Conventions

In this section, we will describe the conventions used in the documentation and code.

Folders and file types

• Documentation is written in markdown.
• Tutorials are written in markdown.

File naming conventions

• Documentation files are named using CamelCase.
• Image files in the docs folder are named using snake_case

Mathematical conventions

The imaginary unit will be denoted \(\mathfrak i\), \mathfrak i to avoid confusion with the index \(i\). Index symmetrization \(()\) and anti-symmetrization \([]\) will be used throughout. They are defined for an tensor \(A\) with two indices by

\[ A_{(ij)} = \frac{1}{2} (A_{ij} + A_{ji}), \]

\[ A_{[ij]} = \frac{1}{2} (A_{ij} - A_{ji}) \]

The Fourier transform of a field \(\psi\) will be denoted \(\psi_{\mathfrak f}\), \psi_{\mathfrak f}, and is defined as

\[ \psi_{\mathfrak f} (\mathbf k) = \int d^d r e^{-\mathfrak i \mathbf k \cdot \mathbf r} f(\mathbf r), \]

and the inverse is given by

\[ \psi(\mathbf r) = \frac{1}{(2\pi)^d} \int d^d k e^{\mathfrak i\mathbf k\cdot \mathbf r} \psi_{\mathfrak f}(\mathbf k), \]

where \(d\) is the spatial dimension.

Vectors \(\mathbf a, \mathbf b, \mathbf c, \boldsymbol \Omega\) are denoted using boldfont (\mathbf, \boldsymbol) , while rank 2 tensors vary more. Typical choices however are non-bold greek letters (\(\sigma\)) lower case Fraktur letters (\(\mathfrak h\), \mathfrak h) or capital letters (\(Q\)).

The dot product (\(\cdot\)) is a contraction over the last index

(\nabla \cdot \sigma)_i = \partial_j {\sigma}_{ij}

while the double dot product \(\dot \cdot\) is a contraction over the last two indices

\[ (\mathcal C \dot \cdot \mathfrak e)_ {ij} = \mathcal C_ {ijkl} \mathfrak e_ {kl} \]

Programming notation conventions

• PEP8 for python programming, and loosely PEP257/Google Python Style Guide for doc strings. Functions are documented as follows:

  def function_name(arg1, arg2):
      """Short description of the function.
  
      Optional longer description of the function.
  
      Args:
          arg1: Description of arg1. No need to state default values.
          arg2: Description of arg2.
  
      Returns:
          Description of the return value. Data type.
  
      Raises:
          Exception: Description of the exception.
  
      Example:
          Optional example usage
      """
      pass
  

• markdownlint for markdown documents.