)].
For the entire collection see [Zbl 1490.26001].

MSC:

26-03 History of real functions
01A60 History of mathematics in the 20th century

Citations:

Zbl 1511.26013
Full Text: DOI

References:

[1] Moulay A. Barkatou. On Rational Solutions of Systems of Linear Differential Equations. J. Symb. Comput., 28(4):547-567, October 1999. · Zbl 0943.34008
[2] Laurent Bertrand. Computing a Hyperelliptic Integral using Arithmetic in the Jacobian of the Curve. Appl. Algebra Eng. Commun. Comput., 6(4-5):275-298, 1995. · Zbl 0838.12005
[3] Janko Böhm, Wolfram Decker, Santiago Laplagne, Gerhard Pfister, Andreas Steenpass, and Stefan Steidel. Parallel algorithms for normalization. J. Symb. Comput., 51:99-114, 2013. Effective Methods in Algebraic Geometry. · Zbl 1408.13072
[4] Manuel Bronstein. Integration of Elementary Functions. J. Symb. Comput., 9(2):117-173, February 1990. · Zbl 0718.12006
[5] Manuel Bronstein. The Lazy Hermite Reduction. Technical report, Technical Report RR-3562, INRIA, November, 1998.
[6] David G. Cantor. Computing in the Jacobian of a Hyperelliptic Curve. Math. Comput., 48(177):95-101, 1987. · Zbl 0613.14022
[7] Shaoshi Chen, Lixin Du, and Manuel Kauers. Lazy Hermite Reduction and Creative Telescoping for Algebraic Functions. In Proc. ISSAC ’21, pages 75-82, New York, NY, USA, 2021. ACM.
[8] Shaoshi Chen, Manuel Kauers, and Christoph Koutschan. Reduction-Based Creative Telescoping for Algebraic Functions. In Proc. ISSAC ’16, pages 175-182, New York, NY, USA, 2016. ACM. · Zbl 1360.68928
[9] Shaoshi Chen, Manuel Kauers, and Michael F. Singer. Telescopers for Rational and Algebraic Functions via Residues. In Proc. ISSAC ’12, pages 130-137, New York, NY, USA, 2012. ACM. · Zbl 1323.68592
[10] Shaoshi Chen, Mark van Hoeij, Manuel Kauers, and Christoph Koutschan. Reduction-based creative telescoping for Fuchsian D-finite functions. J. Symb. Comput., 85:108-127, 2018. 41st International Symposium on Symbolic and Algebraic Computation (ISSAC ’16). · Zbl 1379.68363
[11] John Coates. Construction of rational functions on a curve. Math. Proc. Cambridge Philos. Soc., 68(1):105-123, 1970. · Zbl 0215.37302
[12] Thierry Combot. Elementary Integration of Superelliptic Integrals. In Proc. ISSAC ’21, pages 99-106. ACM, 2021.
[13] Olivier Cormier, Michael F. Singer, Barry M. Trager, and Felix Ulmer. Linear Differential Operators for Polynomial Equations. J. Symb. Comput., 34(5):355 - 398, 2002. · Zbl 1030.12002
[14] Giorgio Dalzotto, Patrizia Gianni, and Barry M. Trager. Good Reduction of Plane Curves. Unpublished, N.D.
[15] James H. Davenport. Algorithms for the integration of algebraic functions. In Proc. EUROSAM ’79, pages 415-425, London, UK, 1979. Springer-Verlag. · Zbl 0411.34002
[16] James H. Davenport. On the Integration of Algebraic Functions, volume 102 of Lect. Notes in Comput. Sci. Springer, Berlin, 1981. · Zbl 0471.14009
[17] Theo de Jong. An Algorithm for Computing the Integral Closure. J. Symb. Comput., 26:273-277, 1998. · Zbl 0932.13021
[18] Jean Della Dora, Claire Dicrescenzo, and Dominique Duval. About a New Method for Computing in Algebraic Number Fields. In Research Contributions from the European Conference on Computer Algebra-Volume 2, EUROCAL ’85, pages 289-290, Berlin, Heidelberg, 1985. Springer-Verlag.
[19] Dominique Duval. Rational Puiseux expansions. Compos. Math., 70(2):119-154, 1989. · Zbl 0699.14034
[20] Dominique Duval. Absolute Factorization of Polynomials: A Geometric Approach. SIAM J. Comput., 20(1):1-21, 1991. · Zbl 0716.68052
[21] David J. Ford. On the computation of the maximal order in a Dedekind domain. PhD thesis, The Ohio State University, 1978.
[22] William Fulton. Hurwitz Schemes and Irreducibility of Moduli of Algebraic Curves. Ann. Math., 90(3):542-575, 1969. · Zbl 0194.21901
[23] Patrizia Gianni and Barry M. Trager. Integral Closure of Noetherian Rings. In Proc. ISSAC ’97, pages 212-216, New York, NY, USA, 1997. ACM. · Zbl 0927.13012
[24] Gert-Martin Greuel, Santiago Laplagne, and Frank Seelisch. Normalization of rings. J. Symb. Comput., 45(9):887-901, 2010. · Zbl 1200.13015
[25] Charles Hermite. Sur l’intégration des fractions rationnelles. Annales Scientifiques de l’É.N.S., 1:215-218, 1872. · JFM 04.0125.05
[26] Florian Hess. Computing Riemann-Roch Spaces in Algebraic Function Fields and Related Topics. J. Symb. Comput., 33(4):425-445, 2002. · Zbl 1058.14071
[27] Erich Kaltofen. Fast Parallel Absolute Irreducibility Testing. J. Symb. Comput., 1(1):57-67, 1985. · Zbl 0599.68038
[28] Nicholas M. Katz. Galois properties of torsion points on abelian varieties. Invent. Math., 62(3):481-502, Oct 1980. · Zbl 0471.14023
[29] Robert H. Risch. On the integration of elementary functions which are built up using algebraic operations. Technical report, System Development Corp Santa Monica Calif, 1968.
[30] Robert H. Risch. The solution of the problem of integration in finite terms. Bull. Amer. Math. Soc., 76(3):605-608, 1970. · Zbl 0196.06801
[31] Daniel Schultz. Trager’s Algorithm for Integration of Algebraic Functions Revisited. https://sites.psu.edu/dpsmath/files/2016/12/IntegrationOnCurves-2hhuby8.pdf.
[32] Barry M. Trager. Algebraic factoring and rational function integration. In Proc. ISSAC ’76, pages 219-226. ACM, 1976. · Zbl 0498.12005
[33] Barry M. Trager. Integration of Algebraic Functions. PhD thesis, Massachusetts Institute of Technology, 1984.
[34] Carlo Traverso. A study on algebraic algorithms: the normalization. Rend. Sem. Mat. Univ. Politec. Torino, 44:111-130, 1986. · Zbl 0643.14001
[35] Mark van Hoeij. An Algorithm for Computing an Integral Basis in an Algebraic Function Field. J. Symb. Comput., 18(4):353-363, 1994. · Zbl 0834.68059
[36] Emil J. Volcheck. Computing in the Jacobian of a plane algebraic curve. In Leonard M. Adleman and Ming-Deh Huang, editors, Algorithmic Number Theory, pages 221-233, Berlin, Heidelberg, 1994. Springer Berlin Heidelberg. · Zbl 0826.14040
[37] Umberto Zannier. Elementary integration of differentials in families and conjectures of Pink. In Proceedings of the International Congress of Mathematicians—Seoul 2014. Vol. II, pages 531-555. Kyung Moon Sa, Seoul, 2014. · Zbl 1373.11049
[38] Hans Zassenhaus. On the Second Round of the Maximal Order Program. In Applications of Number Theory to Numerical Analysis, pages 389-431. Elsevier, 1972. · Zbl 0248.12011
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