The Kontsevich deformation quantization combines Poisson dynamics,
noncommutative geometry, number theory, and calculus of oriented graphs. To
manage the algebra and differential calculus of series of weighted graphs, we
present software modules: these allow generating the Kontsevich graphs,
expanding the noncommutative $\star$-product by using a priori undetermined
coefficients, and deriving linear relations between the weights of graphs.
Throughout this text we illustrate the assembly of the Kontsevich
$\star$-product up to order 4 in the deformation parameter $\hbar$. Already at
this stage, the $\star$-product involves hundreds of graphs; expressing all
their coefficients via 149 weights of basic graphs (of which 67 weights are now
known exactly), we express the remaining 82 weights in terms of only 10
parameters (more specifically, in terms of only 6 parameters modulo
gauge-equivalence). Finally, we outline a scheme for computer-assisted proof of
the associativity, modulo $\bar{o}(\hbar^4)$, for the newly built
$\star$-product expansion.