covariants background

covariants

/koʊˈveəriənts/ /ˌkoʊˈveəriənts/

Illustration covariants - Image 1

noun

协变量，共变式

A bihomogeneous polynomial in x, y, ... and the coefficients of some homogeneous form in x, y, ... that is invariant under some group of linear transformations.

Examples :

"In advanced mathematics, students study covariants to understand how certain polynomial expressions remain unchanged even when the coordinate system is altered. "

在高等数学中，学生们学习协变量（共变式），从而理解某些多项式表达式如何在坐标系改变时保持不变。

Illustration covariants - Image 1

noun

协变式簇，共变式族

The variety defined by a covariant.

Examples :

"In geometry, the covariants of a set of shapes determine other shapes that are intrinsically linked to the original set. "

在几何学中，一组形状的协变式簇决定了与其他原始形状集合内在相关的其他形状。