An OpenMath Content Dictionary for Tensor Concepts

TL;DR

This paper presents a new OpenMath content dictionary, tensor1, designed to facilitate the expression of tensor formulas, including non-Cartesian and invariant multilinear expressions, addressing limitations of existing linear algebra symbols.

Contribution

The paper introduces tensor1, a new OpenMath content dictionary that enables the representation of general tensor formulas beyond Cartesian coordinates.

Findings

Supports non-Cartesian coordinate expressions

Maintains consistency with existing linear algebra symbols

Enhances OpenMath's capability for tensor mathematics

Abstract

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.