By combining the ideas of Cartan's equivalence method and the method of the equivariant moving frame for pseudo-groups, we develop an efficient method for solving a wide variety of equivalence problems. The key is a pseudo-group analog of the classic result that characterizes congruence of submanifolds in Lie groups in terms of equivalence of the Lie group's Maurer-Cartan forms. This result, when combined with the fundamental recurrence formulas for the moving frame for pseudo-groups, will allow for a hybrid equivalence method that computationally improves on and illuminates both its progenitors.

中文翻译：

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渐进式移动镜架

通过将Cartan的等价方法和伪组的等变运动框架方法的思想相结合，我们开发了一种有效的方法来解决各种各样的等价问题。关键是经典结果的伪群类似物，该特征以李群Maurer-Cartan形式的等效性来表征李群中子流形的全等。当与伪组移动帧的基本递归公式结合使用时，此结果将允许使用一种混合等效方法，该方法在计算上改进并阐明了其祖细胞。