  We introduce a unital associative algebra A over degenerate CP^1. We show
that A is a commutative algebra and whose Poincar'e series is given by the
number of partitions. Thereby we can regard A as a smooth degeneration limit of
the elliptic algebra introduced by one of the authors and Odesskii. Then we
study the commutative family of the Macdonald difference operators acting on
the space of symmetric functions. A canonical basis is proposed for this family
by using A and the Heisenberg representation of the commutative family studied
by one of the authors. It is found that the Ding-Iohara algebra provides us
with an algebraic framework for the free filed construction. An elliptic
deformation of our construction is discussed, showing connections with the
Drinfeld quasi-Hopf twisting a la Babelon Bernard Billey, the Ruijsenaars
difference operator and the operator M(q,t_1,t_2) of Okounkov-Pandharipande.
