平面/轴向张量对称的约化代数条件
Reduced algebraic conditions for plane/axial tensorial symmetries
摘要：
在这篇文章中，我们制定的必要和充分的多项式方程的对称平面或二阶轴对称的阶数为n $\ge$ 1的全对称张量的存在。这些条件是有效的，并且在平面的法线（或轴对称方向）的分量中具有n次（张量的阶）。然后将这些结果推广到弹性张量、压电张量和压磁伪张量存在这种对称性的充要多项式条件。
英文摘要：
In this article, we formulate necessary and sufficient polynomial equations for the existence of a symmetry plane or an order-two axial symmetry for a totally symmetric tensor of order n $\ge$ 1. These conditions are effective and of degree n (the tensor's order) in the components of the normal to the plane (or the direction of the axial symmetry). These results are then extended to obtain necessary and sufficient polynomial conditions for the existence of such symmetries for an Elasticity tensor, a Piezo-electricity tensor or a Piezo-magnetism pseudo-tensor.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
