The paper relies on some computations by computer algebra. Below are Mathematica toolbooks for these computations.

- Comment before Theorem 3.2: Conjugation by Hodge operator for (++++) corresponds to conjugation by Sigma for an area metric. [ notebook, pdf ]
- Theorem 3.2: Compute the
*B*matrix [notebook, pdf] - Theorem 3.2: Compute
*S*matrices:- General routine for finding
*S*matrices in each metaclass [notebook, pdf] - Solve the
*S*matrix for metaclass XIII [notebook, pdf] - Solve the
*S*matrix for metaclass XIV [notebook, pdf] - Solve the
*S*matrix for metaclass XV [notebook, pdf] - Solve the
*S*matrix for metaclass XX [notebook, pdf] - Solve the
*S*matrix for metaclass XXII [notebook, pdf]

- General routine for finding
- Compute normal form for metaclass I [notebook, pdf]
- Compute normal form for metaclass II [notebook, pdf]
- Compute normal form for metaclass III [notebook, pdf]
- Compute normal form for metaclass IV [notebook, pdf]
- Compute normal form for metaclass V [notebook, pdf]
- Compute normal form for metaclass VI [notebook, pdf]
- Compute normal form for metaclass VII [notebook, pdf]
- Compute normal form for metaclass VIII [notebook, pdf]
- Compute normal form for metaclass IX [notebook, pdf]
- Compute normal form for metaclass X [notebook, pdf]
- Compute normal form for metaclass XI [notebook, pdf]
- Compute normal form for metaclass XII [notebook, pdf]
- Compute normal form for metaclass XIII [notebook, pdf]
- Compute normal form for metaclass XIV [notebook, pdf]
- Compute normal form for metaclass XV [notebook, pdf]
- Compute normal form for metaclass XVI [notebook, pdf]
- Compute normal form for metaclass XVII [notebook, pdf]
- Compute normal form for metaclass XVIII [notebook, pdf]
- Compute normal form for metaclass XIX [notebook, pdf]
- Compute normal form for metaclass XX [notebook, pdf]
- Compute normal form for metaclass XXI [notebook, pdf]
- Compute normal form for metaclass XXII [notebook, pdf]
- Compute normal form for metaclass XXIII [notebook, pdf]
- Conjugations by Hodge star operators for metaclass I [notebook, pdf]
- Conjugations by Hodge star operators for metaclass II [notebook, pdf]
- Conjugations by Hodge star operators for metaclass III [notebook, pdf]
- Conjugations by Hodge star operators for metaclass IV [notebook, pdf]
- Conjugations by Hodge star operators for metaclass V [notebook, pdf]
- Conjugations by Hodge star operators for metaclass VI [notebook, pdf]
- Conjugations by Hodge star operators for metaclass VII [notebook, pdf]
- Theorem A.1: Matrix representations of Hodge operators [ notebook, pdf ]
- Theorem A.1: Matrix representations of Hodge operators (without KappaLib) [ notebook, pdf ]
- Explicit verification of Proposition B.2 for blocks in a
*6x6*matrices. [ notebook, pdf ] - Script Petrov.m used above: [script]

To run the above notebooks, you will need kappaLib version 1.1, which is a collection of Mathematica routines for manipulation of electromagnetic medium tensors. To install this library, first download the file. Then load kappaLib into a Mathematica session by typing

<<kappaLib.m

If this generates an error, Mathematica can not find the file. The command Directory[] shows what directory Mathematica is currently in, and you can use SetDirectory["/user/mydir"] to change this directory.

KappaLib 1.0 was used in this paper.

Last modified 18.8.2011.