  Based on an idea in Hironaka's proof of resolution of singularities, we
present an algorithmic smoothness test for algebraic varieties. The test is
inherently parallel and does not involve the calculation of codimension-sized
minors of the Jacobian matrix of the variety. We also describe a hybrid method
which combines the new method with the Jacobian criterion, thus making use of
the strengths of both approaches. We have implemented all algorithms in the
computer algebra system Singular, and compare the different approaches with
respect to timings and memory usage. The test examples originate from questions
in algebraic geometry, where the use of the Jacobian criterion is impractical
due to the number and size of the minors involved.

Algebraic Geometry