CTenC is a Cartesian TENsor Calculus package for performing manipulations of tensor expressions using index notation in Mathematica. The package is designed and optimized for problems in engineering and material science, including solutions of field equations (Stokes, Laplace, etc.) and developing constitutive equations in tensor-based formalisms such as GENERIC. Functions are given for the manipulations of free and dummy indices. Tensors in the package can be assigned symmetries (symmetric, antisymmetric, irreducible, mixed) and these symmetries are automatically accounted for through the use of projection operators in differentiation. Several scalar and tensor functions are built into the package (norm, trace, determinant, matrix power, etc.). The package is easily extensible through the addition of new functions.
The package is stored in CTenC.wl and can be loaded in a Mathematica notebook using
Get["NewTensor'"]
A tutorial describing the basic usage of the package is given in Tutorial.nb.
Please cite as
Benjamin E. Dolata and Jonathan E. Seppala, CTenC: Cartesian TENsor Calculus package for Mathematica using index notation, National Institute of Standards and Technology, https://doi.org/10.18434/mds2-3504.
- Ehrentraut, Harald, and Wolfgang Muschik. "On symmetric irreducible tensors in d-dimensions." ARI-An International Journal for Physical and Engineering Sciences 51 (1998): 149-159.
- Mane, S. R. "Irreducible Cartesian tensors of highest weight, for arbitrary order." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 813 (2016): 62-67.
