Computable Linearizations of Well-partial-orderings

We analyze results on well-partial-orderings from the viewpoint of computability theory, and we answer a question posed by Diana Schmidt. We obtain the following results. De Jongh and Parikh showed that every well-partial-order has a linearization of maximal order type. We show that such a linearization can be found computably. We also show that the process of finding such a linearization is not computably uniform, not even hyperarithmetically.