  Based on previous studies deriving the chiral Lagrangian for pseudo scalar
mesons from the first principle of QCD, we derive the electroweak chiral
Lagrangian and build up a formulation for computing its coefficients from
one-doublet technicolor model and a schematic topcolor-assisted technicolor
model. We find that the coefficients of the electroweak chiral Lagrangian for
the topcolor-assisted technicolor model are divided into three parts: direct
TC2 interaction part, TC1 and TC2 induced effective Z' particle contribution
part, and ordinary quarks contribution part. The first two parts are computed
in this paper and we show that the direct TC2 interaction part is the same as
that in the one-doublet technicolor model, while effective Z' contributions are
at least proportional to the p^2 order parameter \beta_1 in the electroweak
chiral Lagrangian and typical features of topcolor-assisted technicolor model
are that it only allows positive T and U parameters and the T parameter varies
in the range 0\sim 1/(25\alpha), the upper bound of T parameter will decrease
as long as Z' mass become large. The S parameter can be either positive or
negative depending on whether the Z' mass is large or small. The Z' mass is
also bounded above and the upper bound depend on value of T parameter. We
obtain the values for all the coefficients of the electroweak chiral Lagrangian
up to order of p^4.
