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In this paper, the Faddeev-Jackiw approach is improved by the Wu elimination method, so a great many complicated computations in solving constraints for the finite-dimensional polynomial-type constrained dynamics can be executed easily by using computers. Moreover, based on the Faddeev-Jackiw approach, a new algorithm of solving the constrained dynamics is presented. The new algorithm is simpler and stricter than the Faddeev-Jackiw approach. Using the new algorithm, the second Cawley counterexample is solved.

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