  The Bohnenblust-Hille inequality for $m$-linear forms was proven in 1931 as a
generalization of the famous 4/3-Littlewood inequality. The optimal constants
(or at least their asymptotic behavior as $m$ grows) is unknown, but
significant for applications. A recent result, obtained by Cavalcante, Teixeira
and Pellegrino, provides a kind of algorithm, composed by finitely many
elementary steps, giving as the final outcome the optimal truncated
Bohnenblust-Hille constants of any order. But the procedure of Cavalcante
\textit{et al.} has a fairly large number of calculations and computer
assistance cannot be avoided. In this paper we present a computational solution
to the problem, using the Wolfram Language. We also use this approach to
investigate a conjecture raised by Pellegrino and Teixeira, asserting that
$C_m=2^{1-1/m}$ for all $m\in\mathbb{N}$ and to reveal interesting unknown
facts about the geometry of $B_{\mathcal{L}(^3\mathbb{R}^3)}$.
