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## A restatement of the normal form theorem for area metrics

### Notebooks for paper

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]
• 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]

### KappaLib v1.1

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.