  A rational number can be naturally presented by an arithmetic computation
(AC): a sequence of elementary arithmetic operations starting from a fixed
constant, say 1. The asymptotic complexity issues of such a representation are
studied e.g. in the framework of the algebraic complexity theory over arbitrary
field.
  Here we study a related problem of the complexity of performing arithmetic
operations and computing elementary predicates, e.g. ``='' or ``>'', on
rational numbers given by AC.
  In the first place, we prove that AC can be efficiently simulated by the
exact semidefinite programming (SDP).
  Secondly, we give a BPP-algorithm for the equality predicate.
  Thirdly, we put ``>''-predicate into the complexity class PSPACE.
  We conjecture that ``>''-predicate is hard to compute. This conjecture, if
true, would clarify the complexity status of the exact SDP - a well known open
problem in the field of mathematical programming.
