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In this paper we show how to compute algorithmically the full set ofalgebraically independent constraints for singular mechanical andfield-theoretical models with polynomial Lagrangians. If a model underconsideration is not singular as a whole but has domains of dynamical (field)variables where its Lagrangian becomes singular, then our approach allows todetect such domains and compute the relevant constraints. In doing so, weassume that the Lagrangian of a model is a differential polynomial and applythe differential Thomas decomposition algorithm to the Euler-Lagrangeequations.

Lagrangian Constraints and Differential Thomas Decomposition