mathcommands-basic.sty

\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{basicmathcommands}[2021/10/12 Basic mathematics commands]

% Packages
\RequirePackage{mathtools}
\RequirePackage{bm}


% ======================= Formatting =======================

% Alternative overline (daleif p. 64 + email correspondence)
\DeclareRobustCommand\altoverline[2][0.8]{%
\mathmakebox[\widthof{\ensuremath{#2}}][c]{\overline{\mathmakebox[\widthof{\ensuremath{#2}}*\real{#1}][c]{#2}}}}


% ================= Symbols and operators ==================

% Constants
\DeclareMathOperator{\e}{\mathrm{e}}

% Greek letters
\renewcommand{\epsilon}{\varepsilon}
\renewcommand{\phi}{\varphi}

% Definitions
\newcommand{\defn}{\coloneqq}
\newcommand{\nfed}{\eqqcolon}


% ======================= Set theory =======================

% Set builder notation
\DeclarePairedDelimiterX{\set}[2]{\lbrace}{\rbrace}{#1\;\delimsize\vert\;#2} % Daleif uses \, on page 66

% Products
\let\oldprod\prod
\renewcommand*\prod\times
\newcommand*\bigprod\oldprod

% Unions and intersections
\newcommand*\union\cup
\newcommand*\intersect\cap
% New bigcup, bigcap, but use mathchoice to make sure it works between math styles (inline, display, etc.)
% \bigunion has to use \DeclareMathOperator and not \newcommand! Otherwise the limits don't work properly.
\DeclareMathOperator*{\smallbigcup}{\textstyle\bigcup}
\DeclareMathOperator*{\bigunion}{\mathchoice
    {\smallbigcup}%
    {\bigcup}%
    {\bigcup}%
    {\bigcup}%
}
\DeclareMathOperator*{\smallbigcap}{\textstyle\bigcap}
\DeclareMathOperator*{\bigintersect}{\mathchoice
    {\smallbigcap}%
    {\bigcap}%
    {\bigcap}%
    {\bigcap}%
}

% Symmetric difference
\newcommand{\symdiff}{\mathbin{\Delta}}


% ========================= Algebra =========================

% Miscellaneous
\newcommand\inv{^{-1}}
\newcommand{\preim}{^{-1}}

% Lattice operations
\newcommand{\meet}{\land}
\newcommand{\join}{\lor}

\DeclareMathOperator*{\smallbigvee}{\textstyle\bigvee}
\DeclareMathOperator*{\bigjoin}{\mathchoice
    {\smallbigvee}%
    {\bigvee}%
    {\bigvee}%
    {\bigvee}%
}
\DeclareMathOperator*{\smallbigwedge}{\textstyle\bigwedge}
\DeclareMathOperator*{\bigmeet}{\mathchoice
    {\smallbigwedge}%
    {\bigwedge}%
    {\bigwedge}%
    {\bigwedge}%
}


% ====================== Miscellaneous ======================

% Logic
\renewcommand{\implies}{\Rightarrow}

% Set theory
\DeclarePairedDelimiter{\card}{\lvert}{\rvert}
\newcommand{\powerset}[1]{2^{#1}}

% Functions
\DeclareMathOperator{\id}{id}
\newcommand*{\indicator}[1]{\mathbf{1}_{#1}}

% Number sets
\newcommand{\naturals}{\mathbb{N}}
\newcommand{\ints}{\mathbb{Z}}
\newcommand{\rationals}{\mathbb{Q}}
\newcommand{\reals}{\mathbb{R}}
\newcommand{\complex}{\mathbb{C}}

% Number sets for compatibility
\newcommand{\setN}{\naturals}
\newcommand{\setZ}{\ints}
\newcommand{\setQ}{\rationals}
\newcommand{\setR}{\reals}
\newcommand{\setC}{\complex}

% Complex numbers
\newcommand{\dotlessi}{\i}
\newcommand{\iu}{\operatorname{i}}
\renewcommand{\Re}{\operatorname{Re}}
\renewcommand{\Im}{\operatorname{Im}}
\newcommand{\conj}[1]{\altoverline{#1}}









% Vectors
\renewcommand{\vec}[1]{\bm{#1}}
\newcommand*\dotp\cdot
\newcommand*\crossp\times

% Norms and inner products
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
\DeclarePairedDelimiterX{\inner}[2]{\langle}{\rangle}{#1,#2}

% Calculus
\newcommand*\dif{\mathop{}\!\mathrm{d}}


\endinput

% Issues:
% - Need to implement big meet and join.
% - Need to implement different types of arrows, monos and epis.
% - Implement isomorphism symbol \cong.
% - Factor out linear algebra and calculus + more calculus commands like derivatives.