Literature

The following is a non-comprehensive list of publications that were used as a theoretical foundation for implementing the Diofant.

[Kozen89]D. Kozen, S. Landau, Polynomial decomposition algorithms, Journal of Symbolic Computation 7 (1989), pp. 445-456
[Liao95]Hsin-Chao Liao, R. Fateman, Evaluation of the heuristic polynomial GCD, International Symposium on Symbolic and Algebraic Computation (ISSAC), ACM Press, Montreal, Quebec, Canada, 1995, pp. 240–247
[Gathen99]J. von zur Gathen, J. Gerhard, Modern Computer Algebra, First Edition, Cambridge University Press, 1999
[Weisstein09]Eric W. Weisstein, Cyclotomic Polynomial, From MathWorld - A Wolfram Web Resource, http://mathworld.wolfram.com/CyclotomicPolynomial.html
[Wang78]P. S. Wang, An Improved Multivariate Polynomial Factoring Algorithm, Math. of Computation 32, 1978, pp. 1215–1231
[Geddes92]K. Geddes, S. R. Czapor, G. Labahn, Algorithms for Computer Algebra, Springer, 1992
[Monagan93]Michael Monagan, In-place Arithmetic for Polynomials over Z_n, Proceedings of DISCO ‘92, Springer-Verlag LNCS, 721, 1993, pp. 22–34
[Kaltofen98]E. Kaltofen, V. Shoup, Subquadratic-time Factoring of Polynomials over Finite Fields, Mathematics of Computation, Volume 67, Issue 223, 1998, pp. 1179–1197
[Shoup95]V. Shoup, A New Polynomial Factorization Algorithm and its Implementation, Journal of Symbolic Computation, Volume 20, Issue 4, 1995, pp. 363–397
[Gathen92]J. von zur Gathen, V. Shoup, Computing Frobenius Maps and Factoring Polynomials, ACM Symposium on Theory of Computing, 1992, pp. 187–224
[Shoup91]V. Shoup, A Fast Deterministic Algorithm for Factoring Polynomials over Finite Fields of Small Characteristic, In Proceedings of International Symposium on Symbolic and Algebraic Computation, 1991, pp. 14–21
[Cox97]D. Cox, J. Little, D. O’Shea, Ideals, Varieties and Algorithms, Springer, Second Edition, 1997
[Ajwa95]I.A. Ajwa, Z. Liu, P.S. Wang, Gröbner Bases Algorithm, 1995
[Bose03]N.K. Bose, B. Buchberger, J.P. Guiver, Multidimensional Systems Theory and Applications, Springer, 2003
[Giovini91]A. Giovini, T. Mora, “One sugar cube, please” or Selection strategies in Buchberger algorithm, ISSAC ‘91, ACM
[Bronstein93]M. Bronstein, B. Salvy, Full partial fraction decomposition of rational functions, Proceedings ISSAC ‘93, ACM Press, Kiev, Ukraine, 1993, pp. 157–160
[Buchberger01]B. Buchberger, Gröbner Bases: A Short Introduction for Systems Theorists, In: R. Moreno-Diaz, B. Buchberger, J. L. Freire, Proceedings of EUROCAST‘01, February, 2001
[Davenport88]J.H. Davenport, Y. Siret, E. Tournier, Computer Algebra Systems and Algorithms for Algebraic Computation, Academic Press, London, 1988, pp. 124–128
[Collins67]G.E. Collins, Subresultants and Reduced Polynomial Remainder Sequences. J. ACM 14 (1967) 128-142
[BrownTraub71]W.S. Brown, J.F. Traub, On Euclid’s Algorithm and the Theory of Subresultants. J. ACM 18 (1971) 505-514
[Brown78]W.S. Brown, The Subresultant PRS Algorithm. ACM Transaction of Mathematical Software 4 (1978) 237-249
[Monagan00]M. Monagan and A. Wittkopf, On the Design and Implementation of Brown’s Algorithm over the Integers and Number Fields, Proceedings of ISSAC 2000, pp. 225-233, ACM, 2000.
[Brown71]W.S. Brown, On Euclid’s Algorithm and the Computation of Polynomial Greatest Common Divisors, J. ACM 18, 4, pp. 478-504, 1971.
[Hoeij04]M. van Hoeij and M. Monagan, Algorithms for polynomial GCD computation over algebraic function fields, Proceedings of ISSAC 2004, pp. 297-304, ACM, 2004.
[Wang81]P.S. Wang, A p-adic algorithm for univariate partial fractions, Proceedings of SYMSAC 1981, pp. 212-217, ACM, 1981.
[Hoeij02]M. van Hoeij and M. Monagan, A modular GCD algorithm over number fields presented with multiple extensions, Proceedings of ISSAC 2002, pp. 109-116, ACM, 2002
[ManWright94]Yiu-Kwong Man and Francis J. Wright, “Fast Polynomial Dispersion Computation and its Application to Indefinite Summation”, Proceedings of the International Symposium on Symbolic and Algebraic Computation, 1994, Pages 175-180 https://dl.acm.org/citation.cfm?doid=190347.190413
[Koepf98]Wolfram Koepf, “Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities”, Advanced lectures in mathematics, Vieweg, 1998
[Abramov71]S. A. Abramov, “On the Summation of Rational Functions”, USSR Computational Mathematics and Mathematical Physics, Volume 11, Issue 4, 1971, Pages 324-330
[Man93]Yiu-Kwong Man, “On Computing Closed Forms for Indefinite Summations”, Journal of Symbolic Computation, Volume 16, Issue 4, 1993, Pages 355-376 https://www.sciencedirect.com/science/article/pii/S0747717183710539
[BenOr81]M. Ben-Or, Probabilistic algorithms in finite fields. In Proc. 22nd IEEE Symp. FoundationsComputer Science (1981), pp. 394-398.
[Adams94]W. Adams and P. Loustaunau, An Introduction to Gröbner Bases. AMS, Providence, Rhode Island., pp. 97-101, 1994.
[BeckerWeispfenning93]Thomas Becker, Volker Weispfenning, Gröbner bases: A computational approach to commutative algebra, 1993.
[KredelWeispfennig88]Computing dimension and independent sets for polynomial ideals. J. Symbolic Computation, 6(1):231–247, November 1988.
[Alkiviadis05]Alkiviadis G. Akritas and Adam W. Strzebonski: A Comparative Study of Two Real Root Isolation Methods. Nonlinear Analysis: Modelling and Control, Vol. 10, No. 4, 297-304, 2005.
[Alkiviadis08]Alkiviadis G. Akritas, Adam W. Strzebonski and Panagiotis S. Vigklas: Improving the Performance of the Continued Fractions Method Using new Bounds of Positive Roots. Nonlinear Analysis: Modelling and Control, Vol. 13, No. 3, 265-279, 2008.
[Alkiviadis09]Alkiviadis G. Akritas: Linear and Quadratic Complexity Bounds on the Values of the Positive Roots of Polynomials. Journal of Universal Computer Science, Vol. 15, No. 3, 523-537, 2009.
[Faugère94]J.C. Faugère, P. Gianni, D. Lazard, T. Mora (1994). Efficient Computation of Zero-dimensional Gröbner Bases by Change of Ordering.
[Niven91]Ivan Niven, Zuckerman and Montgomery. An introduction to the Theory of Numbers, 5th Edition, 1991.
[SunWang10]Yao Sun, Dingkang Wang: A New Proof for the Correctness of F5 (F5-Like) Algorithm”, https://arxiv.org/abs/1004.0084, 2010.
[Yokoyama89]Kazuhiro Yokoyama, Masayuki Noro, Taku Takeshima, Computing primitive elements of extension fields, Journal of Symbolic Computation, Volume 8, Issue 6, 1989, pp. 553-580, https://linkinghub.elsevier.com/retrieve/pii/S0747717189800616.
[Arno96]Steven Arno, M.L. Robinson, Ferell S. Wheeler, On Denominators of Algebraic Numbers and Integer Polynomials, Journal of Number Theory, Volume 57, Issue 2, 1996, pp. 292-302, https://linkinghub.elsevier.com/retrieve/pii/S0022314X96900499
[Bostan02]A. Bostan, P. Flajolet, B. Salvy and E. Schost “Fast Computation with Two Algebraic Numbers”, (2002) Research Report 4579, Institut National de Recherche en Informatique et en Automatique.
[Karr81]Michael Karr, “Summation in Finite Terms”, Journal of the ACM, Volume 28 Issue 2, April 1981, Pages 305-350, https://dl.acm.org/citation.cfm?doid=322248.322255
[Petkovšek97]Marko Petkovšek, Herbert S. Wilf, Doron Zeilberger, A = B, AK Peters, Ltd., Wellesley, MA, USA, 1997.
[AbramovBronstein95]S. A. Abramov, M. Bronstein and M. Petkovšek, On polynomial solutions of linear operator equations, in: T. Levelt, ed., Proc. ISSAC ‘95, ACM Press, New York, 1995, 290-296.
[Petkovšek92]M. Petkovšek, Hypergeometric solutions of linear recurrences with polynomial coefficients, J. Symbolic Computation, 14 (1992), 243-264.
[Abramov95]S. A. Abramov, Rational solutions of linear difference and q-difference equations with polynomial coefficients, in: T. Levelt, ed., Proc. ISSAC ‘95, ACM Press, New York, 1995, 285-289.
[Wester1999]Michael J. Wester, A Critique of the Mathematical Abilities of CA Systems, 1999, http://www.math.unm.edu/~wester/cas/book/Wester.pdf