added some ideas for the case of intervalls [a,b] of R

documents/math-minimal-distance-to-cubic-function/problem-description.tex

@@ -19,3 +19,11 @@ But minimizing $d_{P,f}$ is the same as minimizing $d_{P,f}^2$:
 
     Then: $f'(x_0) = 0$.
 \end{theorem}
+
+Let $S_n$ be the function that returns the set of solutions for a
+polynomial of degree $n$ and a point:
+
+\[S_n: \Set{\text{Polynomials of degree } n \text{ defined on } \mdr} \times \mdr^2 \rightarrow \mathcal{P}({\mdr})\]
+\[S_n(f, P) := \underset{x\in\mdr}{\arg \min d_{P,f}(x)}\]
+
+If possible, I will explicitly give this function.