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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

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

Citations:

Zbl 0635.00018