\documentclass[fleqn]{article}
\usepackage{mathptmx}

\DeclareMathSymbol{\Gamma}  {\mathalpha}{letters}{"00}
\DeclareMathSymbol{\Delta}  {\mathalpha}{letters}{"01}
\DeclareMathSymbol{\Theta}  {\mathalpha}{letters}{"02}
\DeclareMathSymbol{\Lambda} {\mathalpha}{letters}{"03}
\DeclareMathSymbol{\Xi}     {\mathalpha}{letters}{"04}
\DeclareMathSymbol{\Pi}     {\mathalpha}{letters}{"05}
\DeclareMathSymbol{\Sigma}  {\mathalpha}{letters}{"06}
\DeclareMathSymbol{\Upsilon}{\mathalpha}{letters}{"07}
\DeclareMathSymbol{\Phi}    {\mathalpha}{letters}{"08}
\DeclareMathSymbol{\Psi}    {\mathalpha}{letters}{"09}
\DeclareMathSymbol{\Omega}  {\mathalpha}{letters}{"0A}

\DeclareMathSymbol{\alpha}  {\mathalpha}{letters}{"0B}
\DeclareMathSymbol{\beta}   {\mathalpha}{letters}{"0C}
\DeclareMathSymbol{\gamma}  {\mathalpha}{letters}{"0D}
\DeclareMathSymbol{\delta}  {\mathalpha}{letters}{"0E}
\DeclareMathSymbol{\epsilon}{\mathalpha}{letters}{"0F}
\DeclareMathSymbol{\zeta}   {\mathalpha}{letters}{"10}
\DeclareMathSymbol{\eta}    {\mathalpha}{letters}{"11}
\DeclareMathSymbol{\theta}  {\mathalpha}{letters}{"12}
\DeclareMathSymbol{\iota}   {\mathalpha}{letters}{"13}
\DeclareMathSymbol{\kappa}  {\mathalpha}{letters}{"14}
\DeclareMathSymbol{\lambda} {\mathalpha}{letters}{"15}
\DeclareMathSymbol{\mu}     {\mathalpha}{letters}{"16}
\DeclareMathSymbol{\nu}     {\mathalpha}{letters}{"17}
\DeclareMathSymbol{\xi}     {\mathalpha}{letters}{"18}
\DeclareMathSymbol{\pi}     {\mathalpha}{letters}{"19}
\DeclareMathSymbol{\rho}    {\mathalpha}{letters}{"1A}
\DeclareMathSymbol{\sigma}  {\mathalpha}{letters}{"1B}
\DeclareMathSymbol{\tau}    {\mathalpha}{letters}{"1C}
\DeclareMathSymbol{\upsilon}{\mathalpha}{letters}{"1D}
\DeclareMathSymbol{\phi}    {\mathalpha}{letters}{"1E}
\DeclareMathSymbol{\chi}    {\mathalpha}{letters}{"1F}
\DeclareMathSymbol{\psi}    {\mathalpha}{letters}{"20}
\DeclareMathSymbol{\omega}  {\mathalpha}{letters}{"21}
\DeclareMathSymbol{\varepsilon} {\mathalpha}{letters}{"22}
\DeclareMathSymbol{\vartheta}   {\mathalpha}{letters}{"23}
\DeclareMathSymbol{\varpi}      {\mathalpha}{letters}{"24}
\DeclareMathSymbol{\varrho}     {\mathalpha}{letters}{"25}
\DeclareMathSymbol{\varsigma}   {\mathalpha}{letters}{"26}
\DeclareMathSymbol{\varphi}     {\mathalpha}{letters}{"27}

\DeclareMathSymbol{\dit}{\mathord}{letters}{`d}
\DeclareMathSymbol{\dup}{\mathord}{operators}{`d}

\nofiles

\parindent 0pt
\mathindent 1em

\def\test#1{#1}

\def\testnums{%
  \test 0 \test 1 \test 2 \test 3 \test 4 \test 5 \test 6 \test 7
  \test 8 \test 9 }
\def\testupperi{%
  \test A \test B \test C \test D \test E \test F \test G \test H
  \test I \test J \test K \test L \test M }
\def\testupperii{%
  \test N \test O \test P \test Q \test R \test S \test T \test U
  \test V \test W \test X \test Y \test Z }
\def\testupper{%
  \testupperi\testupperii}

\def\testloweri{%
  \test a \test b \test c \test d \test e \test f \test g \test h
  \test i \test j \test k \test l \test m }
\def\testlowerii{%
  \test n \test o \test p \test q \test r \test s \test t \test u
  \test v \test w \test x \test y \test z 
  \test\imath \test\jmath }
\def\testlower{%
  \testloweri\testlowerii}

\def\testupgreeki{%
  \test A \test B \test\Gamma \test\Delta \test E \test Z \test H
  \test\Theta \test I \test K \test\Lambda \test M }
\def\testupgreekii{%
  \test N \test\Xi \test O \test\Pi \test P \test\Sigma \test T
  \test\Upsilon \test\Phi \test X \test\Psi \test\Omega 
  \test\nabla }
\def\testupgreek{%
  \testupgreeki\testupgreekii}

\def\testlowgreeki{%
  \test\alpha \test\beta \test\gamma \test\delta \test\epsilon
  \test\zeta \test\eta \test\theta \test\iota \test\kappa \test\lambda
  \test\mu }
\def\testlowgreekii{%
  \test\nu \test\xi \test o \test\pi \test\rho \test\sigma \test\tau
  \test\upsilon \test\phi \test\chi \test\psi \test\omega }
\def\testlowgreekiii{%
  \test\varepsilon \test\vartheta \test\varpi \test\varrho
  \test\varsigma \test\varphi}
\def\testlowgreek{%
  \testlowgreeki\testlowgreekii\testlowgreekiii}


\begin{document}

\section{Math Alphabets}

Math Italic (\texttt{\string\mathnormal})
\def\test#1{\mathnormal{#1},}
\begin{eqnarray*}
  && {\testnums}\\
  && {\testupper}\\
  && {\testlower}\\ 
  && {\testupgreek}\\
  && {\testlowgreek}
\end{eqnarray*}%

Math Roman (\texttt{\string\mathrm})
\def\test#1{\mathrm{#1},}
\begin{eqnarray*}
  && {\testnums}\\
  && {\testupper}\\
  && {\testlower}\\ 
  && {\testupgreek}
\end{eqnarray*}%

%Math Italic Bold
%\def\test#1{\mathbm{#1},}
%\begin{eqnarray*}
%  && {\testnums}\\
%  && {\testupper}\\
%  && {\testlower}\\ 
%  && {\testupgreek}\\
%  && {\testlowgreek}
%\end{eqnarray*}%

%Math Bold (\texttt{\string\mathbf})
%\def\test#1{\mathbf{#1},}
%\begin{eqnarray*}
%  && {\testnums}\\
%  && {\testupper}\\
%  && {\testlower}\\ 
%  && {\testupgreek}
%\end{eqnarray*}%

Caligraphic (\texttt{\string\mathcal})
\def\test#1{\mathcal{#1},}
\begin{eqnarray*}
  && {\testupper}
\end{eqnarray*}%

%Script (\texttt{\string\mathscr})
%\def\test#1{\mathscr{#1},}
%\begin{eqnarray*}
%  && {\testupper}
%\end{eqnarray*}%

%Fraktur (\texttt{\string\mathfrak})
%\def\test#1{\mathfrak{#1},}
%\begin{eqnarray*}
%  && {\testupper}\\
%  && {\testlower}
%\end{eqnarray*}%

%Blackboard Bold (\texttt{\string\mathbb})
%\def\test#1{\mathbb{#1},}
%\begin{eqnarray*}
%  && {\testupper}
%\end{eqnarray*}%


\clearpage
\section{Character Sidebearings}

\def\test#1{|#1|+}
\begin{eqnarray*}
  && {\testupperi}\\
  && {\testupperii}\\
  && {\testloweri}\\ 
  && {\testlowerii}\\ 
  && {\testupgreeki}\\
  && {\testupgreekii}\\
  && {\testlowgreeki}\\
  && {\testlowgreekii}\\
  && {\testlowgreekiii}
\end{eqnarray*}%
%
\def\test#1{|\mathrm{#1}|+}%
\begin{eqnarray*}
  && {\testupperi}\\
  && {\testupperii}\\
  && {\testloweri}\\ 
  && {\testlowerii}\\ 
  && {\testupgreeki}\\
  && {\testupgreekii}
\end{eqnarray*}%
%
%\def\test#1{|\mathbm{#1}|+}%
%\begin{eqnarray*}
%  && {\testupperi}\\
%  && {\testupperii}\\
%  && {\testloweri}\\ 
%  && {\testlowerii}\\ 
%  && {\testupgreeki}\\
%  && {\testupgreekii}\\
%  && {\testlowgreeki}\\
%  && {\testlowgreekii}\\
%  && {\testlowgreekiii}
%\end{eqnarray*}%
%%
%\def\test#1{|\mathbf{#1}|+}%
%\begin{eqnarray*}
%  && {\testupperi}\\
%  && {\testupperii}\\
%  && {\testloweri}\\ 
%  && {\testlowerii}\\ 
%  && {\testupgreeki}\\
%  && {\testupgreekii}
%\end{eqnarray*}%
%
\def\test#1{|\mathcal{#1}|+}%
\begin{eqnarray*}
  && {\testupperi}\\
  && {\testupperii}
\end{eqnarray*}%


\clearpage
\section{Superscript positioning}

\def\test#1{#1^{2}+}%
\begin{eqnarray*}
  && {\testupperi}\\
  && {\testupperii}\\
  && {\testloweri}\\ 
  && {\testlowerii}\\ 
  && {\testupgreeki}\\
  && {\testupgreekii}\\
  && {\testlowgreeki}\\
  && {\testlowgreekii}\\
  && {\testlowgreekiii}
\end{eqnarray*}%
%
\def\test#1{\mathrm{#1}^{2}+}%
\begin{eqnarray*}
  && {\testupperi}\\
  && {\testupperii}\\
  && {\testloweri}\\ 
  && {\testlowerii}\\ 
  && {\testupgreeki}\\
  && {\testupgreekii}
\end{eqnarray*}%
%
%\def\test#1{\mathbm{#1}^{2}+}%
%\begin{eqnarray*}
%  && {\testupperi}\\
%  && {\testupperii}\\
%  && {\testloweri}\\ 
%  && {\testlowerii}\\ 
%  && {\testupgreeki}\\
%  && {\testupgreekii}\\
%  && {\testlowgreeki}\\
%  && {\testlowgreekii}\\
%  && {\testlowgreekiii}
%\end{eqnarray*}%
%
%\def\test#1{\mathbf{#1}^{2}+}%
%\begin{eqnarray*}
%  && {\testupperi}\\
%  && {\testupperii}\\
%  && {\testloweri}\\ 
%  && {\testlowerii}\\ 
%  && {\testupgreeki}\\
%  && {\testupgreekii}
%\end{eqnarray*}
%
\def\test#1{\mathcal{#1}^{2}+}%
\begin{eqnarray*}
  && {\testupperi}\\
  && {\testupperii}
\end{eqnarray*}%


\clearpage
\section{Subscript positioning}

\def\test#1{\mathnormal{#1}_{i}+}%
\begin{eqnarray*}
  && {\testupperi}\\
  && {\testupperii}\\
  && {\testloweri}\\ 
  && {\testlowerii}\\ 
  && {\testupgreeki}\\
  && {\testupgreekii}\\
  && {\testlowgreeki}\\
  && {\testlowgreekii}\\
  && {\testlowgreekiii}
\end{eqnarray*}%
%
\def\test#1{\mathrm{#1}_{i}+}%
\begin{eqnarray*}
  && {\testupperi}\\
  && {\testupperii}\\
  && {\testloweri}\\ 
  && {\testlowerii}\\ 
  && {\testupgreeki}\\
  && {\testupgreekii}
\end{eqnarray*}%
%
%\def\test#1{\mathbm{#1}_{i}+}%
%\begin{eqnarray*}
%  && {\testupperi}\\
%  && {\testupperii}\\
%  && {\testloweri}\\ 
%  && {\testlowerii}\\ 
%  && {\testupgreeki}\\
%  && {\testupgreekii}\\
%  && {\testlowgreeki}\\
%  && {\testlowgreekii}\\
%  && {\testlowgreekiii}
%\end{eqnarray*}
%%
%\def\test#1{\mathbf{#1}_{i}+}%
%\begin{eqnarray*}
%  && {\testupperi}\\
%  && {\testupperii}\\
%  && {\testloweri}\\ 
%  && {\testlowerii}\\ 
%  && {\testupgreeki}\\
%  && {\testupgreekii}
%\end{eqnarray*}%
%
\def\test#1{\mathcal{#1}_{i}+}%
\begin{eqnarray*}
  && {\testupperi}\\
  && {\testupperii}
\end{eqnarray*}%


\clearpage
\section{Accent positioning}

\def\test#1{\hat{#1}+}%
\begin{eqnarray*}
  && {\testupperi}\\
  && {\testupperii}\\
  && {\testloweri}\\ 
  && {\testlowerii}\\ 
  && {\testupgreeki}\\
  && {\testupgreekii}\\
  && {\testlowgreeki}\\
  && {\testlowgreekii}\\
  && {\testlowgreekiii}
\end{eqnarray*}%
%
\def\test#1{\hat{\mathrm{#1}}+}%
\begin{eqnarray*}
  && {\testupperi}\\
  && {\testupperii}\\
  && {\testloweri}\\ 
  && {\testlowerii}\\ 
  && {\testupgreeki}\\
  && {\testupgreekii}
\end{eqnarray*}%
%
%\def\test#1{\hat{\mathbm{#1}}+}%
%\begin{eqnarray*}
%  && {\testupperi}\\
%  && {\testupperii}\\
%  && {\testloweri}\\ 
%  && {\testlowerii}\\ 
%  && {\testupgreeki}\\
%  && {\testupgreekii}\\
%  && {\testlowgreeki}\\
%  && {\testlowgreekii}\\
%  && {\testlowgreekiii}
%\end{eqnarray*}%
%%
%\def\test#1{\hat{\mathbf{#1}}+}%
%\begin{eqnarray*}
%  && {\testupperi}\\
%  && {\testupperii}\\
%  && {\testloweri}\\ 
%  && {\testlowerii}\\ 
%  && {\testupgreeki}\\
%  && {\testupgreekii}
%\end{eqnarray*}
%
\def\test#1{\hat{\mathcal{#1}}+}%
\begin{eqnarray*}
  && {\testupperi}\\
  && {\testupperii}
\end{eqnarray*}%


\clearpage
\section{Differentials}

\begin{eqnarray*}
\gdef\test#1{\dit #1+}%
  && {\testupperi}\\
  && {\testupperii}\\
  && {\testloweri}\\ 
  && {\testlowerii}\\ 
  && {\testupgreeki}\\
  && {\testupgreekii}\\
  && {\testlowgreeki}\\
  && {\testlowgreekii}\\
  && {\testlowgreekiii}\\
\gdef\test#1{\dit \mathrm{#1}+}%
  && {\testupgreeki}\\
  && {\testupgreekii}
\end{eqnarray*}%
%
\begin{eqnarray*}
\gdef\test#1{\dup #1+}%
  && {\testupperi}\\
  && {\testupperii}\\
  && {\testloweri}\\ 
  && {\testlowerii}\\ 
  && {\testupgreeki}\\
  && {\testupgreekii}\\
  && {\testlowgreeki}\\
  && {\testlowgreekii}\\
  && {\testlowgreekiii}\\
\gdef\test#1{\dup \mathrm{#1}+}%
  && {\testupgreeki}\\
  && {\testupgreekii}
\end{eqnarray*}%
%
\begin{eqnarray*}
\gdef\test#1{\partial #1+}%
  && {\testupperi}\\
  && {\testupperii}\\
  && {\testloweri}\\ 
  && {\testlowerii}\\ 
  && {\testupgreeki}\\
  && {\testupgreekii}\\
  && {\testlowgreeki}\\
  && {\testlowgreekii}\\
  && {\testlowgreekiii}\\
\gdef\test#1{\partial \mathrm{#1}+}%
  && {\testupgreeki}\\
  && {\testupgreekii}
\end{eqnarray*}%


\clearpage
\section{Slash kerning}

\def\test#1{1/#1+}
\begin{eqnarray*}
  && {\testupperi}\\
  && {\testupperii}\\
  && {\testloweri}\\ 
  && {\testlowerii}\\ 
  && {\testupgreeki}\\
  && {\testupgreekii}\\
  && {\testlowgreeki}\\
  && {\testlowgreekii}\\
  && {\testlowgreekiii}
\end{eqnarray*}

\def\test#1{#1/2+}
\begin{eqnarray*}
  && {\testupperi}\\
  && {\testupperii}\\
  && {\testloweri}\\ 
  && {\testlowerii}\\ 
  && {\testupgreeki}\\
  && {\testupgreekii}\\
  && {\testlowgreeki}\\
  && {\testlowgreekii}\\
  && {\testlowgreekiii}
\end{eqnarray*}


\clearpage
\section{Big operators}

\def\testop#1{#1_{i=1}^{n} x^{n} \quad}
\begin{displaymath}
  \testop\sum 
  \testop\prod 
  \testop\coprod 
  \testop\int 
  \testop\oint
\end{displaymath}
\begin{displaymath}
  \testop\bigotimes 
  \testop\bigoplus
  \testop\bigodot
  \testop\bigwedge 
  \testop\bigvee 
  \testop\biguplus 
  \testop\bigcup 
  \testop\bigcap 
  \testop\bigsqcup 
% \testop\bigsqcap
\end{displaymath}


\section{Radicals}

\begin{displaymath}
  \sqrt{x+y} \qquad \sqrt{x^{2}+y^{2}} \qquad 
  \sqrt{x_{i}^{2}+y_{j}^{2}} \qquad
  \sqrt{\left(\frac{\cos x}{2}\right)} \qquad 
  \sqrt{\left(\frac{\sin x}{2}\right)}
\end{displaymath}
  
\begingroup
\delimitershortfall-1pt
\begin{displaymath}
  \sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{x+y}}}}}}}
\end{displaymath}
\endgroup % \delimitershortfall


\section{Over- and underbraces}

\begin{displaymath}
  \overbrace{x} \quad
  \overbrace{x+y} \quad
  \overbrace{x^{2}+y^{2}} \quad
  \overbrace{x_{i}^{2}+y_{j}^{2}} \quad
  \underbrace{x} \quad
  \underbrace{x+y} \quad
  \underbrace{x_{i}+y_{j}} \quad
  \underbrace{x_{i}^{2}+y_{j}^{2}} \quad
\end{displaymath}


\section{Normal and wide accents}

\begin{displaymath}
  \dot{x} \quad 
  \ddot{x} \quad 
  \vec{x} \quad 
  \bar{x} \quad
  \overline{x} \quad
  \overline{xx} \quad
  \tilde{x} \quad
  \widetilde{x} \quad
  \widetilde{xx} \quad
  \widetilde{xxx} \quad
  \hat{x} \quad 
  \widehat{x} \quad 
  \widehat{xx} \quad 
  \widehat{xxx} \quad
\end{displaymath}


\section{Long arrows}

\begin{displaymath}
  \leftarrow \mathrel{-} \rightarrow \quad
  \leftrightarrow \quad
  \longleftarrow  \quad
  \longrightarrow \quad
  \longleftrightarrow \quad
  \Leftarrow = \Rightarrow \quad
  \Leftrightarrow \quad
  \Longleftarrow  \quad
  \Longrightarrow \quad
  \Longleftrightarrow \quad
\end{displaymath}


\section{Left and right delimters}

\def\testdelim#1#2{ - #1 f #2 - }
\begin{displaymath}
  \testdelim() 
  \testdelim[] 
  \testdelim\lfloor\rfloor 
  \testdelim\lceil\rceil 
  \testdelim\langle\rangle 
  \testdelim\{\} 
\end{displaymath}

\def\testdelim#1#2{ - \left#1 f \right#2 - }
\begin{displaymath}
  \testdelim() 
  \testdelim[] 
  \testdelim\lfloor\rfloor 
  \testdelim\lceil\rceil 
  \testdelim\langle\rangle 
  \testdelim\{\} 
% \testdelim\lgroup\rgroup
% \testdelim\lmoustache\rmoustache
\end{displaymath}
\begin{displaymath}
  \testdelim)(
  \testdelim][
  \testdelim// 
  \testdelim\backslash\backslash
  \testdelim/\backslash 
  \testdelim\backslash/
\end{displaymath}


\clearpage
\section{Big-g-g delimters}

\def\testdelim#1#2{%
  - \left#1\left#1\left#1\left#1\left#1\left#1\left#1\left#1 - 
  \right#2\right#2\right#2\right#2\right#2\right#2\right#2\right#2 -}

\begingroup
\delimitershortfall-1pt
\begin{displaymath}
  \testdelim\lfloor\rfloor 
  \qquad 
  \testdelim()
\end{displaymath}
\begin{displaymath}
  \testdelim\lceil\rceil 
  \qquad 
  \testdelim\{\} 
\end{displaymath}
\begin{displaymath}
  \testdelim[] 
  \qquad 
  \testdelim\lgroup\rgroup
\end{displaymath}
\begin{displaymath}
  \testdelim\langle\rangle
  \qquad 
  \testdelim\lmoustache\rmoustache
\end{displaymath}
\begin{displaymath}
  \testdelim\uparrow\downarrow \quad
  \testdelim\Uparrow\Downarrow \quad
\end{displaymath}
\endgroup % \delimitershortfall



\end{document}

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