Evaluating the likelihood function of parameters in complex population genetic models from extant deoxyribonucleic acid (DNA) sequences is computationally prohibitive. In such cases, one may approximately infer the parameters from various summary statistics of the data. Such method are known as approximate likelihood/Bayesian computations. We employ computational commutative algebraic methods to obtain the exact likelihood of a large class of summary statistics that are linear combinations of the site frequency spectrum.