.. _math_convention:

Mathematical notation convention
================================

In `sisl` we strive to make the documentation as consistent
as possible.
This should make reading different parts of the documentation
simple to understand.

Here is a list of rules that sisl will strive to adhere to.
If you find any inconsistencies in the documentation,
please let us know!

* upper case characters such as :math:`I` and :math:`J` refer
  to atomic indices
* lower case characters such as :math:`i` and :math:`j` refer
  to orbital indices, e.g. :math:`i\in I`
* scalars are represented via lower case italics, such
  as :math:`a`
* vectors are represented via lower case bold faced, such
  as :math:`\mathbf a`

  One may use :math:`\hat{\mathbf a}` to signal normal vectors

  * dot-products between vectors should be explicit :math:`\mathbf a\cdot\mathbf b`

* matrices are represented via upper case bold faced, such
  as :math:`\mathbf A`

  * vector-matrix products are implicit :math:`\mathbf a\mathbf B`

  * matrix-matrix products are implicit :math:`\mathbf A\mathbf B`

* Greek letters are used for other indices, such as spin (:math:`\sigma`),
  Cartesian or lattice vectors.

* range of indices are denoted with :math:`\{ \}`, such that,
  :math:`\{i\}` is an orbital index range, :math:`\{I\}`
  is an atomic index range and :math:`\{\alpha\}` refers
  to some *other* range which should be inferred from
  the context

* the imaginary number is generally referred to as :math:`i` in
  physics, its meaning should be implicit from the context.