Full order_alpha electroweak and order alpha_s corrections to e^+e^- --> t t H

We present the full ${{cal O}}(alpha)$ electroweak radiative corrections to associated Higgs top pair production in $e^+e^-$ collisions. We combine these results with a new calculation of the full one-loop QCD corrections. The computation is performed with the help of {tt GRACE-loop}. We find that the ${{cal O}}(alpha)$ correction can be larger than the ${{cal O}}(alpha_s)$ corrections around the peak of the cross section especially for a light Higgs mass. At threshold these corrections are swamped by the QCD corrections which are enhanced by the gluon Coulomb contribution. We have also subtracted the complete QED corrections and expressed the genuine weak correction both in the $alpha$-scheme and the $G_mu$-scheme. This reveals that the genuine weak corrections are not negligible and should be taken into account for a precision measurement of this cross section and the extraction of the Yukawa $t bar t H$ coupling.