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?



Groebner basis with parameters
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.](https://www.sciencedirect.com/science/article/pii/S0747717111002082)
[Dehghani Darmian, Mahdi (IR-TEH-SMC); Hashemi, Amir (IR-IUT)
Parametric FGLM algorithm. (English summary)
J. Symbolic Comput. 82 (2017), 38–56.](https://www.sciencedirect.com/science/article/pii/S0747717116301705)
[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.](https://link.springer.com/chapter/10.1007/978-3-030-26831-2_13)
[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.](https://link.springer.com/article/10.1007/s10898-021-01082-3)








