Improved polynomial arithmetic algorithm implementations

Polynomial, as one of the most basic mathematical forms, is widely applied to theories and practical engineering. And the effective machinery calculation of polynomial can greatly contribute to the practical uses. Hence, a new approach of polynomial storage, coefficients and index number stored in an array, has been put forward for study. In this article, different methods of three vital calculations have been theoretically deduced, partially verified and realized in program via the new approach previously mentioned, and its detailed steps have been proposed as well to show the advantages of the new storage method.