文献

以下是用于实现多项式操作模块的理论基础的非详尽出版物列表。

[Kozen89]

D. Kozen, S. Landau, Polynomial decomposition algorithms, Journal of Symbolic Computation 7 (1989), pp. 445-456

[Liao95]

Hsin-Chao Liao, R. Fateman, 启发式多项式GCD的评估, 符号与代数计算国际研讨会 (ISSAC), ACM Press, 蒙特利尔, 魁北克, 加拿大, 1995, pp. 240–247

[Gathen99]

J. von zur Gathen, J. Gerhard, Modern Computer Algebra, First Edition, Cambridge University Press, 1999

[Weisstein09]

Eric W. Weisstein, 分圆多项式, 来自 MathWorld - A Wolfram 网络资源, 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, 关于 Z_n 上多项式的就地算术, DISCO ‘92 会议论文集, Springer-Verlag LNCS, 721, 1993, 第 22–34 页

[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. 博斯, B. 布赫伯格, J.P. 吉弗, 多维系统理论与应用, 斯普林格, 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, 《计算机代数系统与代数计算算法》，学术出版社，伦敦，1988年，第124–128页

[Greuel2008]

G.-M. Greuel, Gerhard Pfister, 《交换代数导论》, Springer, 2008

[Atiyah69]

M.F. Atiyah, I.G. MacDonald, 《交换代数导论》, Addison-Wesley, 1969

[Collins67]

G.E. Collins, 子结式与简化多项式余数序列。J. ACM 14 (1967) 128-142

[BrownTraub71]

W.S. Brown, J.F. Traub, 关于欧几里得算法与子结式理论。J. ACM 18 (1971) 505-514

[Brown78]

W.S. Brown, 《子结式PRS算法。ACM数学软件交易 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, 关于欧几里得算法和多项式最大公约数的计算, J. ACM 18, 4, 第478-504页, 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, 一种单变量部分分式的p-adic算法, SYMSAC 1981会议论文集, 第212-217页, 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 和 Francis J. Wright，“快速多项式分散计算及其在不定求和中的应用”，国际符号和代数计算研讨会论文集，1994年，第175-180页 https://dl.acm.org/doi/10.1145/190347.190413

[Koepf98]

Wolfram Koepf, 《超几何求和：求和与特殊函数恒等式的算法方法》，高等数学讲座，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, “关于计算不定和的封闭形式”，《符号计算杂志》，第16卷，第4期，1993年，第355-376页 https://www.sciencedirect.com/science/article/pii/S0747717183710539

[Kapur1994]

Deepak Kapur, Tushar Saxena, 和 Lu Yang. “使用Dixon结式的代数和几何推理”, 在国际符号和代数计算研讨会(ISSAC ‘94)的会议录中, 1994年, 第99-107页. https://www.researchgate.net/publication/2514261_Algebraic_and_Geometric_Reasoning_using_Dixon_Resultants

[Palancz08]

B Paláncz, P Zaletnyik, JL Awange, EW Grafarend. “Dixon 结式的解法用于大地测量多项式方程组”, 《大地测量学杂志》, 2008, Springer, https://www.researchgate.net/publication/225607735_Dixon_resultant’s_solution_of_systems_of_geodetic_polynomial_equations.

[Bruce97]

Bruce Randall Donald, Deepak Kapur, 和 Joseph L. Mundy (编). “人工智能的符号和数值计算”, 第二章, Academic Press, Inc., Orlando, FL, USA, 1997, https://donaldlab.cs.duke.edu/Books/SymbolicNumericalComputation/045-087.pdf

[Stiller96]

P Stiller. “关于结式理论的介绍”，《数学与计算机科学》，T&M 大学，1996年，Citeseer，https://isc.tamu.edu/resources/preprints/1996/1996-02.pdf

[Cohen93]

Henri Cohen. 《计算代数数论课程》，Springer，1993年。

[Trager76]

Barry M. Trager. “代数因式分解与有理函数积分”，SYMSAC 1976 会议论文集，第219-226页，ACM，1976年。https://dl.acm.org/doi/abs/10.1145/800205.806338

[Yun76]

David Y.Y. Yun. “关于无平方分解算法”，《SYMSAC 1976会议论文集》，第219-226页，ACM，1976年。https://dl.acm.org/doi/10.1145/800205.806320

[Abbott13]

John Abbott. “Z[x] 中的因子界限”. 《符号计算杂志》50 (2013), pp. 532-563 https://doi.org/10.1016/j.jsc.2012.09.004