 It implies that computing, up to the formula_26-th power of formula_19, the Hamiltonian cycle polynomial of a unitary "n"×"n"-matrix over the infinite extension of any ring of characteristic q (not necessarily prime) by the formal variable formula_19 is a #q-P-complete problem if formula_32 isn't 2 and computing the Hamiltonian cycle polynomial of a formula_33-semi-unitary matrix (i.e.an "n"×"n"-matrix formula_34 such that formula_35) over such an extension of any ring of characteristic 2 is a #2-P-complete problem for any formula_33 > 0 (because any formula_33-semi-unitary matrix can be received from a unitary matrix via removing formula_33 rows and formula_33 columns).For formula_40 the latter statement can be re-formulated as the #2-P-completeness of computing, for a given unitary "n"×"n"-matrix formula_12 over a field of characteristic 2, the "n"×"n"-matrix formula_42 whose "i","j"-th entry is the Hamiltonian cycle polynomial of the matrix received from formula_12 via removing its "i"-th row and "j"-th column.