Spherical geometry other geometric concepts are defined as in plane geometry, but with straight lines replaced by great circles. Thus, in spherical geometry, angles are defined between great circles, resulting in a spherical trigonometry that differs from ordinary trigonometry in many respects; for example, the sum of the interior angles of a triangle exceeds 180 degrees. Spherical geometry is "not" elliptic geometry, but is rather a "subset" of elliptic geometry. For example, it shares with that geometry the property that a line has no parallels through a given point. Contrast this with Euclidean geometry, in which a line has one parallel through
Algebraic geometry point in every connected component of a semi-algebraic set, and thus to test if a semi-algebraic set is empty. On the other hand, CAD is yet, in practice, the best algorithm to count the number of connected components. The basic general algorithms of computational geometry have a double exponential worst case complexity. More precisely, if "d" is the maximal degree of the input polynomials and "n" the number of variables, their complexity is at most formula_16 for some constant "c", and, for some inputs, the complexity is at least formula_17 for another constant "c"′. During the last 20 years of