  When considering a real log canonical threshold (RLCT) that gives a Bayesian
generalization error, in general, papers replace a mean error function with a
relatively simple polynomial whose RLCT corresponds to that of the mean error
function, and obtain its RLCT by resolving its singularities through an
algebraic operation called blow-up. Though it is known that the singularities
of any polynomial can be resolved by a finite number of blow-up iterations, it
is not clarified whether or not it is possible to resolve singularities of a
specific polynomial by applying a specific blow-up algorithm. Therefore this
paper considers the blow-up algorithm for the polynomials called
sum-of-products (sop) polynomials and its RLCT.
