<> Marcus Hausdorf <> An Efficient Algebraic Algorithm for the Geometric Completion to Involution <> Applicable Algebra in Engineering, Communication and Computing <> 13 (2002) 163-207 <> www.springer.com/journal/200 <> doi.org/10.1007/s002000200099 <>

This paper contains mainly the results of the diploma thesis of my co-author (written under my supervision). It describes how the algebraic theory of involutive bases may be married with the geometric completion of differential equations according to the Cartan-Kuranishi theorem. By introducing a clever book-keeping, the simple completion algorithm of the Janet-Riquier theory is modified such that it returns intrinsic geometric information. The new algorithm returns precisely the same results as the one underlying our earlier works described in but needs much less computations. The algorithm has been implemented in our MuPAD environment for differential equations (see ).

We present in addition a new and very cheap method to detect singular coordinate systems in which the completion does not terminate. This new method even shows how one may algorithmically construct a regular coordinate system.

<> journals <> postscript <> 2002 <> involutive basis, differential equation, completion <> computer algebra, differential equations <>