  By using the algebraic separability criterion of R. Simon, we present an
explicit determination of squeezing parameters for which the P-representation
condition saturates the $Sp(2,R)\otimes Sp(2,R)$ invariant separability
condition for continuous variable two-party Gaussian systems. We thus give for
the first time the explicit analytic formulas of squeezing parameters which
establish the equivalence of the separability condition with the
P-representation condition. The implications of our algebraic analysis on some
of the past related works are discussed.
