Literature

The following is a non-comprehensive list of publications that were used as a theoretical foundation for implementing polynomials manipulation module.

[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, Groebner Bases Algorithm, https://citeseer.ist.psu.edu/myciteseer/login, 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, Groebner 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
[Greuel2008]G.-M. Greuel, Gerhard Pfister, A Singular Introduction to Commutative Algebra, Springer, 2008
[Atiyah69]M.F. Atiyah, I.G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley, 1969
[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 http://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 http://www.sciencedirect.com/science/article/pii/S0747717183710539

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