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Using Maple’s RegularChains library to automatically classify plane geometric loci. (English) Zbl 1437.13043
Hong, Hoon (ed.) et al., Mathematical software – ICMS 2014. 4th international congress, Seoul, South Korea, August 5–9, 2014. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 8592, 500-503 (2014).
Summary: We report a preliminary discussion on the usability of the RegularChains library of Maple for the automatic computation of plane geometric loci and envelopes in graphical interactive environments. We describe a simple implementation of a recently proposed taxonomy of algebraic loci, and its extension to envelopes of families of curves is also discussed. Furthermore, we sketch how currently unsolvable problems in interactive environments can be approached by using the RegularChains library.
For the entire collection see [Zbl 1293.65003].
MSC:
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
14Q65 Geometric aspects of numerical algebraic geometry
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
Software:
Maple; RegularChains
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