Investigation of a real algebraic surface. (English. Russian original) Zbl 1349.14178

Program. Comput. Softw. 41, No. 2, 74-83 (2015); translation from Programmirovanie 41, No. 2 (2015).
Summary: A description of a real algebraic variety in \(\mathbb{R}^{3}\) is given. This variety plays an important role in the investigation of the Einstein metrics whose evolution is studied using the normalized Ricci flow. To reveal the internal structure of this variety, a description of all its singular points is given. Due to the internal symmetry of this variety, a part of the investigation uses elementary symmetric polynomials. All the computations are performed using computer algebra algorithms (in particular, Gröbner bases) and algorithms for dealing with polynomial ideals. As an auxiliary result, a proposition about the structure of the discriminant surface of a cubic polynomial is proved.


14P05 Real algebraic sets
14Q10 Computational aspects of algebraic surfaces
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
53A05 Surfaces in Euclidean and related spaces
68W30 Symbolic computation and algebraic computation


desing; PGeomlib
Full Text: DOI


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