An OpenMath Content Dictionary for Tensor Concepts
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.
Unable to display preview. Download preview PDF.
- 1.Morse, P.M., Feshbach, H.: Methods of Theoretical Physics, Part I, pp. 655–666. McGraw-Hill, New York (1953)Google Scholar
- 2.Technical Committee ISO/TC 12, Quantities and units: Part 2: Mathematical signs and symbols to be used in the natural sciences and technology, Draft International Standard ISO/DIS 80000-2, International Organization for Standardization (2008)Google Scholar
- 3.Buswell, S., Caprotti, O., Carlisle, D.P., Dewar, M.C., Gäetano, M., Kohlhase, M.: The OpenMath Standard 2.0 (2004), http://www.openmath.org
- 4.Kohlhase, M., Rabe, F.: Semantics of OpenMath and MathML3. In: 22nd OpenMath Workshop Editor: James H Davenport, July 9. Grand Bend Ontario (University of Bath Press and the OpenMath Society) (2009), ISBN: 978-1-86197-172-2 Google Scholar