  We calculate the RT-invariants of all oriented Seifert manifolds directly
from surgery presentations. We work in the general framework of an arbitrary
modular category as in [V. G. Turaev, Quantum invariants of knots and
3--manifolds, de Gruyter Stud. Math. 18, Walter de Gruyter (1994)], and the
invariants are expressed in terms of the S- and T-matrices of the modular
category. In another direction we derive a rational surgery formula, which
states how the RT-invariants behave under rational surgery along framed links
in arbitrary closed oriented 3-manifolds with embedded colored ribbon graphs.
The surgery formula is used to give another derivation of the RT-invariants of
Seifert manifolds with orientable base.
