Computational algorithm for Boozer realizability

Develop a computational algorithm based on the Cartan–Kähler construction for obtaining local analytic magnetic fields that realize a prescribed field strength and specified Boozer-coordinate flux functions.

Background

The proof uses exterior differential systems, prolongation, and the Cartan–Kähler theorem to establish local existence, but it does not provide an implemented computational procedure for constructing the corresponding magnetic fields.

The authors observe that the sequence of Cauchy problems can in principle be recovered in local coordinates, while also noting that unpacking the tableau is algebraically complex. Turning this existence proof into an appropriate computational algorithm is therefore left unresolved.