Groebner basis with parameters

Question

I need to compute a Groebner basis of a polynomial system with parameters. The only recent results I found is Groebner cover:

https://www.sciencedirect.com/science/article/pii/S0747717110000970

Are there any more advanced algorithms for the study of parametric polynomial systems?

Answer 1

Mathscinet mentions some 30 papers citing the paper you mention, among which the following looks like potentially relevant:

Kapur, Deepak (1-NM-C); Sun, Yao (PRC-ASBJ-MML); Wang, Dingkang (PRC-ASBJ-MML) An efficient algorithm for computing a comprehensive Gröbner system of a parametric polynomial system. (English summary) J. Symbolic Comput. 49 (2013), 27–44.

Dehghani Darmian, Mahdi (IR-TEH-SMC); Hashemi, Amir (IR-IUT) Parametric FGLM algorithm. (English summary) J. Symbolic Comput. 82 (2017), 38–56.

Hashemi, Amir (IR-IUT); Kazemi, Mahsa (IR-IUT) Parametric standard bases and their applications. (English summary) Computer algebra in scientific computing, 179–196, Lecture Notes in Comput. Sci., 11661, Springer, Cham, 2019.

Ponleitner, Bettina (A-WIENM); Schichl, Hermann (A-WIENM) Exclusion regions for parameter-dependent systems of equations. (English summary) J. Global Optim. 81 (2021), no. 3, 621–644.