Buchberger, Bruno Applications of Gröbner bases in nonlinear computational geometry. (English) Zbl 0653.13012 Trends in computer algebra, Int. Symp., Bad Neuenahr/FRG 1987, Lect. Notes Comput. Sci. 296, 52-80 (1988). [For the entire collection see Zbl 0635.00018.] The method of Gröbner bases provides an algorithmic method to attack a huge number of problems in algebraic geometry and polynomial ideal theory, whereas classically algebraic geometry only was concerned for existence theorems. Apart from a review of the most important results in the subject, we get various applications of the method: inverse robot kinematics, implicitization of parametric objects, detection of singularities, geometrical theorem proving and primary decomposition of ideals and algebraic manifolds. Reviewer: G.Molenbergh Cited in 6 Documents MSC: 13F20 Polynomial rings and ideals; rings of integer-valued polynomials 68W30 Symbolic computation and algebraic computation 13-04 Software, source code, etc. for problems pertaining to commutative algebra Keywords:Gröbner bases; polynomial ideal theory; inverse robot kinematics; parametric objects; geometrical theorem proving Citations:Zbl 0635.00018 PDFBibTeX XML