Integral Rational Syzygies in the System of Hemitropic Invariants for Two Asymmetric Second Rank Tensors. Examples

In present paper, the systems of entire rational hemitropic invariants for two asymmetric second-rank tensors in three-dimensional space are discussed and examples of rational syzygies for individual invariants are considered. The notion of a pseudo-invariant of a given algebraic weight for a pseudo-affinor are recalled. A generalization of the Hamilton–Cayley theorem for pseudo-affinors are revisited. The two equivalent systems of pseudo-invariants: the (S)-system and the (I)-system are introduced and employed. The Newton and Waring formulae for relations between these systems are discussed. A complete set of 86 irreducible absolute invariants for two symmetric and two antisymmetric affinors are represented. For individual invariants, the examples of integral rational syzygies are considered. The examples of syzygies are chosen to demonstrate the difference between correct and incorrect, regular and irregular syzygies.