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Lagrangian constraints and differential Thomas decomposition. (English) Zbl 1334.70050

Summary: In this paper we show how to compute algorithmically the full set of algebraically independent constraints for singular mechanical and field-theoretical models with polynomial Lagrangians. If a model under consideration is not singular as a whole but has domains of dynamical (field) variables where its Lagrangian becomes singular, then our approach allows to detect such domains and compute the relevant constraints. In doing so, we assume that the Lagrangian of a model is a differential polynomial and apply the differential Thomas decomposition algorithm to the Euler-Lagrange equations.

MSC:

70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
12H05 Differential algebra
68W30 Symbolic computation and algebraic computation
81T10 Model quantum field theories
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