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, https://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://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=2bb46c0852bf74c9d74d1a12af6d11f69f7e8363, 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 https://dl.acm.org/doi/10.1145/190347.190413

[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

[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://donaldlab.cs.duke.edu/Books/SymbolicNumericalComputation/045-087.pdf

[Stiller96]

P Stiller. “An introduction to the theory of resultants”, Mathematics and Computer Science, T&M University, 1996, Citeseer, https://isc.tamu.edu/resources/preprints/1996/1996-02.pdf

[Cohen93]

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

[Trager76]

Barry M. Trager. “Algebraic factoriing and rational function integration”, Proceedings of SYMSAC 1976, pp. 219-226, ACM, 1976. https://dl.acm.org/doi/abs/10.1145/800205.806338

[Yun76]

David Y.Y. Yun. “On square-free decomposition algorithms”, Proceedings of SYMSAC 1976, pp. 219-226, ACM, 1976. https://dl.acm.org/doi/10.1145/800205.806320

[Abbott13]

John Abbott. “Bounds on factors in Z[x]”. Journal of Symbolic Computation 50 (2013), pp. 532-563 https://doi.org/10.1016/j.jsc.2012.09.004