Range Enclosure
Enclosure property
Let $p$ be a polynomial $n$ variables of degree $l = (l_1, \ldots, l_n)$,
\[ p(x) = \sum_{i=0}^l a_i x^i,\qquad x = (x_1, \ldots, x_n),\]
and the axis-aligned hyperrectangular set $X$.
Range enclosure using Bernstein expansion is to compute a tight outer approximation for $p(X)$, the range of $p$ over $X$. Such bounds can be determined by using the coefficients of the expansion of the given polynomial into Bernstein polynomials.
TODO: add property
\[ \min_{i} b_i ≤ p(x) ≤ \max b_i.\]
Examples
using BernsteinExpansions, DynamicPolynomials
@polyvar x y(x, y)