Equations, inequations and inequalities characterizing the configurations of two real projective conics

Details Equations, inequations and inequalities characterizing the configurations of two real projective conics Equations, inequations and inequalities characterizing the configurations of two real projective conics

2005-05-29

arxiv.org/abs/math/0505628v2

Applicable Algebra in Engineering, Communication and Computing, Volume 18, Numbers 1-2 / february 2007, Page 21-52

Mathematics

Commutative Algebra

31 pages. See also http://emmanuel.jean.briand.free.fr/publications/twoconics/ Added references to important prior work on t

Scientific paper

10.1007/s00200-006-0023-8

Couples of proper, non-empty real projective conics can be classified modulo rigid isotopy and ambient isotopy. We characterize the classes by equations, inequations and inequalities in the coefficients of the quadratic forms defining the conics. The results are well--adapted to the study of the relative position of two conics defined by equations depending on parameters.

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