Computable Coordinate System Objects: Theory and Applications

Matrix operations are often used in coordinate system transformations, while tensoroperations are utilized in more general situations. The former belongs to the category of "raw"mathematical objects, which are not designed for coordinate system transformations andhave problems with redundancy and convenience in the calculation process. The latter isdifficult to master and challenging to use numerically. This paper introduces a specializedstructure object for coordinate system transformation as a substitute for matrix and tensoroperations.