Literature¶
The following is a non-comprehensive list of publications that were used as a theoretical foundation for implementing polynomials manipulation module.
D. Kozen, S. Landau, Polynomial decomposition algorithms, Journal of Symbolic Computation 7 (1989), pp. 445-456
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
J. von zur Gathen, J. Gerhard, Modern Computer Algebra, First Edition, Cambridge University Press, 1999
Eric W. Weisstein, Cyclotomic Polynomial, From MathWorld - A Wolfram Web Resource, http://mathworld.wolfram.com/CyclotomicPolynomial.html
P. S. Wang, An Improved Multivariate Polynomial Factoring Algorithm, Math. of Computation 32, 1978, pp. 1215–1231
K. Geddes, S. R. Czapor, G. Labahn, Algorithms for Computer Algebra, Springer, 1992
Michael Monagan, In-place Arithmetic for Polynomials over Z_n, Proceedings of DISCO ‘92, Springer-Verlag LNCS, 721, 1993, pp. 22–34
E. Kaltofen, V. Shoup, Subquadratic-time Factoring of Polynomials over Finite Fields, Mathematics of Computation, Volume 67, Issue 223, 1998, pp. 1179–1197
V. Shoup, A New Polynomial Factorization Algorithm and its Implementation, Journal of Symbolic Computation, Volume 20, Issue 4, 1995, pp. 363–397
J. von zur Gathen, V. Shoup, Computing Frobenius Maps and Factoring Polynomials, ACM Symposium on Theory of Computing, 1992, pp. 187–224
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
D. Cox, J. Little, D. O’Shea, Ideals, Varieties and Algorithms, Springer, Second Edition, 1997
I.A. Ajwa, Z. Liu, P.S. Wang, Groebner Bases Algorithm, https://citeseer.ist.psu.edu/myciteseer/login, 1995
N.K. Bose, B. Buchberger, J.P. Guiver, Multidimensional Systems Theory and Applications, Springer, 2003
A. Giovini, T. Mora, “One sugar cube, please” or Selection strategies in Buchberger algorithm, ISSAC ‘91, ACM
M. Bronstein, B. Salvy, Full partial fraction decomposition of rational functions, Proceedings ISSAC ‘93, ACM Press, Kiev, Ukraine, 1993, pp. 157–160
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
J.H. Davenport, Y. Siret, E. Tournier, Computer Algebra Systems and Algorithms for Algebraic Computation, Academic Press, London, 1988, pp. 124–128
G.-M. Greuel, Gerhard Pfister, A Singular Introduction to Commutative Algebra, Springer, 2008
M.F. Atiyah, I.G. MacDonald, Introduction to Commutative Algebra, Addison-Wesley, 1969
G.E. Collins, Subresultants and Reduced Polynomial Remainder Sequences. J. ACM 14 (1967) 128-142
W.S. Brown, J.F. Traub, On Euclid’s Algorithm and the Theory of Subresultants. J. ACM 18 (1971) 505-514
W.S. Brown, The Subresultant PRS Algorithm. ACM Transaction of Mathematical Software 4 (1978) 237-249
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.
W.S. Brown, On Euclid’s Algorithm and the Computation of Polynomial Greatest Common Divisors, J. ACM 18, 4, pp. 478-504, 1971.
M. van Hoeij and M. Monagan, Algorithms for polynomial GCD computation over algebraic function fields, Proceedings of ISSAC 2004, pp. 297-304, ACM, 2004.
P.S. Wang, A p-adic algorithm for univariate partial fractions, Proceedings of SYMSAC 1981, pp. 212-217, ACM, 1981.
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
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
Wolfram Koepf, “Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities”, Advanced lectures in mathematics, Vieweg, 1998
S. A. Abramov, “On the Summation of Rational Functions”, USSR Computational Mathematics and Mathematical Physics, Volume 11, Issue 4, 1971, Pages 324-330
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
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
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.
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.
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.
Henri Cohen. “A Course in Computational Algebraic Number Theory”, Springer, 1993.
