@article{865973,
      recid = {865973},
      author = {Montes, Antonio,},
      title = {The Gröbner cover /},
      pages = {1 online resource (xiv, 268 pages) :},
      abstract = {This book is divided into two parts, one theoretical and  one focusing on applications, and offers a complete  description of the Canonical Gröbner Cover, the most  accurate algebraic method for discussing parametric  polynomial systems. It also includes applications to the  Automatic Deduction of Geometric Theorems, Loci Computation  and Envelopes. The theoretical part is a self-contained  exposition on the theory of Parametric Gröbner Systems and  Bases. It begins with Weispfenning's introduction of  Comprehensive Gröbner Systems (CGS) in 1992, and provides a  complete description of the Gröbner Cover (GC), which  includes a canonical discussion of a set of parametric  polynomial equations developed by Michael Wibmer and the  author. In turn, the application part selects three  problems for which the Gröbner Cover offers valuable new  perspectives. The automatic deduction of geometric theorems  (ADGT) becomes fully automatic and straightforward using  GC, representing a major improvement on all previous  methods. In terms of loci and envelope computation, GC  makes it possible to introduce a taxonomy of the components  and automatically compute it. The book also generalizes the  definition of the envelope of a family of hypersurfaces,  and provides algorithms for its computation, as well as for  discussing how to determine the real envelope. All the  algorithms described here have also been included in the  software library "grobcov.lib" implemented in Singular by  the author, and serve as a User Manual for it.},
      url = {http://library.usi.edu/record/865973},
      doi = {https://doi.org/10.1007/978-3-030-03904-2},
}