Jz. Zhang et al., A CRITERION FOR DEPENDENCY OF ALGEBRAIC EQUATIONS WITH APPLICATIONS TO AUTOMATED THEOREM-PROVING, Science in China. Series A, Mathematics, Physics, Astronomy & Technological Sciences, 37(5), 1994, pp. 547-554
In this paper, a characteristic-set-based criterion is given to verify
whether a polynomial is vanishing over an algebraic variety. The algo
rithm is feasible in practice, and does not depend on the decompositio
n of the variety.