  The coordinate Bethe Ansatz solution of the log-gamma polymer is extended to
boundary conditions with one fixed end and the other attached to one half of a
one-dimensional lattice. The large-time limit is studied using a saddle-point
approximation,and the cumulative distribution function of the rescaled free
energy of a long polymer is expressed as a Fredholm determinant. Scaling limits
of the kernel are identified, leading to a crossover from the GUE to the GOE
Tracy--Widom distributions. The continuum limit reproduces the crossover from
droplet to flat initial conditions of the Kardar--Parisi--Zhang equation.
