Before revision:  We show that both problems of minimizing either the number of variables (i.e., molecular species) or the number of mono-mials (i.e. elementary reactions) in a binomial transformation of a PIVP are NP-hard.
After revision:  We show that both problems of minimizing either the number of variables (i.e., molecular species) or the number of mono-mials (i.e. elementary reactions) in a quadratic transformation of a PIVP are NP-hard.