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Okay, I found the solution. Finite vector spaces support iteration, so one can simply do

particular_soln = A.solve_right(b)
for homogeneous_soln in A.right_kernel():
    particular_soln + homogeneous_soln

Okay, I found the solution. Finite vector spaces support iteration, so one can simply dodo:

particular_soln = A.solve_right(b)
for homogeneous_soln in A.right_kernel():
    particular_soln + homogeneous_soln