An OpenMath Content Dictionary for Tensor Concepts

Details An OpenMath Content Dictionary for Tensor Concepts An OpenMath Content Dictionary for Tensor Concepts

2010-05-24

arxiv.org/abs/1005.4395v1

Computer Science

Mathematical Software

To appear in The 9th International Conference on Mathematical Knowledge Management: MKM 2010

Scientific paper

We introduce a new OpenMath content dictionary, named tensor1, containing symbols for the expression of tensor formulas. These symbols support the expression of non-Cartesian coordinates and invariant, multilinear expressions in the context of coordinate transformations. While current OpenMath symbols support the expression of linear algebra formulas using matrices and vectors, we find that there is an underlying assumption of Cartesian, or standard, coordinates that makes the expression of general tensor formulas difficult, if not impossible. In introducing these new OpenMath symbols for the expression of tensor formulas, we attempt to maintain, as much as possible, consistency with prior OpenMath symbol definitions for linear algebra.

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