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

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 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

Kapur1994

Deepak Kapur, Tushar Saxena, and Lu Yang. “Algebraic and geometric reasoning using Dixon resultants”, In Proceedings of the international symposium on Symbolic and algebraic computation (ISSAC ‘94), 1994, pages 99-107. https://www.researchgate.net/publication/2514261_Algebraic_and_Geometric_Reasoning_using_Dixon_Resultants

Palancz08

B Paláncz, P Zaletnyik, JL Awange, EW Grafarend. “Dixon resultant’s solution of systems of geodetic polynomial equations”, Journal of Geodesy, 2008, Springer, https://www.researchgate.net/publication/225607735_Dixon_resultant’s_solution_of_systems_of_geodetic_polynomial_equations.

Bruce97

Bruce Randall Donald, Deepak Kapur, and Joseph L. Mundy (Eds.). “Symbolic and Numerical Computation for Artificial Intelligence”, Chapter 2, Academic Press, Inc., Orlando, FL, USA, 1997, https://www2.cs.duke.edu/donaldlab/Books/SymbolicNumericalComputation/045-087.pdf.

Stiller96

P Stiller. “An introduction to the theory of resultants”, Mathematics and Computer Science, T&M University, 1996, Citeseer, http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.590.2021&rep=rep1&type=pdf.

Cohen93

Henri Cohen. “A Course in Computational Algebraic Number Theory”, Springer, 1993.

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