default.tex

% https://docs.ourbigbook.com/built-in-math-macros

% Scientific notation helper:
% https://www.reddit.com/r/LaTeX/comments/3yjzz6/comment/cye8u5v/?utm_source=reddit&utm_medium=web2x&context=3
\newcommand{\e}[1]{\times 10^{#1}}

%% physics package
%% http://mirrors.ibiblio.org/CTAN/macros/latex/contrib/physics/physics.pdf
% Absolute value.
\newcommand{\abs}[1]{\left|#1\right|}
\newcommand{\curl}[1]{\nabla \times #1}
\renewcommand{\div}[1]{\nabla \cdot #1}
\newcommand{\grad}[1]{\nabla #1}
\newcommand{\laplacian}[1]{\nabla^2 #1}
% Partial derivative.
% https://tex.stackexchange.com/questions/412439/is-there-a-short-hand-command-to-write-derivatives
\newcommand{\pdv}[2]{\frac{\partial #1}{\partial #2}}
% Non-partial derivative.
\newcommand{\dv}[2]{\frac{d #1}{d #2}}
% Vector Arrow.
\newcommand{\va}[1]{\overrightarrow{#1}}
% https://tex.stackexchange.com/questions/214728/braket-notation-in-latex
\newcommand{\bra}[1]{\langle#1|}
\newcommand{\ket}[1]{|#1\rangle}

%% Calculus

% Derivative evaluated at point.
% https://tex.stackexchange.com/questions/294499/evaluated-at-bar-for-derivatives-bigr-biggr-or-left-right
\newcommand{\evalat}[2]{#1\biggr\rvert_{#2}}

%% Complex numbers
% Complex conjugate.
\newcommand\conj[1]{\bar{#1}}

%% Algebra

\newcommand{\projectiveSpace}[0]{\mathbf{P}}

%% Real and complex analysis
\newcommand{\C}[0]{\mathbb{C}}
% Field.
\newcommand{\F}[0]{\mathbb{F}}
% Quaternions.
\renewcommand{\H}[0]{\mathbb{H}}
\renewcommand{\R}[0]{\mathbb{R}}
\newcommand{\Q}[0]{\mathbb{Q}}
\renewcommand{\Z}[0]{\mathbb{Z}}

%%% Lebesgue spaces.
\newcommand{\LP}[0]{L^p}
\newcommand{\LTwo}[0]{L^2}

%% Electromagnetism
% Magnetic field vector
\newcommand{\B}[0]{\va{\mathbf{B}}}
% Electric field vector
\newcommand{\E}[0]{\va{\mathbf{E}}}
% Electric current vector.
\newcommand{\J}[0]{\va{\mathbf{J}}}
\newcommand{\vacuumPermittivity}[0]{\varepsilon_0}
\newcommand{\vacuumPermeability}[0]{\mu_0}

%% esvect
% https://tex.stackexchange.com/questions/261591/arrow-above-text-like-widehat
\newcommand{\vv}[1]{\overrightarrow#1}