# A Polynomially Irreducible Functional Basis of Hemitropic Invariants of Piezoelectric Tensors

## TL;DR

This paper introduces a new, smaller functional basis of hemitropic invariants for piezoelectric tensors, reducing the number of invariants needed compared to previous minimal integrity bases, thus simplifying tensor analysis.

## Contribution

The authors construct a polynomially irreducible functional basis for piezoelectric tensors, significantly decreasing the number of invariants from prior minimal integrity bases.

## Key findings

- New basis has 260 invariants, fewer than previous 495.
- The basis is polynomially irreducible, ensuring minimal redundancy.
- Simplifies the analysis of piezoelectric tensors.

## Abstract

For piezoelectric tensors, Olive (2014) proposed a minimal integrity basis of 495 hemitropic invariants, which is also a functional basis. In this article, we construct a new functional basis of hemitropic invariants of piezoelectric tensors, using the approach of Smith and Zheng. By eliminating invariants that are polynomials in other invariants, we obtain a new functional basis with 260 polynomially irreducible hemitropic invariants. Thus, the number of hemitropic invariants in the new functional basis is substantially smaller than the number of invariants in a minimal integrity basis.