- Journal page
- preprint,
- full text pdf. By permission. Copyright 2013 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

- Theorem 3.1: Coordinate transformations for twisted normal forms. [notebook, pdf]
- Theorem 3.5: Coordinate transformations for permutating constants in Metaclass I. [notebook, pdf]
- Theorem 3.5: Explicitly verify that converse direction. [notebook, pdf]
- Theorem 3.6
*(i)*: Non-birefringence implies*A=0*or*rho=0*: [notebook, pdf] - Theorem 3.6
*(ii)*: Symbolic expressions for*det kappa*and*det H*, proof that*g*and*H*can not be proportional: [notebook, pdf] - Theorem 4.4: Hodge + Axion is not decomposable for Lorentz signature [notebook, pdf]
- Theorem 4.4: Hodge + Axion is not decomposable for
*(--++)*signature [notebook, pdf] - Section 4.3: Compute epsilon matrix: [notebook, pdf]
- Discussion at end of Section 4.3 regarding factorisability for the Fresnel polynomial for
algebraically decomposable medium tensors with
*gamma != 0*and*beta*:^{2}-alpha gamma=0 *5*-parameter family with at least one linear factor: [notebook, pdf]- Example with exactly one linear factor: [notebook, pdf]
*3*-parameter family with exactly two linear factors: [notebook, pdf]*1*-parameter family with four linear factors: [notebook, pdf]- notebook for finding algebraically decomposable medium tensors with
*beta*: [notebook, pdf]^{2}-alpha gamma=0 - Discussion at end of Section 4.3 regarding factorisability for the Fresnel polynomial for
algebraically decomposable medium tensors when
*gamma != 0*,*beta*and the nonlinear equation for^{2}-alpha gamma!=0*D*has no solutions: *beta*and Fresnel polynomial is product of quadratic forms of signatures^{2}-alpha gamma<0*(++--)*: [notebook, pdf]*4*-parameter family for which*beta*and Fresnel polynomial is product two linear factors and a quadratic form: [notebook, pdf]^{2}-alpha gamma>0*1*-parameter family for which*beta*and Fresnel polynomial is product two quadratic forms: [notebook, pdf]^{2}-alpha gamma<0- Notebook to find tensors for which the equation for
*D*is not solvable. [notebook, pdf] - Theorem 5.1: Proof of
*(i) => (ii)*: -
Metaclass I, Case
*alpha1 = alpha2*: [notebook, pdf] - Metaclass I, Case
*alpha1 != alpha2*: [notebook, pdf] - Metaclass II: [notebook, pdf]
- Metaclass IV, Case
*alpha1 = alpha3*: [notebook, pdf] - Metaclass IV, Case
*alpha1 != alpha3*: [notebook, pdf] - Theorem 5.1: Proof of
*(ii) => (i)*: - Metaclass I representation of Hodge+Axion medium: [notebook, pdf]
- Metaclass I: [notebook, pdf]
- Metaclass II: [notebook, pdf]
- Metaclass III: [notebook, pdf]
- Metaclass IV: [notebook, pdf]
- Metaclass V: [notebook, pdf]
- Metaclass VI: [notebook, pdf]
- Metaclass VII: [notebook, pdf]
- Theorem 5.1: Proof of
*(i) => (iii)*: - Not all medium can be represented by a bivector
*A*that is simple: [notebook, pdf] - Script helper.m: [script]

- For Lorentz metrics
*g*and*h*,*N(g) subset N(h)*implies that*g*and*h*are confromally related: [notebook, pdf] - Doublecheck identities before Lemma 2.3: [notebook, pdf]
- Doublecheck the factorisation of the Fresnel polynomials in
I. Lindell, L. Bergamin, A. Favaro,
*Decomposable Medium Conditions in Four-Dimensional Representation*, IEEE Transactions on Antennas and propagation, Vol. 60, No. 1, 2012 [preprint, print]: