4. Disposal

Given a polynomial $f \in ℝ [X, Y]$ and the algebraic curve C with equation f (x,y) = 0, it's fairly easy to deduce geometric properties of the curve (or its projective closure $\bar{C} \subset {ℝℙ}^{2}$ ): for example, deciding whether C is smooth, finding the genus of $\bar{C}$ ...

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Disposal

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Bibliography

(1) - BENNEDETTI (R.), RISLER (J.-J.) - Real algebraic and semi-algebraic sets - Hermann (1990).
(2) - BASU (S.), POLLACK (R.), ROY (M.-F.) - Basic algorithms in real Algebraic Geometry - Springer (2003).
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