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The relationship between the strength of a differential equation as introducedby Einstein, its Cartan characters and its Hilbert polynomial is studied. Usingthe framework of formal theory previous results are extended to non-linearequations of arbitrary order and to over-determined systems. The problem ofcomputing the number of arbitrary functions in the general solution is treated.Finally, the effect of gauge symmetries is considered.PACS: 02.30.J Partial Differential Equations1...

On the arbitrariness of the general solution of an involutive partial differential equation