  For two integers $a$ and $b$, the plum-blossom product of $a$ and $b$ is
defined as the ones of the usual product of $a$ and $b$ if the ones is less
than or equal to $3$, or otherwise as the ones minus $10$. Under this
operation, all integers is a commutative semigroup. Since some fine properties
of this semigroup, the plum-blossom product method is the efficient method of
multiplication and division of long integers, can be used to mental arithmetic
and to computer science. In this paper, we improve the theory of plum-blossom
products so that the new concept--the plum-blossom wedge product is proposed.
The plum-blossom wedge product is also of some good features so that it can be
applied to multiplication and division of long integers. The plum-blossom wedge
product method of multiplication and division is not only efficient in mental
arithmetic, but also could applied to improve the design of multipliers and
dividers of computer.
