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Summary: The $r$-th order variational sequence is the quotient sequence of the De Rham sequence on the $r$th jet prolongation of a fibered manifold, factored through its contact subsequence.\par In this paper, the first order variational sequence on a fibered manifold with one-dimensional base is considered. A new representation of all quotient spaces as some spaces of (global) forms is given. The factorization procedure is based on a modification of the interior Euler operator, used in the theory of (infinite) variational bicomplexes.
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