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We consider recently developed Cohomological Field Theory soliton countingdiagram technique for Khovanov and Khovanov-Rozansky invariants [1,2]. Althoughthe expectation to obtain a new way for computing the invariants has not yetcome true, we demonstrate that soliton counting technique can be totallyformalized at an intermediate stage, at least in particular cases. We presentthe corresponding algorithm, based on the approach involving deformed$\mathcal{R}$-matrix and minimal positive division, developed previously in[3]. We start from a detailed review of the minimal positive division approach,comparing it with other methods, including the rigorous mathematical treatment[4]. Pieces of data obtained within our approach are presented in theAppendices.

Towards formalization of the soliton counting technique for the Khovanov-Rozansky invariants in the deformed $\mathcal{R}$-matrix approach