  It is known that B\'{e}zier curves and surfaces may have multiple
representations by different control polygons. The polygons may have different
number of control points and may even be disjoint. Up to our knowledge,
Pekerman et al. (2005) were the first to address the problem of testing two
parametric polynomial curves for coincidence. Their approach is based on
reduction of the input curves into canonical irreducible form. They claimed
that their approach can be extended for testing tensor product surfaces but
gave no further detail. In this paper we develop a new technique and provide a
comprehensive solution to the problem of testing tensor product B\'ezier
surfaces for coincidence. In (Vlachkova, 2017) an algorithm for testing
B\'ezier curves was proposed based on subdivision. There a partial solution to
the problem of testing tensor product B\'ezier surfaces was presented. Namely,
the case where the irreducible surfaces are of same degree $(n,m)$, $n,m \in
\mathbb{N}$, was resolved under certain additional condition. The other cases
where one of the surfaces is of degree $(n,m)$ and the other is of degree
either $(n,n+m)$, or $(n+m,m)$, or $(n+m,n+m)$ remained open. We have
implemented our algorithm for testing tensor product B\'ezier surfaces for
coincidence using Mathematica package. Experimental results and their analysis
are presented.
