Combining the process-chain method with a symbolized evaluation we work out in detail a highorder symbolic strong-coupling expansion (HSSCE) for determining the quantum phase boundaries between the Mott insulator and the superfluid phase of the Bose-Hubbard model for different fillings in hypercubic lattices of different dimensions. With a subsequent Padé approximation we achieve for the quantum phase boundaries a high accuracy, which is comparable to high-precision quantum Monte-Carlo simulations, and show that all the Mott lobes can be rescaled to a single one. As a further cross-check, we find that the HSSCE results coincide with a hopping expansion of the quantum phase boundaries, which follow from the effective potential Landau theory (EPLT).In order to obtain higher orders than the 10th order, Eckardt et al. developed a computer assisted processchain algorithm (PCA) 19,20 based on Kato's formulation of the perturbation calculus. 21 Using the PCA, highprecision results were obtained for both the ground-state energy and the correlation function within the Mott insulator. 20 Furthermore, by implementing PCA for the effective potential Landau theory (EPLT), 22,23 the critical line of the quantum phase transition from the Mott insulator to the superfluid phase was determined with high precision 20,24 so that even the corresponding critical exponents can be extracted. 25 In order to deal with degenerate states, such as particle-hole excitations, the