% MTPro2 Math Full: ordinary LaTeX input, sections 1--5.
\documentclass[a4paper,10pt]{article}
\usepackage[margin=25mm]{geometry}
\usepackage{mathtools,unicode-math}
\setmainfont{NimbusRoman-Regular.otf}[
  BoldFont=NimbusRoman-Bold.otf,
  ItalicFont=NimbusRoman-Italic.otf,
  BoldItalicFont=NimbusRoman-BoldItalic.otf]
\unimathsetup{math-style=ISO}
\setmathfont{MTPro2Math.otf}[Path=../out/]

\begin{document}
\noindent{\Large\textbf{MTPro2 Math specimens}}\par\medskip

\section*{1 Three math sizes and compound expressions}
Compare expressions in normal, superscript and nested superscript positions.

Inline example: $x^n+y^n=z^n$.

% I01
\[
\sum_{i=1}^n \sin x+i^{\sin x}+i^{i^{\sin x}}
\]

% T01_L0
\[
A,\ldots,Z\qquad a,\dots,z\qquad \Gamma,\ldots,\Omega\qquad
\symup{\Gamma},\ldots,\symup{\Omega} \qquad\alpha,\ldots,\omega
\]

% T01_L1
\[
2^{A,\ldots,Z\qquad a,\dots,z\qquad \Gamma,\ldots,\Omega\qquad
\symup{\Gamma},\ldots,\symup{\Omega} \qquad\alpha,\ldots,\omega}
\]

% T01_L2
\[
2^{2^{A,\ldots,Z\qquad a,\dots,z\qquad \Gamma,\ldots,\Omega\qquad
\symup{\Gamma},\ldots,\symup{\Omega} \qquad\alpha,\ldots,\omega}}
\]

% T02_L0
\[
\aleph_\alpha\times\aleph_\beta=\beta \iff \alpha\le\beta
\]

% T02_L1
\[
2^{\aleph_\alpha\times\aleph_\beta=\beta \iff \alpha\le\beta}
\]

% T02_L2
\[
2^{2^{\aleph_\alpha\times\aleph_\beta=\beta \iff \alpha\le\beta}}
\]

% T03_L0
\[
\forall \varepsilon>\alpha,
\Gamma_\alpha\hookrightarrow\Gamma_\varepsilon
\]

% T03_L1
\[
2^{\forall \varepsilon>\alpha,
\Gamma_\alpha\hookrightarrow\Gamma_\varepsilon}
\]

% T03_L2
\[
2^{2^{\forall \varepsilon>\alpha,
\Gamma_\alpha\hookrightarrow\Gamma_\varepsilon}}
\]

% T04_L0
\[
|x-a|<\delta\Longrightarrow|f(x)-l|<\varepsilon
\]

% T04_L1
\[
2^{|x-a|<\delta\Longrightarrow|f(x)-l|<\varepsilon}
\]

% T04_L2
\[
2^{2^{|x-a|<\delta\Longrightarrow|f(x)-l|<\varepsilon}}
\]

% T05_L0
\[
\underbrace{V\times\cdots\times V}_k\times\underbrace{V\times\cdots\times
V}_l \to \underbrace{V\times\cdots\times V}_{k+l}
\]

% T05_L1
\[
2^{\underbrace{V\times\cdots\times V}_k\times\underbrace{V\times\cdots\times
V}_l \to \underbrace{V\times\cdots\times V}_{k+l}}
\]

% T05_L2
\[
2^{2^{\underbrace{V\times\cdots\times V}_k\times\underbrace{V\times\cdots\times
V}_l \to \underbrace{V\times\cdots\times V}_{k+l}}}
\]

% T06_L0
\[
\{x|x\ne x\}=\emptyset\qquad(A\cap B)^\circ\subset A^\circ\cap
B^\circ
\]

% T06_L1
\[
2^{\{x|x\ne x\}=\emptyset\qquad(A\cap B)^\circ\subset A^\circ\cap
B^\circ}
\]

% T06_L2
\[
2^{2^{\{x|x\ne x\}=\emptyset\qquad(A\cap B)^\circ\subset A^\circ\cap
B^\circ}}
\]

% T07_L0
\[
\omega=\nu+v(x,y)\,dx +w(x,y)\,dy +d\varkappa
\]

% T07_L1
\[
2^{\omega=\nu+v(x,y)\,dx +w(x,y)\,dy +d\varkappa}
\]

% T07_L2
\[
2^{2^{\omega=\nu+v(x,y)\,dx +w(x,y)\,dy +d\varkappa}}
\]

% T08_L0
\[
d\omega=d\nu+\left(\frac{\partial w}{\partial x}-\frac{\partial v}{\partial y}\right)\,dx\wedge dy
\]

% T08_L1
\[
2^{d\omega=d\nu+\left(\frac{\partial w}{\partial x}-\frac{\partial v}{\partial y}\right)\,dx\wedge dy}
\]

% T08_L2
\[
2^{2^{d\omega=d\nu+\left(\frac{\partial w}{\partial x}-\frac{\partial v}{\partial y}\right)\,dx\wedge dy}}
\]

% T09_L0
\[
\hat x+\widehat X+\widehat{xy}+\widehat{xyz}+\vec A
\]

% T09_L1
\[
2^{\hat x+\widehat X+\widehat{xy}+\widehat{xyz}+\vec A}
\]

% T09_L2
\[
2^{2^{\hat x+\widehat X+\widehat{xy}+\widehat{xyz}+\vec A}}
\]

% T10_L0
\[
R_{ijkl}=-R_{jikl}=-R_{ijlk}=R_{klij}
\]

% T10_L1
\[
2^{R_{ijkl}=-R_{jikl}=-R_{ijlk}=R_{klij}}
\]

% T10_L2
\[
2^{2^{R_{ijkl}=-R_{jikl}=-R_{ijlk}=R_{klij}}}
\]

% T11_L0
\[
(f\circ g)'(x)=f'(g(x))\cdot g'(x)
\]

% T11_L1
\[
2^{(f\circ g)'(x)=f'(g(x))\cdot g'(x)}
\]

% T11_L2
\[
2^{2^{(f\circ g)'(x)=f'(g(x))\cdot g'(x)}}
\]

% T12_L0
\[
f(x)=\begin{cases}
  |x|  & x>a \\
  -|x| & x\le a
\end{cases}
\]

% T12_L1
\[
2^{f(x)=\left\{
\begin{smallmatrix*}[l]
  |x|  & x>a \\
  -|x| & x\le a
\end{smallmatrix*}\right.}
\]

% T12_L2
\[
2^{2^{f(x)=\left\{
\begin{smallmatrix*}[l]
  \scriptscriptstyle |x|  & \scriptscriptstyle x>a \\
  \scriptscriptstyle -|x| & \scriptscriptstyle x\le a
\end{smallmatrix*}\right.}}
\]

% T13_L0
\[
\int_{-\infty}^\infty e^{-x\cdot x}\,dx =\sqrt\pi
\]

% T13_L1
\[
2^{\int_{-\infty}^\infty e^{-x\cdot x}\,dx =\sqrt\pi}
\]

% T13_L2
\[
2^{2^{\int_{-\infty}^\infty e^{-x\cdot x}\,dx =\sqrt\pi}}
\]

% T14_L0
\[
X=\sum_i\xi^i\frac{\partial}{\partial x^i}+\sum_j x^j\frac{\partial}{\partial\dot{x}^j}
\]

% T14_L1
\[
2^{X=\sum_i\xi^i\frac{\partial}{\partial x^i}+\sum_j x^j\frac{\partial}{\partial\dot{x}^j}}
\]

% T14_L2
\[
2^{2^{X=\sum_i\xi^i\frac{\partial}{\partial x^i}+\sum_j x^j\frac{\partial}{\partial\dot{x}^j}}}
\]

\clearpage
\section*{2 Standard accents}
Compare ordinary accents with wide accents over longer expressions.

% B19
\[
\mathring{x}
\]

% B20
\[
\dot{\Gamma}+\ddot{\Gamma}
\]

% B22
\[
\begin{aligned}
 & \hat{A},\quad\hat{M} \\
 & \widehat{A},\quad\widehat{M},\quad\widehat{xy},\quad
   \widehat{xyz},\quad\widehat{xyzw},\quad\widehat{x+y+z+\cdots+w}
\end{aligned}
\]

% B23
\[
\begin{aligned}
 & \tilde{A},\quad\tilde{M} \\
 & \widetilde{A},\quad\widetilde{M},\quad\widetilde{xy},\quad
   \widetilde{xyz},\quad\widetilde{xyzw},\quad\widetilde{x+y+z+\cdots+w}
\end{aligned}
\]

% B24
\[
\begin{aligned}
 & \check{A},\quad\check{M} \\
 & \widecheck{A},\quad\widecheck{M},\quad\widecheck{xy},\quad
   \widecheck{xyz},\quad\widecheck{xyzw},\quad\widecheck{x+y+z+\cdots+w}
\end{aligned}
\]

% B25
\[
\bar{M},\qquad\overline{M},\qquad\overline{x+y+z}
\]

\section*{3 Math alphabets}
Compare alphabet styles and letters in subscript and superscript positions.

% B15
\[
A_{\symbfup{X}}(f)=\symbfup{X(f)}=2^{\symbfup{2^{X(g)}}}
\]

% A31--A39: nine Unicode alphabet styles present in Full.
\[
\begin{aligned}
& \symup{ABGMXYZ} \\
& \symit{ABGMXYZ} \\
& \symbfup{ABGMXYZ} \\
& \symbfit{ABGMXYZ} \\
& \symscr{ABGMXYZ} \\
& \symbfscr{ABGMXYZ} \\
& \symfrak{ABGMXYZ} \\
& \symbffrak{ABGMXYZ} \\
& \symbb{ABGMXYZ}
\end{aligned}
\]

% Replacement Section 4 body; Fourier matrices use positive-exponent convention.
% Candidate row counts 24/26; actual delimiter choice requires the user's PDF.
% Section 4 replacement. No scaling, artificial struts, or delimiter tuning.
\clearpage
\section*{4 Parentheses at four matrix sizes}

\[
\hat J_x^{(1/2)}=\frac{\hbar}{2}
\begin{pmatrix}
0 & 1 \\
1 & 0
\end{pmatrix}
\qquad
\hat J_x^{(3/2)}=\frac{\hbar}{2}
\begin{pmatrix}
0 & \sqrt{3} & 0 & 0 \\
\sqrt{3} & 0 & 2 & 0 \\
0 & 2 & 0 & \sqrt{3} \\
0 & 0 & \sqrt{3} & 0
\end{pmatrix}
\]

\[
\hat J_x^{(5/2)}=\frac{\hbar}{2}
\begin{pmatrix}
0 & \sqrt{5} & 0 & 0 & 0 & 0 \\
\sqrt{5} & 0 & 2\sqrt{2} & 0 & 0 & 0 \\
0 & 2\sqrt{2} & 0 & 3 & 0 & 0 \\
0 & 0 & 3 & 0 & 2\sqrt{2} & 0 \\
0 & 0 & 0 & 2\sqrt{2} & 0 & \sqrt{5} \\
0 & 0 & 0 & 0 & \sqrt{5} & 0
\end{pmatrix}
\]

\[
\hat J_x^{(7/2)}=\frac{\hbar}{2}
\begin{pmatrix}
0 & \sqrt{7} & 0 & 0 & 0 & 0 & 0 & 0 \\
\sqrt{7} & 0 & 2\sqrt{3} & 0 & 0 & 0 & 0 & 0 \\
0 & 2\sqrt{3} & 0 & \sqrt{15} & 0 & 0 & 0 & 0 \\
0 & 0 & \sqrt{15} & 0 & 4 & 0 & 0 & 0 \\
0 & 0 & 0 & 4 & 0 & \sqrt{15} & 0 & 0 \\
0 & 0 & 0 & 0 & \sqrt{15} & 0 & 2\sqrt{3} & 0 \\
0 & 0 & 0 & 0 & 0 & 2\sqrt{3} & 0 & \sqrt{7} \\
0 & 0 & 0 & 0 & 0 & 0 & \sqrt{7} & 0
\end{pmatrix}
\]


% Replacement Section 5 body. Existing mathtools + unicode-math only.
% No individual equation titles; subject labels below are source comments.
\clearpage
\section*{5 Formulas from physics and mathematics}

% P01: Analytical mechanics; regular Lagrangian and canonical variables.
\[
\begin{aligned}
\frac{\mathrm d}{\mathrm dt}\frac{\partial L}{\partial\dot q_i}
 -\frac{\partial L}{\partial q_i}&=0,
 & p_i&=\frac{\partial L}{\partial\dot q_i},\\[4pt]
\dot q_i&=\frac{\partial H}{\partial p_i},
 & \dot p_i&=-\frac{\partial H}{\partial q_i}.
\end{aligned}
\]

% P02: Maxwell equations, microscopic SI form (rho and j are total sources).
\[
\left\{
\begin{aligned}
\nabla\cdot\symbfit{E}&=\frac{\rho}{\varepsilon_0},\\[4pt]
\nabla\cdot\symbfit{B}&=0,\\[4pt]
\nabla\times\symbfit{E}&=-\frac{\partial\symbfit{B}}{\partial t},\\[4pt]
\nabla\times\symbfit{B}&=\mu_0\symbfit{j}
  +\mu_0\varepsilon_0\frac{\partial\symbfit{E}}{\partial t}.
\end{aligned}
\right.
\]

% P03: Nonrelativistic spinless particle in a scalar potential.
\[
i\hbar\frac{\partial\psi}{\partial t}
 =\hat H\psi
 =\left[-\frac{\hbar^2}{2m}\nabla^2+V(\symbfit{r},t)\right]\psi.
\]

% P04: Quantum canonical ensemble; assume the partition function exists.
\[
\hat\rho=\frac{e^{-\beta\hat H}}{Z},\qquad
Z=\operatorname{tr}\!\left(e^{-\beta\hat H}\right),\qquad
\beta=\frac{1}{k_{\mathrm B}T}.
\]

% P05: Einstein field equation with cosmological constant.
\[
R_{\mu\nu}-\frac12 Rg_{\mu\nu}+\Lambda g_{\mu\nu}
 =\frac{8\pi G}{c^4}T_{\mu\nu}.
\]

% P06: Incompressible Newtonian fluid with constant rho and dynamic viscosity mu.
% f is body force per unit mass.
\[
\begin{aligned}
\rho\left(\frac{\partial\symbfit{u}}{\partial t}
 +(\symbfit{u}\cdot\nabla)\symbfit{u}\right)
 &=-\nabla p+\mu\nabla^2\symbfit{u}+\rho\symbfit{f},\\
\nabla\cdot\symbfit{u}&=0.
\end{aligned}
\]

% M01: Retain r52 S5_11 verbatim, except its subsection title.
% A_n are events in one probability space; independence is not required.
\begin{equation*}
\begin{aligned}
\sum_{n=1}^{\infty}\symbb{P}(A_n)<\infty
\quad\Longrightarrow\quad
\symbb{P}\!\left(\limsup_{n\to\infty}A_n\right)
&=\symbb{P}\!\left(
 \bigcap_{m=1}^{\infty}\bigcup_{n=m}^{\infty}A_n
 \right)\\
&=0.
\end{aligned}
\end{equation*}

% M02: Retain r52 S5_12 verbatim, except its subsection title.
% n is a nonnegative integer. Preserve display-size binomial in cases.
\begin{equation*}
\sum_{k=0}^{n}(-1)^k\binom{n}{k}^{2}
=\begin{cases}
 (-1)^{n/2}\dbinom{n}{n/2},&n\text{ even},\\[5pt]
 0,&n\text{ odd}.
\end{cases}
\end{equation*}

\end{document}