# Generic separating sets for 3D elasticity tensors

## TL;DR

This paper introduces new sets of polynomial and rational invariants that can uniquely identify 3D elasticity tensors, simplifying their analysis and classification.

## Contribution

It presents the first explicit construction of generic separating sets for 3D elasticity tensors, including polynomial and rational invariants, and a new basis for harmonic tensors.

## Key findings

- Two polynomial invariant sets with 19 and 21 polynomials
- An 18-invariant rational set that is easier to compute
- A new integrity basis for the fourth-order harmonic tensor

## Abstract

We define what is a generic separating set of invariant functions (a.k.a. a weak functional basis) for tensors. We produce then two generic separating sets of polynomial invariants for 3D elasticity tensors, one made of 19 polynomials and one made of 21 polynomials (but easier to compute) and a generic separating set of 18 rational invariants. As a byproduct, a new integrity basis for the fourth-order harmonic tensor is provided.