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We present a new high-order coupled cluster method (CCM) formalism for theground states of lattice quantum spin systems for general spin quantum number,$s$. This new ``general-$s$'' formalism is found to be highly suitable for acomputational implementation, and the technical details of this implementationare given. To illustrate our new formalism we perform high-order CCMcalculations for the one-dimensional spin-half and spin-one antiferromagnetic{\it XXZ} models and for the one-dimensional spin-half/spin-one ferrimagnetic{\it XXZ} model. The results for the ground-state properties of the isotropicpoints of these systems are seen to be in excellent quantitative agreement withexact results for the special case of the spin-half antiferromagnet and resultsof density matrix renormalisation group (DMRG) calculations for the othersystems. Extrapolated CCM results for the sublattice magnetisation of thespin-half antiferromagnet closely follow the exact Bethe Ansatz solution, whichcontains an infinite-order phase transition at $\Delta=1$. By contrast,extrapolated CCM results for the sublattice magnetisation of the spin-oneantiferromagnet using this same scheme are seen to go to zero at $\Delta\approx 1.2$, which is in excellent agreement with the value for the onset ofthe Haldane phase for this model. Results for sublattice magnetisations of theferrimagnet for both the spin-half and spin-one spins are non-zero and finiteacross a wide range of $\Delta$, up to and including the Heisenberg point at$\Delta=1$.Comment: 5 Figures. J. Stat. Phys. 108, p. 401 (2002

Coupled Cluster Method Calculations Of Quantum Magnets With Spins Of General Spin Quantum Number