  A practical version of the polynomial canonical formalism is developed for
normal mesoscopic systems consisting of N independent electrons. Drastic
simplification of calculations is attained by means of proper ordering excited
states of the system. In consequence the exact canonical partition function can
be represented as a series in which the first term corresponds to the ground
state whereas successive groups of terms belong to many particle-hole
excitations (one particle-hole two particle-hole and so on). At small
temperatures (T<10 inter-level spacings near the Fermi level) the number of
terms which should be taken into account is weakly dependent on N and remains
<10 even if N~100000. The elaborated method makes canonical calculations to be
not more complicated than the grand canonical ones and is free from any
limitations on N and T.
