example SageMath script solving underdetermined matrix

solve_right.sage

def solve_right(A, b):
  try: a = A.solve_right(b)
  except: return "no solution"
  if A.rank() == len(b): return a
  return (a, matrix(A.right_kernel().basis()))
         
# Solve matrix A with rank 2
F = IntegerModRing(5)
A = matrix(F, [[0,2,1,3],[4,0,1,0],[2,4,0,1]])
b = vector([4,2,4]) 
sol = solve_right(A, b)

# solution has more degrees of freedom (in this example 2)
if len(sol) == 2:
  c, x = sol
  print "x = %s + F^%s * [%s]" % (c, x.rank(), str(x).replace("\n", ""))
  # x = (3, 2, 0, 0) + F^2 * [[1 0 1 3][0 1 0 1]]
else:
  print "x = %s" % sol