  We compare the capabilities of two approaches to approximating graph
isomorphism using linear algebraic methods: the \emph{invertible map tests}
(introduced by Dawar and Holm) and proof systems with algebraic rules, namely
\emph{polynomial calculus}, \emph{monomial calculus} and \emph{Nullstellensatz
calculus}. In the case of fields of characteristic zero, these variants are all
essentially equivalent to the the Weisfeiler-Leman algorithms. In positive
characteristic we show that the invertible map method can simulate the monomial
calculus and identify a potential way to extend this to the monomial calculus.
