Abstract
Formula manipulation is surveyed from two viewpoints, as a research tool and research theme in mathematical science. From the former viewpoint, current representative systems on formula manipulation are surveyed and how to utilize them effectively in actual research is explained. From the latter viewpoint, algorithms on symbolic determinant, polynomial GCD, polynomial factorization, standard basis of polynomial ideal, approximate sqaure-free decomposition, and approximate factorization are explained elementarily. By this, the author emphasizes that formula manipulation is now being developed rapidly and it is a very interesting and challenging research theme.
