Abstract. Center conditions for plane differential systems may be derived from Liapunov constants (also called focal values). The derivation, which involves very complicated polynomial calculations, was done traditionally with paper and pencil and is now performed mostly in computer algebra systems, making use of resultants, triangular sets, and Gröbner bases. The conditions derived with hand calculation or on computer interactively are often incomplete, or have redundancies, or contain errors. We propose to carry out a systematic and automated verification of the existing center conditions by means of irreducible decomposition of algebraic varieties. We shall present several examples to illustrate the need and significance of such a verification and show the computational difficulties that challenge the methods and software tools of polynomial elimination and decomposition.