In this article, we discuss how to algebraically compute (approximates of) partial invariants I of a dynamical system by comparison of coefficients. Because for a certain value C of a partial invariant function I the level set solving \(I(x)=C\) is an invariant manifold, the discussed algebraic approach is an alternative to the well-known graph transform resp. parametrization method for the computation of invariant manifolds. We particularly explore the algebraic computation of invariant manifolds in case of (non-integrable) Hamiltonian systems, which can be considered as models of energy-preserving mechanical systems.