## A survey on algorithms for computing comprehensive Gröbner systems and comprehensive Gröbner bases.(English)Zbl 1417.68295

Summary: V. Weispfenning in [J. Symb. Comput. 14, No. 1, 1–29 (1992; Zbl 0784.13013)] introduced the concepts of comprehensive Gröbner system/basis of a parametric polynomial system, and he also presented an algorithm to compute them. Since then, this research field has attracted much attention over the past several decades, and many efficient algorithms have been proposed. Moreover, these algorithms have been applied to many different fields, such as parametric polynomial equations solving, geometric theorem proving and discovering, quantifier elimination, and so on. This survey brings together the works published between 1992 and 2018, and we hope that this survey is valuable for this research area.

### MSC:

 68W30 Symbolic computation and algebraic computation 13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 68-02 Research exposition (monographs, survey articles) pertaining to computer science

Zbl 0784.13013

### Software:

PGB; dpgb; parametric GCD
Full Text:

### References:

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