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A restatement of the normal form theorem for area metrics
M.F. Dahl
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.
Last modified 18.8.2011.
