New algorithms for relaxed multiplication

In previous work, we have introduced the technique of relaxed power series computations. With this technique, it is possible to solve implicit equations almost as quickly as doing the operations which occur in the implicit equation. Here almost as quickly means that we need to pay a logarithmic overhead. In this paper, we will show how to reduce this logarithmic factor in the case when the constant ring has suuciently many 2 p-th roots of unity.