Parametric greatest common divisors using comprehensive Gröbner systems. (English) Zbl 1458.13037
Burr, Michael (ed.), Proceedings of the 42nd international symposium on symbolic and algebraic computation, ISSAC 2017, Kaiserslautern, Germany, July 25–28, 2017. New York, NY: Association for Computing Machinery (ACM). 341-348 (2017).
MSC:
| 13P10 | Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) |
| 68W30 | Symbolic computation and algebraic computation |
Citations:
Zbl 0761.12005References:
| [1] | S. A. Abramov and K. Yu. Kvashenko. 1993. On the Greatest Common Divisor of Polynomials Which Depend on a Parameter. In Proceedings of the 18th International Symposium on Symbolic and Algebraic Computation (ISSAC 1993). ACM, New York, pages 152-156. x0-89791-604-2 10.1145/164081.164112 · Zbl 0925.13009 |
| [2] | Ali Ayad. 2010. Complexity of algorithms for computing greatest common divisors of parametric univariate polynomials. Int. J. Algebra 4, 1-4 (2010), pages 173-188. 1312-8868 · Zbl 1205.11133 |
| [3] | Ali Ayad, Ali Fares, and Youssef Ayyad. 2013. Parametric euclidean algorithm. Theoretical Mathematics and Applications 3, 3 (2013), pages 13-21. · Zbl 1321.68520 |
| [4] | Donna K. Dunaway. 1974. Calculation of zeros of a real polynomial through factorization using Euclid’s algorithm. SIAM J. Numer. Anal. 11 (1974), pages 1087-1104. 0036-1429 · Zbl 0292.65024 |
| [5] | Ioannis Z. Emiris, André Galligo, and Henri Lombardi. |
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