压电张量半透不变量的多项式不可约泛函基
A Polynomially Irreducible Functional Basis of Hemitropic Invariants of Piezoelectric Tensors
摘要：
对于压电张量，Olive（2014）提出了495个半向不变量的最小完整性基，这也是一个函数基。本文利用Smith和Zheng的方法，构造了压电张量的一个新的半度不变量泛函基。通过消除在其他不变量中为多项式的不变量，我们得到了一个新的具有260个多项式不可约半透不变量的函数基。因此，在新的功能基础的hemotropic不变量的数量是远远小于不变量的最小完整性基础。
英文摘要：
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.
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