# Invariants for sets of vectors and rank 2 tensors, and differential invariants for vector functions

## TL;DR

This paper presents an algorithm for constructing complete sets of invariants under rotation for sets of vectors and rank 2 tensors, including differential invariants for vector functions, extending previous results to antisymmetric tensors.

## Contribution

It introduces a new algorithm for generating functional bases of invariants for vectors and tensors, incorporating antisymmetric tensors and differential invariants for vector functions.

## Key findings

- Constructed functional bases of invariants under rotation.
- Extended results to include antisymmetric tensors.
- Developed differential invariants for vector functions, including Maxwell's equations.

## Abstract

We outline an algorithm for construction of functional bases of absolute invariants under the rotation group for sets of rank 2 tensors and vectors in the Euclidean space of arbitrary dimension. We will use our earlier results for symmetric tensors and add results for sets including antisymmetric tensors of rank 2. That allowed, in particular, constructing of functional bases of differential invariants for vector functions, in particular, of first-order invariants of Poincar\'e algebra (invariance algebra of Maxwell equations for vector potential).