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 |
| [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 |
| [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 |
