Ac = Bd "theory And Wu Differential Characteristic And Its Applications

With the development of the computer and the constantly expanding of it's applied domain, symbol computation present gradually powerful bioenergy. In this paper, using the computer algebra as the tool and the differential algebra as the background , we discuss the theory of "AC=BD" and the differential characteristic method and their application in the differential equations .In 1978, professor Zhang hong qing uses the method of gebraic elimination and factorization in differential equations and successfully solve a great kind of the reducing problem of the over determined differential equations. He gives the method of "AC=BD" which used to solve the differential equations. Recently, this theories have a new development, and he forwards the C-D integrable system and C-D pairs. In chapter one, we discuss this theory and it's applications.In 1989,academician Wu Wen-tsun forwards wu differential characteristic method which establish theoretical basis for mechanical theorem proving of differential geometry and the research of automatic reasoning. We discuss the theories and applications of wu differential characteristic method in chapter two.As the particular case of the wu-differential characteristic sequence method Reid-standard form algorithm which play a great function in linear ordinary differential equations' system. Basing on it ,we discuss the applications of wu-method in differential equations in last chapter.