  We show thatthe double reversing algorithm proposed by dehornoy for solving
the word problem in the braid group can also be used to recognize the
conjugates of powers of the generators in an Artin group of spherical type. The
proof uses a characterization of these powers in terms of their fractional
decomposition. This algorithm could have potential applications to braid-based
cryptography; it also provides a fast method for testing a necessary condition
in the classification of surfaces in algebraic geometry.
