  Solving of regular equations via Arden's Lemma is folklore knowledge.
  We first give a concise algorithmic specification of all elementary solving
steps.
  We then discuss a computational interpretation of solving in terms of
coercions that transform parse trees of regular equations into parse trees of
solutions.
  Thus, we can identify some conditions on the shape of regular equations under
which resulting solutions are unambiguous.
  We apply our result to convert a DFA to an unambiguous regular expression.
  In addition, we show that operations such as subtraction and shuffling can be
expressed via some appropriate set of regular equations.
  Thus, we obtain direct (algebraic) methods without having to convert to and
from finite automaton.
