<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\NeedsTeXFormat{LaTeX2e}

%Package to simplify loading of newtxmath with a text font family such as newtxtext for all latex engines, or for newtxtext and an otf math package.
\def\fileversion{1.751}
\def\filedate{2024/06/22}
\ProvidesPackage{newtx}[%
\filedate\space v\fileversion (Michael Sharpe) latex and unicode latex support for newtxmath and a supported text font family, or for newtxtext and an otf math package]

\message{`newtx'v\fileversion,\space\filedate\space Integrated\space loading\space of\space newtxmath\space and\space a\space text\space font
\space for\space all\space latex\space engines\space (msharpe)}

\RequirePackage{fontenc,fontaxes}
\RequirePackage{ifthen,iftex,etoolbox,scalefnt}

% \textfrac macro for type1 libertine and libertinus 
\newcommand{\lbtntextfrac}[3][]{% like \lbtntextfrac[1]{7}{8}
  \mbox{%
    \ifthenelse{\not\equal{#1}{}}%Test for integer portion [optional #1]
      {\textlf{#1}\kern.1em}{}%         
    {\sustyle#2}% numerator
    \StrRight{#2}{1}[\@digit@]%
    % look for  1, 2, 3, 7, 8
    \ifcase\@digit@% 0
    \or%\kern.03em% 1
    \or\kern.04em% 2
    \or%\kern-.01em% 3
    \or\kern.04em% 4
    \or%\kern.01em% 5
    \or%\kern.01em% 6
    \or\kern-.06em% 7
     \or\kern.04em% 8
    %\or\kern-.02em% 9
   \fi%
%    \kern\ntx@foresolidus{\fontencoding{TS1}\selectfont\char"2F}%
%    \kern\ntx@aftsolidus%
    {\fontencoding{TS1}\selectfont\char"2F}%
	\StrLeft{#3}{1}[\@digit@]%
    % look for 1, 4, 7
    \ifcase\@digit@% 0
    \or%\kern -.02em% 1
    \or% 2
    \or% 3
    \or\kern -.06em% 4
    \or\kern -.02em% 5
    \or\kern-.03em% 6
    \or\kern .01em% 7
   \or%\kern .01em% 8
   \or\kern -.01em% 9
    \fi%
    {\destyle #3}%       denominator [#3]
  }%mbox
} % lbtntextfrac

% options for newtxmath as etoolbox internal list allowing \ifinlist
%\def\ntx@mathlstr{vecsep,amsthm,nosubscriptcorrection,subscriptcorrection,timesmathacc,varbb,vvarbb,nosymbolsc,noamssymbols,amssymbols,uprightscript,uprightGreek,slantedGreek,frenchmath,nonewtxmathopt,upint,smallerops,useBImacros,varg,varvw,noOT1}
\forcsvlist{\listadd\ntx@mathlst}{vecsep,amsthm,nosubscriptcorrection,subscriptcorrection,
timesmathacc,varbb,vvarbb,nosymbolsc,noamssymbols,amssymbols,uprightscript,uprightGreek,
slantedGreek,frenchmath,nonewtxmathopt,upint,smallerops,useBImacros,varg,varvw,noOT1,
propmathfigs,curlybraces,cochrho,cochf,alty,alth,liby,nochvw}
%\show\ntx@mathlst

% Note that subscriptcorrectionfile is not on the list---we process it in this sty file
%\def\ntx@mathlst{}
%\ifinlist{amsthm}{\ntx@mathlst}{%
%\typeout{amsthm YES}}{ \typeout{amsthm NO}}

%\endinput

%\DeclareListParser*{\forcsvlist}{,}
%\@for\ntx@opt:=\ntx@mathlstr\do{%
%\listxadd{\ntx@mathlst}{\ntx@opt}}%
%\show\ntx@opt
%\show\ntx@mathlst
\RequirePackage{xstring}% must load this after \@for
% Needed for \StrLeft and \StrRight

%Enginecheck
%iftex's \iftutex is true for LuaTeX and XeTeX
\newif\ifntx@otftext
\iftutex\ntx@otftexttrue\fi 
\def\ntx@Mopt{}
\def\ntx@Topt{}

%%%%%%%%%%%%%%%%%%
 \RequirePackage{xkeyval}%
%\traceon
\DeclareOptionX*{% what to do with unknown options
\xifinlist{\CurrentOption}{\ntx@mathlst}
% true branch
{\xdef\ntx@Mopt{\ntx@Mopt \CurrentOption,}
\expandafter\PassOptionsToPackage\expandafter{\CurrentOption}{newtxmath}}
{%  false branch
\xdef\ntx@Topt{\ntx@Topt \CurrentOption,}\expandafter\PassOptionsToPackage\expandafter{\CurrentOption}{\ntx@TF}}
}%
%\traceoff
%%%%StartOptions
%\newif\ifntx@nofontspec 
% must load fontspec if unicode engine
\newif\ifntx@otfmath %\ntx@otfmathfalse % default is type1 math
%\newdimen\ntx@dima
%\def\tx@divide#1#2{\ntx@dima=\dimexpr 1pt * (\dimexpr #1pt\relax) / \dimexpr #2pt\relax\relax}
%\tx@divide{300}{400}\showthe\ntx@dima

\newcommand*{\ntxtext@RM}{1}
\newcommand*{\ntxtext@SF}{1}
\newcommand*{\ntxtext@TT}{.88}
%\newcommand*{\ntxtext@llscale}{1}
%\newcommand*{\ntxtext@ttscale}{.85}
\newcommand*{\ntxtext@rm}{} % not understood by libertinus-otf
\newcommand*{\ntxtext@sf}{}% not understood by libertinus-otf

\newcommand*{\ntxtext@scale}{0}
\newcommand*{\ntxmath@scale}{1} 
%\traceon
\DeclareOptionX{scaled}[1]{\renewcommand*{\ntxmath@scale}{#1}}
\DeclareOptionX{scale}[1]{\renewcommand*{\ntxmath@scale}{#1}}
\DeclareOptionX{textscale}[1]{\renewcommand*{\ntxtext@scale}{#1}}
\DeclareOptionX{textscaled}[1]{\renewcommand*{\ntxtext@scale}{#1}}
\DeclareOptionX{mathscale}[1]{\renewcommand*{\ntxmath@scale}{#1}}
\DeclareOptionX{mathscaled}[1]{\renewcommand*{\ntxmath@scale}{#1}}
\DeclareOptionX{ScaleBaseRM}[]{\renewcommand*{\ntxtext@RM}{#1}}
\DeclareOptionX{ScaleBaseSF}[]{\renewcommand*{\ntxtext@SF}{#1}}
\DeclareOptionX{ScaleBaseTT}[]{\renewcommand*{\ntxtext@TT}{#1}}
\DeclareOptionX{llscale}[]{\renewcommand*{\ntxtext@llscale}{#1}}
\DeclareOptionX{ttscale}[]{\renewcommand*{\ntxtext@ttscale}{#1}}
\DeclareOptionX{rm}[true]{\renewcommand*{\ntxtext@rm}{#1}}
\DeclareOptionX{sf}[true]{\renewcommand*{\ntxtext@sf}{#1}}
\newif\iftx@helv \tx@helvtrue
\newif\iftx@tt \tx@tttrue
\DeclareOptionX{nohelv}[true]{%
\@nameuse{if#1}\tx@helvfalse\fi}
\DeclareOptionX{nott}[true]{%
\@nameuse{if#1}\tx@ttfalse\fi}
\def\tx@helvratio{.94}
\DeclareOptionX{helvratio}[0.94]{%
\def\tx@helvratio{#1}
}

\DeclareOptionX{type1}[true]{}% no effect now
%{%\@nameuse{if#1}\ntx@otftextfalse\fi}

\DeclareOptionX{type1text}[true]{} %no effect now
%{% same as type1--use type1 for text
%\@nameuse{if#1}\ntx@otftextfalse\fi}

\DeclareOptionX{nofontspec}[true]{} % no effect
%{\@nameuse{if#1}\ntx@nofontspectrue\fi}

\DeclareOptionX{otfmath}[true]{%
\@nameuse{if#1}\iftutex\ntx@otfmathtrue\fi\fi}

%\DeclareOptionX{no-math}[true]{%
%\@nameuse{if#1}\ntx@nomathtrue\fi}
%\DeclareOptionX{no-otfmath}[true]{% forces use of newtxmath
%\@nameuse{if#1}\ntx@nomathtrue\fi}

\DeclareOptionX{subscriptcorrectionfile}{\def\tx@subs{#1}\tx@subsfiletrue}

%\newif\ifntx@fourier
\def\ntx@dfltTF{newtxtext} % the default text font package name
\def\ntx@text{\let\ntx@TF=\ntx@dfltTF % the text font package name
\def\ntx@MF{} % option name for flavor of newtxmath 
\def\ntx@id{0} % identifier for font properties
\def\ntx@sc{ntx@scale} % macro name for scale factor in font package 
\def\ntx@minfam{minntx} %roman font, tabular lining fd, used in math
}
\ntx@text % set the default
\DeclareOptionX{libertine}[true]{%
	\@nameuse{if#1}\def\ntx@sc{LinuxLibertineT@scale}%
	\def\ntx@TF{libertine}\def\ntx@MF{libertine}
	\def\ntx@id{1}\def\ntx@minfam{MinLibertinus}\def\textlf##1{{\liningnums##1}}
\def\nustyle{\sufigures}\def\destyle{}\fi}
\DeclareOptionX{libertinus}[true]{%
\@nameuse{if#1}\def\ntx@sc{LibertinusSerif@scale}%
	\def\ntx@TF{libertinus}\def\ntx@MF{libertine}
\def\ntx@id{10}\def\ntx@minfam{MinLibertinus}
}
\DeclareOptionX{etbb}[true]{%
	\@nameuse{if#1}\def\ntx@TF{ETbb}\def\ntx@MF{libertine}
	\def\ntx@id{2}\def\ntx@minfam{minlibertine}%
	\def\ntx@sc{ETbb@scale}\fi}
\DeclareOptionX{ebgaramond}[true]{\@nameuse{if#1}
	\def\ntx@sc{EBGaramond@scale}\def\ntx@TF{ebgaramond}
	\let\ntx@MF\ntx@TF\def\ntx@id{3}\def\ntx@minfam{minebgaramond}\fi}
\DeclareOptionX{MinionPro}[true]{\@nameuse{if#1}
	\def\ntx@sc{}\def\ntx@TF{MinionPro}\def\ntx@MF{minion}
	\def\ntx@id{4}\def\ntx@minfam{mincochineal}\def\ntx@TF{MinionPro}\fi}
\DeclareOptionX{minion}[true]{\@nameuse{if#1}
	\def\ntx@sc{}\def\ntx@TF{MinionPro}\def\ntx@MF{minion}
	\def\ntx@id{4}\def\ntx@minfam{mincochineal}\def\ntx@TF{MinionPro}\fi}
\DeclareOptionX{cochineal}[true]{\@nameuse{if#1}
	\def\ntx@sc{Cochineal@scale}\def\ntx@TF{cochineal}
	\let\ntx@MF\ntx@TF\def\ntx@id{5}\def\ntx@minfam{mincochineal}\fi}
\DeclareOptionX{garamondx}[true]{\@nameuse{if#1}
	\def\ntx@sc{zgm@Scale}\def\ntx@TF{garamondx}
	\let\ntx@MF\ntx@TF
	\def\ntx@id{6}\def\ntx@minfam{minzgm}\fi}
\DeclareOptionX{baskerville}[true]{\@nameuse{if#1}
	\def\ntx@sc{BaskervilleF@scale}\def\ntx@TF{baskervillef}
	\let\ntx@MF\ntx@TF\def\ntx@id{7}\def\ntx@minfam{minbaskervillef}\fi}
\DeclareOptionX{Baskerville}[true]{\@nameuse{if#1}
	\def\ntx@sc{BaskervilleF@scale}\def\ntx@TF{baskervillef}
	\let\ntx@MF\ntx@TF\def\ntx@id{7}\def\ntx@minfam{minbaskervillef}\fi}
\DeclareOptionX{baskervillef}[true]{\@nameuse{if#1}
	\def\ntx@sc{BaskervilleF@scale}\def\ntx@TF{baskervillef}
	\let\ntx@MF\ntx@TF\def\ntx@id{7}\def\ntx@minfam{minbaskervillef}\fi}
\DeclareOptionX{BaskervilleF}[true]{\@nameuse{if#1}
	\def\ntx@sc{BaskervilleF@scale}\def\ntx@TF{baskervillef}
	\let\ntx@MF\ntx@TF\def\ntx@id{7}\def\ntx@minfam{minbaskervillef}\fi}
\DeclareOptionX{baskervaldx}[true]{\@nameuse{if#1}
	\def\ntx@sc{Baskervaldx@scale}\def\ntx@TF{baskervaldx}
	\let\ntx@MF\ntx@TF\def\ntx@id{8}\def\ntx@minfam{minbaskervaldx}\fi}
\DeclareOptionX{Baskervaldx}[true]{\@nameuse{if#1}
	\def\ntx@sc{Baskervaldx@scale}\def\ntx@TF{baskervaldx}
	\let\ntx@MF\ntx@TF\def\ntx@id{8}\def\ntx@minfam{minbaskervaldx}\fi}
%\DeclareOptionX{utopia}[true]{%
%	\@nameuse{if#1}\def\ntx@TF{utopia}\let\ntx@MF\ntx@TF\def\ntx@id{0}\def\ntx@minfam{}\fi}
\DeclareOptionX{heuristica}[true]{\@nameuse{if#1}
	\def\ntx@sc{Heuristica@scale}%
	\def\ntx@TF{heuristica}\def\ntx@MF{utopia}
	\def\ntx@id{9}\def\ntx@minfam{minheuristica}\fi}
\DeclareOptionX{Heuristica}[true]{\@nameuse{if#1}
	\def\ntx@sc{Heuristica@scale}%
	\def\ntx@TF{heuristica}\def\ntx@MF{utopia}
	\def\ntx@id{9}\def\ntx@minfam{minheuristica}\fi}
\DeclareOptionX{erewhon}[true]{\@nameuse{if#1}
	\def\ntx@sc{erewhon@scale}\def\ntx@TF{erewhon}\def\ntx@MF{utopia}
	\def\ntx@id{11}\def\ntx@minfam{minerewhon}\fi}
\DeclareOptionX{Erewhon}[true]{\@nameuse{if#1}
	\def\ntx@sc{erewhon@scale}\def\ntx@TF{erewhon}\def\ntx@MF{utopia}
	\def\ntx@id{11}\def\ntx@minfam{minerewhon}\fi}
\DeclareOptionX{XCharter}[true]{\@nameuse{if#1}
	\def\ntx@sc{XCharter@scale}\def\ntx@TF{XCharter}
	\def\ntx@MF{xcharter}\def\ntx@id{12}\def\ntx@minfam{minxcharter}\fi}
\DeclareOptionX{xcharter}[true]{\@nameuse{if#1}
	\def\ntx@sc{XCharter@scale}\def\ntx@TF{XCharter}
	\def\ntx@MF{xcharter}\def\ntx@id{12}\def\ntx@minfam{minxcharter}\fi}
\DeclareOptionX{Stickstoo}[true]{\@nameuse{if#1}
	\def\ntx@sc{SticksTooText@scale}%
	\def\ntx@TF{stickstootext}\def\ntx@MF{stickstoo}
	\def\ntx@id{13}\def\ntx@minfam{minstickstootext}\fi}
\DeclareOptionX{stickstoo}[true]{\@nameuse{if#1}
	\def\ntx@sc{SticksTooText@scale}%
	\def\ntx@TF{stickstootext}\def\ntx@MF{stickstoo}
	\def\ntx@id{13}\def\ntx@minfam{minstickstootext}\fi}
\DeclareOptionX{stix2}[true]{\@nameuse{if#1}
	\def\ntx@sc{SticksTooText@scale}%
	\def\ntx@TF{stickstootext}\def\ntx@MF{stickstoo}
	\def\ntx@id{13}\def\ntx@minfam{minstickstootext}\fi}
\DeclareOptionX{scholax}[true]{\@nameuse{if#1}
	\def\ntx@sc{TeXGyreScholaX@scale}%
	\def\ntx@TF{scholax}\def\ntx@MF{nc}
	\def\ntx@id{14}\def\ntx@minfam{minscholax}\fi}
\DeclareOptionX{nc}[true]{\@nameuse{if#1}
	\def\ntx@sc{TeXGyreScholaX@scale}%
	\def\ntx@TF{scholax}\def\ntx@MF{nc}
	\def\ntx@id{14}\def\ntx@minfam{minscholax}\fi}
\DeclareOptionX{scholaxf}[true]{\@nameuse{if#1}
	\def\ntx@sc{TeXGyreScholaX@scale}%
	\def\ntx@TF{scholax}\def\ntx@MF{nc}
	\def\ntx@id{14}\def\ntx@minfam{minscholax}\fi}
\DeclareOptionX{ncf}[true]{\@nameuse{if#1}
	\def\ntx@sc{TeXGyreScholaX@scale}%
	\def\ntx@TF{scholax}\def\ntx@MF{nc}
	\def\ntx@id{14}\def\ntx@minfam{minscholax}\fi}
\DeclareOptionX{Gelasio}[true]{\@nameuse{if#1}
	\def\ntx@sc{Gelasio@scale}\def\ntx@TF{gelasio}\def\ntx@MF{gelasio}
	\def\ntx@id{16}\def\ntx@minfam{mingelasio}\fi}
\DeclareOptionX{gelasio}[true]{\@nameuse{if#1}
	\def\ntx@sc{Gelasio@scale}\def\ntx@TF{gelasio}\def\ntx@MF{gelasio}
	\def\ntx@id{16}\def\ntx@minfam{mingelasio}\fi}
% for stacked fractions
\DeclareOptionX{sfracvcenter}{%
\def\tx@sfrVC{#1}}
\DeclareOptionX{sfracvspacing}{%
\def\tx@sfrVS{#1}}
\DeclareOptionX{sfracbarthick}{%
\def\tx@sfrTH{#1}}
\DeclareOptionX{sfracscaling}{%
\def\tx@sfrSC{#1}}
% \ntx@Topt contains all unknown options that are not math options. It contains no scale options. \ntx@Mopt lists all the math options.
\ProcessOptionsX\relax

\def\tx@mathtotextfactor{1}
\ifcase\ntx@id % 0, newtxtext
  \or\or % 1,2
  \or \def\tx@mathtotextfactor{1.05} % 3, ebg
  \or\or % 4,5
  \or \def\tx@mathtotextfactor{.94} % 6, garx
  \or\or % 7,8
  \or \def\tx@mathtotextfactor{.94} % 9, heur
  \or\or % 10, 11
  \or \def\tx@mathtotextfactor{.935} % 12, xch
  \or % 13
  \or \def\tx@mathtotextfactor{.93} % 14, schx
  \or \def\tx@mathtotextfactor{.93} % 15, schx/four
  \or \def\tx@mathtotextfactor{.92} % 16, gel
\fi

\def\tx@divide#1#2{\ntx@dima=\dimexpr 1pt * (\dimexpr #1 pt\relax) / \dimexpr #2pt\relax\relax}
%\show\ntx@Mopt
%\show\ntx@Topt
%\traceon
% Check for conflict between nofontspec and others
%\ifntx@nofontspec
%  \iftutex
%  	\ntx@otfmathfalse
%	\ntx@otftextfalse
%  \fi
%\fi
\newif\ifntx@iszero
\@tempdima=\@ne\p@\@tempdima=\ntxtext@scale\@tempdima
\expandafter\ifnum\number\@tempdima=0\relax\ntx@iszerotrue\fi

\ifntx@iszero%
  \@tempdima=\tx@mathtotextfactor\p@%
  \@tempdima=\ntxmath@scale\@tempdima%
  \edef\ntxtext@scale{\strip@pt\@tempdima}
  %\show\ntxtext@scale
\fi
\def\ntxtext@scaled{s*[\ntxtext@scale]}
  
\ifntx@otfmath
   \ifnum\ntx@id&gt;0
     \PackageWarning{newtx.sty}{Reverting to newtxtext: newtx with option {\tt otfmath} can not handle other text packages.}
     \ntx@id=0
     \ntx@text % revert to newtxtext
   \fi
\fi

\ifnum\ntx@id=0
    \ifthenelse{\not\equal{\sfdefault}{cmss}}%
      {\tx@helvfalse}{}
    \ifthenelse{\not\equal{\ttdefault}{cmtt}}%
      {\tx@ttfalse}{}
\fi
\iftx@helv
      \renewcommand*{\sfdefault}{qhv}
      \@tempdima=\ntxtext@scale\p@
      \@tempdima=\tx@helvratio\@tempdima%
      \edef\qhv@scale{\strip@pt\@tempdima}
\else
      \PassOptionsToPackage{nohelv=true}{newtxtext}
\fi

\ifthenelse{\not\equal{\tx@helvratio}{.94}}%
      {\PassOptionsToPackage{helvratio=\tx@helvratio}%
      {newtxtext}}{}
      
\iftx@tt\renewcommand*{\ttdefault}{ntxtt}\fi
\iftx@tt\else%
      \PassOptionsToPackage{nott=true}{newtxtext}  
\fi
%\ifntx@badnof\PackageError{newtx.sty}{Incompatible options, nofontspec and otfmath}{Incompatible options, nofontspec and otfmath}\fi
% Set the text scale macros appropriately
%\show\ntx@TF
\PassOptionsToPackage{scaled=\ntxmath@scale}{newtxmath}
%\PassOptionsToPackage{scaled=\ntxtext@scale}{\ntx@TF}
\edef\ntxmath@scaled{s*[\ntxmath@scale]}
% For the min text fd files, need to use actual scale macro passed to fd?
%\@namedef{\ntx@sc}{\ntxtext@scale}%

%\newcommand{\PassMathScale}{%\ifntx@iszero\gdef\ntxtext@scale{\ntxmath@scale}
%\gdef\ntxtext@scaled{s*[\ntxtext@scale]}\fi

% The following block sents scale instructions to text package
\ifnum\ntx@id=4 % MinionPro
  \PassOptionsToPackage{scale=\ntxtext@scale}{\ntx@TF}
\else
  \ifnum\ntx@id=10 %libertinus
    \@tempdima=\ntxtext@scale\p@
	\@tempdimb=\ntxtext@RM\@tempdima
		  \PassOptionsToPackage{ScaleRM=\strip@pt\@tempdimb}{\ntx@TF}
	  	  \@tempdimb=\ntxtext@SF\@tempdima
		  \PassOptionsToPackage{ScaleSF=\strip@pt\@tempdimb}{\ntx@TF}
		  \@tempdimb=\ntxtext@TT\@tempdima
		  \PassOptionsToPackage{ScaleTT=\strip@pt\@tempdimb}{\ntx@TF}
  \else
      \ifnum\ntx@id=1 %libertine
      	  \@tempdima=\ntxtext@scale\p@
		  \@tempdimb=\ntxtext@RM\@tempdima
		  \PassOptionsToPackage{llscale=\strip@pt\@tempdimb}{\ntx@TF}
	  	  \@tempdimb=\ntxtext@SF\@tempdima
		  \PassOptionsToPackage{scale=\strip@pt\@tempdimb}{\ntx@TF}
		  \@tempdimb=\ntxtext@TT\@tempdima
		  \PassOptionsToPackage{ttscale=\strip@pt\@tempdimb}{\ntx@TF}

      \else %
          \ifnum\ntx@id=16 % gelasio
              \PassOptionsToPackage{scale=\ntxtext@scale}{\ntx@TF}%
 		  \else
		    \PassOptionsToPackage{scaled=\ntxtext@scale}{\ntx@TF}
		  \fi
	  \fi
  \fi
\fi
%}
%
%\newcommand{\PassMatchingScale}[1]{%
%  \ifntx@iszero%
%    \@tempdima #1\p@ \@tempdima\ntxmath@scale\@tempdima		  	\xdef\ntxtext@scale{\strip@pt\@tempdima}
%  \fi
%  \xdef\ntxtext@scaled{s*[\ntxtext@scale]}
%}
%\fi

%\PassMathScale
%\traceon
% Send parameters for stacked fractions
\def\tx@sfrac{} % X for cases where parameters are given
\ifcase\ntx@id % 0, newtxtext
\def\tx@sfrac{X}
%\PassMathScale
% info for sfrac (stacked fractions) involving newtxtext
\@ifundefined{tx@xht}{\def\tx@xht{450}}{} % lowercase letters
\@ifundefined{tx@deht}{\def\tx@deht{406}}{} % denominator figures ht
\@ifundefined{tx@nubase}{\def\tx@nubase{270}}{} % baseline of numerators
\@ifundefined{tx@debase}{\def\tx@debase{0}}{} % baseline of denoms
\@ifundefined{tx@sfrVC}{\def\tx@sfrVC{331}}{}% vertical center of sfrac
\@ifundefined{tx@sfrVS}{\def\tx@sfrVS{106}}{} % space above/below bar
\@ifundefined{tx@sfrTH}{\def\tx@sfrTH{54}}{} % bar thickness
\@ifundefined{tx@sfrSC}{\def\tx@sfrSC{.9}}{} % scale defigures by this
\or %1, libertine
\def\tx@sfrac{X}
% \PassOptionsToPackage{ttscaled=\ntxtext@scale,
% llscaled=\ntxtext@scale}{\ntx@TF} % for tt and serifed in Libertine
\@ifundefined{tx@xht}{\def\tx@xht{431}}{} % lowercase letters
\@ifundefined{tx@deht}{\def\tx@deht{328}}{} % denominator figures ht
\@ifundefined{tx@nubase}{\def\tx@nubase{365}}{} % baseline of numerators
\@ifundefined{tx@debase}{\def\tx@debase{365}}{} % baseline of denoms
\@ifundefined{tx@sfrVC}{\def\tx@sfrVC{305}}{}% vertical center of sfrac
\@ifundefined{tx@sfrVS}{\def\tx@sfrVS{100}}{} % space above/below bar
\@ifundefined{tx@sfrTH}{\def\tx@sfrTH{46}}{} % bar thickness
\@ifundefined{tx@sfrSC}{\def\tx@sfrSC{.9}}{} % scale defigures by this 
%\def\destyle{\sufigures} \def\nustyle{\sufigures}
%\iflibertine@otf%
%\providecommand{\textfrac}[3][]{{%
%\mbox{%
%    \ifthenelse{\not\equal{#1}{}}%Test for integer portion [optional #1]
%      {\textlf{#1}\kern.02em}{}%         
%{\addfontfeature{RawFeature=+frac}#2/#3}}%
%}}
\or % 2, etbb
\def\tx@sfrac{X}
\@ifundefined{tx@xht}{\def\tx@xht{431}}{} % lowercase letters
\@ifundefined{tx@deht}{\def\tx@deht{357}}{} % denominator figures ht
\@ifundefined{tx@nubase}{\def\tx@nubase{295}}{} % baseline of numerators
\@ifundefined{tx@debase}{\def\tx@debase{0}}{} % baseline of denoms
\@ifundefined{tx@sfrVC}{\def\tx@sfrVC{331}}{}% vertical center of sfrac
\@ifundefined{tx@sfrVS}{\def\tx@sfrVS{106}}{} % space above/below bar
\@ifundefined{tx@sfrTH}{\def\tx@sfrTH{64}}{} % bar thickness
\@ifundefined{tx@sfrSC}{\def\tx@sfrSC{.8}}{} % scale defigures by this
\or % 3, ebgaramond
\def\tx@sfrac{X}
\@ifundefined{tx@xht}{\def\tx@xht{431}}{} % lowercase letters
\@ifundefined{tx@deht}{\def\tx@deht{341}}{} % denominator figures ht
\@ifundefined{tx@nubase}{\def\tx@nubase{443}}{} % baseline of numerators
\@ifundefined{tx@debase}{\def\tx@debase{-143}}{} % baseline of denoms
\@ifundefined{tx@sfrVC}{\def\tx@sfrVC{318}}{}% vertical center of sfrac
\@ifundefined{tx@sfrVS}{\def\tx@sfrVS{90}}{} % space above/below bar
\@ifundefined{tx@sfrTH}{\def\tx@sfrTH{46}}{} % bar thickness
\@ifundefined{tx@sfrSC}{\def\tx@sfrSC{.9}}{} % scale defigures by this 

%\iflibertine@otf%
%\providecommand{\textfrac}[3][]{{%
%{{%
% \mbox{%
%    \ifthenelse{\not\equal{#1}{}}%Test for integer portion [optional #1]
%      {\textlf{#1}\kern.02em}{}%         
%{\addfontfeature{RawFeature=+frac}#2/#3}}%
%}}}}
\or % 4, MinionPro
%\PassMathScale
%\@ifundefined{tx@xht}{\def\tx@xht{437}}{} % lowercase letters
%\@ifundefined{tx@deht}{\def\tx@deht{359}}{} % denominator figures ht
%\@ifundefined{tx@nubase}{\def\tx@nubase{277}}{} % baseline of numerators
%\@ifundefined{tx@debase}{\def\tx@debase{0}}{} % baseline of denoms
%\@ifundefined{tx@sfrVC}{\def\tx@sfrVC{317}}{}% vertical center of sfrac
%\@ifundefined{tx@sfrVS}{\def\tx@sfrVS{106}}{} % space above/below bar
%\@ifundefined{tx@sfrTH}{\def\tx@sfrTH{54}}{} % bar thickness
%\@ifundefined{tx@sfrSC}{\def\tx@sfrSC{.9}}{} % scale defigures by this 
\or % 5, cochineal
\def\tx@sfrac{X}
\@ifundefined{tx@xht}{\def\tx@xht{430}}{} % lowercase letters
\@ifundefined{tx@deht}{\def\tx@deht{378}}{} % denominator figures ht
\@ifundefined{tx@nubase}{\def\tx@nubase{248}}{} % baseline of numerators
\@ifundefined{tx@debase}{\def\tx@debase{0}}{} % baseline of denoms
\@ifundefined{tx@sfrVC}{\def\tx@sfrVC{313}}{}% vertical center of sfrac
\@ifundefined{tx@sfrVS}{\def\tx@sfrVS{106}}{} % space above/below bar
\@ifundefined{tx@sfrTH}{\def\tx@sfrTH{54}}{} % bar thickness
\@ifundefined{tx@sfrSC}{\def\tx@sfrSC{.9}}{} % scale defigures by this amount
\or % 6, garamondx
%\PassMatchingScale{.94}
\or % 7, BaskervilleF
%\PassMathScale
\or % 8, baskervaldx
%\PassMathScale
\or % 9, heuristica
%\PassMatchingScale{.94}
\or % 10, libertinus
\def\tx@sfrac{X}
\@ifundefined{tx@xht}{\def\tx@xht{431}}{} % lowercase letters
\@ifundefined{tx@deht}{\def\tx@deht{324}}{} % denominator figures ht
\@ifundefined{tx@nubase}{\def\tx@nubase{364}}{} % baseline of numerators
\@ifundefined{tx@debase}{\def\tx@debase{-112}}{} % baseline of denoms
\@ifundefined{tx@sfrVC}{\def\tx@sfrVC{305}}{}% vertical center of sfrac
\@ifundefined{tx@sfrVS}{\def\tx@sfrVS{90}}{} % space above/below bar
\@ifundefined{tx@sfrTH}{\def\tx@sfrTH{46}}{} % bar thickness
\@ifundefined{tx@sfrSC}{\def\tx@sfrSC{.9}}{} % scale defigures by this 
%\def\destyle{\sufigures} \def\nustyle{\sufigures}
%\providecommand{\textfrac}[3][]{\textlf{#1}\kern.01em{\addfontfeature{RawFeature=+frac}#2/#3}}
%\iflibertine@otf%
%\providecommand{\textfrac}[3][]{{%
%{{%
% \mbox{%
%    \ifthenelse{\not\equal{#1}{}}%Test for integer portion [optional #1]
%      {\textlf{#1}\kern.02em}{}%         
%{\addfontfeature{RawFeature=+frac}#2/#3}}%
%}}}}
\or % 11, erewhon
\def\tx@sfrac{X}
\@ifundefined{tx@xht}{\def\tx@xht{461}}{} % lowercase letters
\@ifundefined{tx@deht}{\def\tx@deht{384}}{} % denominator figures ht
\@ifundefined{tx@nubase}{\def\tx@nubase{256}}{} % baseline of numerators
\@ifundefined{tx@debase}{\def\tx@debase{0}}{} % baseline of denoms
\@ifundefined{tx@sfrVC}{\def\tx@sfrVC{320}}{}% vertical center of sfrac
\@ifundefined{tx@sfrVS}{\def\tx@sfrVS{106}}{} % space above/below bar
\@ifundefined{tx@sfrTH}{\def\tx@sfrTH{58}}{} % bar thickness
\@ifundefined{tx@sfrSC}{\def\tx@sfrSC{.8}}{} % scale defigures by this 
\or % 12, XCharter
\def\tx@sfrac{X}
\@ifundefined{tx@xht}{\def\tx@xht{481}}{} % lowercase letters
\@ifundefined{tx@deht}{\def\tx@deht{382}}{} % denominator figures ht
\@ifundefined{tx@nubase}{\def\tx@nubase{295}}{} % baseline of numerators
\@ifundefined{tx@debase}{\def\tx@debase{0}}{} % baseline of denoms
\@ifundefined{tx@sfrVC}{\def\tx@sfrVC{341}}{}% vertical center of sfrac
\@ifundefined{tx@sfrVS}{\def\tx@sfrVS{106}}{} % space above/below bar
\@ifundefined{tx@sfrTH}{\def\tx@sfrTH{54}}{} % bar thickness
\@ifundefined{tx@sfrSC}{\def\tx@sfrSC{.8}}{} % scale defigures by this 
\or % 13, stickstoo
\def\tx@sfrac{X}
\@ifundefined{tx@xht}{\def\tx@xht{473}}{} % lowercase letters
\@ifundefined{tx@deht}{\def\tx@deht{411}}{} % denominator figures ht
\@ifundefined{tx@nubase}{\def\tx@nubase{252}}{} % baseline of numerators
\@ifundefined{tx@debase}{\def\tx@debase{0}}{} % baseline of denoms
\@ifundefined{tx@sfrVC}{\def\tx@sfrVC{320}}{}% vertical center of sfrac
\@ifundefined{tx@sfrVS}{\def\tx@sfrVS{106}}{} % space above/below bar
\@ifundefined{tx@sfrTH}{\def\tx@sfrTH{56}}{} % bar thickness
\@ifundefined{tx@sfrSC}{\def\tx@sfrSC{.75}}{} % scale defigures by this 
\or % 14, scholax
\def\tx@sfrac{X}
\@ifundefined{tx@xht}{\def\tx@xht{466}}{} % lowercase letters
\@ifundefined{tx@deht}{\def\tx@deht{423}}{} % denominator figures ht
\@ifundefined{tx@nubase}{\def\tx@nubase{289}}{} % baseline of numerators
\@ifundefined{tx@debase}{\def\tx@debase{-111}}{} % baseline of denoms
\@ifundefined{tx@sfrVC}{\def\tx@sfrVC{352}}{}% vertical center of sfrac
\@ifundefined{tx@sfrVS}{\def\tx@sfrVS{106}}{} % space above/below bar
\@ifundefined{tx@sfrTH}{\def\tx@sfrTH{70}}{} % bar thickness
\@ifundefined{tx@sfrSC}{\def\tx@sfrSC{.8}}{} % scale defigures by this 
\or % 15, scholax/fourier
\def\tx@sfrac{X}
\@ifundefined{tx@xht}{\def\tx@xht{466}}{} % lowercase letters
\@ifundefined{tx@deht}{\def\tx@deht{423}}{} % denominator figures ht
\@ifundefined{tx@nubase}{\def\tx@nubase{289}}{} % baseline of numerators
\@ifundefined{tx@debase}{\def\tx@debase{-111}}{} % baseline of denoms
\@ifundefined{tx@sfrVC}{\def\tx@sfrVC{352}}{}% vertical center of sfrac
\@ifundefined{tx@sfrVS}{\def\tx@sfrVS{106}}{} % space above/below bar
\@ifundefined{tx@sfrTH}{\def\tx@sfrTH{70}}{} % bar thickness
\@ifundefined{tx@sfrSC}{\def\tx@sfrSC{.8}}{} % scale defigures by this
\or % 16, gelasio
\def\tx@sfrac{X}
\@ifundefined{tx@xht}{\def\tx@xht{485}}{} % lowercase letters
\@ifundefined{tx@deht}{\def\tx@deht{473}}{} % denominator figures 
\@ifundefined{tx@nubase}{\def\tx@nubase{246}}{} % baseline of numerators
\@ifundefined{tx@debase}{\def\tx@debase{0}}{} % baseline of denoms
\@ifundefined{tx@sfrVC}{\def\tx@sfrVC{360}}{}% vertical center of sfrac
\@ifundefined{tx@sfrVS}{\def\tx@sfrVS{106}}{} % space above/below bar
\@ifundefined{tx@sfrTH}{\def\tx@sfrTH{70}}{} % bar thickness
\@ifundefined{tx@sfrSC}{\def\tx@sfrSC{.75}}{} % scale defigures by this
\fi
\PassOptionsToPackage{\ntx@MF}{newtxmath}


%\ifblank{\ntx@textopt}{}%
%{\PassOptionsToPackage{\ntx@textopt}{\ntx@TF}}

%\newdimen\tx@sixem\tx@sixem6pt % for checking if a number refers to ex
\newdimen\tx@x \newdimen\tx@y 

% convert numerical entry that may be multiple of ex  or em value
%\def\tx@toex#1{\tx@x#1pt \ifdim\tx@x&lt;\z@\tx@y=-\tx@x\else\tx@y=\tx@x\fi \ifdim\tx@y&gt;\tx@sixem \tx@x=\dimexpr 1pt * (\dimexpr #1pt\relax) / \dimexpr \tx@xht pt\relax\relax\fi}
%\def\tx@chkex#1{\@tx@chkex#1ex\@nil}
%\def\@tx@chkex#1ex#2\@nil{\ifthenelse{\equal{#2}{}}{\tx@toex #1}{\tx@x=#1ex}} # defines dimen \tx@x
\def\tx@toex#1{\tx@x=\dimexpr 1pt * (\dimexpr #1pt\relax) / \dimexpr \tx@xht pt\relax\relax}
%\def\tx@divide#1#2{\ntx@dima=\dimexpr 1pt * (\dimexpr #1 pt\relax) / \dimexpr #2pt\relax\relax}

% Code for stacked fractions---not available in cases 4,6,7,8,9
\if X\tx@sfrac
\newdimen\tx@tmpdima \newdimen\tx@tmpdimb  \newdimen\tx@tmpdimC
\newdimen\tx@dimX \newdimen\tx@dimY \newdimen\tx@dimZ
\newdimen\tx@numrbase \newdimen\tx@dnombase
\newdimen\tx@bartop \newdimen\tx@barbot
\newdimen\tx@bartopex \newdimen\tx@barbotex
\setlength\tx@tmpdimb{\tx@sfrTH pt} % bar thickness
\setlength\tx@tmpdima{\tx@deht pt} % de figure ht
\setlength\tx@tmpdimC{\tx@sfrVC pt} % bar center height
\tx@bartop=\tx@tmpdimC
\advance\tx@bartop by .5\tx@tmpdimb % top of bar
\tx@toex{\strip@pt\tx@bartop}\tx@bartopex=\tx@x % same, in ex units
\tx@barbot=\tx@bartop
\advance\tx@barbot by -\tx@tmpdimb % bottom of bar
\tx@toex{\strip@pt\tx@barbot}\tx@barbotex=\tx@x % same, in ex units
\tx@dimX=\tx@bartop
\advance\tx@dimX by \tx@sfrVS pt % bottom of numr
\tx@dimY=\tx@barbot
\advance\tx@dimY by -\tx@sfrVS pt % top of dnom
\advance\tx@dimY by -\tx@sfrSC\tx@tmpdima % baseline of dnom

\tx@toex{\strip@pt\tx@dimX}\tx@numrbase=\tx@x % num baseline in ex units
\tx@toex{\strip@pt\tx@dimY}\tx@dnombase=\tx@x % dnom baseline in ex units

\newcommand*{\textsfrac}[3][]{% like \textsfrac[1]{23}{34}
\mbox{%
    \ifthenelse{\not\equal{#1}{}}%Test for integer portion [optional #1]
      {\textlf{#1}\kern.04em}{}%         
	{\hmode@bgroup%
\ooalign{%
%  \ifnum\ntx@id=16\relax
	\setbox0=\hbox{\textsmde{#2}}% scaled down denom, baseline 0
	\tx@dimZ=\strip@pt\tx@numrbase ex%
	\hfil \raise \tx@dimZ \box0\hfil \crcr%
	\tx@dimX=\strip@pt\tx@bartopex ex%
	\tx@dimY=-\strip@pt\tx@barbotex ex%
	\leaders\hrule height \tx@dimX depth \tx@dimY \hfill \crcr%
	\setbox1=\hbox{\textsmde{#3}}%
  \tx@dimZ=\strip@pt\tx@dnombase ex	
  \hfil\raise \tx@dimZ \box1\hfil}%
\egroup}}
}
\else
\newcommand*{\textsfrac}[3][]{%
\mbox{%
    \ifthenelse{\not\equal{#1}{}}%Test for integer portion [optional #1]
      {\textlf{#1}\kern.04em}{}%         
#2/#3}}
\fi


% Document setup instructions
\ifntx@otftext
  \ifntx@otfmath %I
  \typeout{I}
    \usepackage[]{newtxtext} %may not load fontspec
    %\RequirePackage{fontspec} % just in case
    \usepackage{unicode-math} %loads amsmath
  \else %II: type1 math, otftext
  \typeout{II}
    \renewcommand*{\rmdefault}{\ntx@minfam} % Roman and Bold text for math
    \usepackage[]{newtxmath} % options will be as passed from newtx
    \@ifpackageloaded{fontspec}{}{%
      \usepackage[no-math]{fontspec}}
    \ifnum\ntx@id=10\relax % libertinus
      \usepackage[nomath]{\ntx@TF}
    \else
      \usepackage{\ntx@TF}
    \fi %\ifnum
  \fi %ifntx@otfmath
  %\show\ntx@otftexttrue
\else % not otftext
  \typeout{IV}
% IV, type1 tex and math
    \renewcommand*{\rmdefault}{\ntx@minfam}% Roman and Bold for math
     \usepackage{newtxmath} % options will be as passed from newtx
    \usepackage{\ntx@TF} % should load tt and sans math before newtx
\fi

%\traceoff
%%%%%%% End of preamble items
\AtEndPreamble{%
\providecommand{\textfrac}[3][]{{%
\mbox{%
    \ifthenelse{\not\equal{#1}{}}%Test for integer portion [optional #1]
      {\textlf{#1}\kern.02em}{}%         
\ifntx@otftext\addfontfeature{RawFeature=+frac}#2/#3
\else\textnu{#2}{\normalfont\fontencoding{TS1}\selectfont\char"2F}%
\textde{#3}\fi}
}}}


% Finally, add code to extend text packages after they load.
% This will depend on the particular package and the state
% of \ntx@otftext
\ifcase\ntx@id % 0, newtxtext
\or % 1, was libertine % switch to libertinus
	\let\sustyle\sufigures
	\let\nustyle\sufigures
	\let\textnu\textsup
	\let\textsu\textsup
 
	\def\minlibfamily{MinLibertinusSerif-Inf}
		\def\infigures{\@nomath\infigures\fontfamily{\minlibfamily}\selectfont}

	\let\instyle\infigures
	\let\destyle\infigures
	\let\defigures\infigures
	\DeclareTextFontCommand{\textinf}{\infigures}
	\let\textde\textinf

  \let\textfrac\lbtntextfrac
\or % 2, etbb
\or % 3, ebgaramond
  \def\destyle{\infigures} \def\nustyle{\sufigures}
  \def\textnu#1{{\sufigures#1}}
  \def\textde#1{{\infigures#1}}
  \ifntx@otftext
    \def\pliningnums{\addfontfeature{RawFeature=-tnum;-onum;+pnum;+lnum}}
  \else % type1
    \DeclareTextFontCommand{\pliningnums}{\fontfamily{EBGaramond-LF}\selectfont}
  \fi
  \def\textlf#1{{\pliningnums#1}}
\or % 4, MinionPro
\or % 5, cochineal
\or % 6, garamondx
\or % 7, BaskervilleF
\or % 8, baskervaldx
\or % 9, heuristica
\or % 10, libertinus
\ifntx@otftext%
 \def\textlf#1{{\addfontfeature{RawFeature=+lnum,RawFeature=+pnum}#1}}
  \let\sustyle\sufigures
  \let\nustyle\sufigures
  \DeclareTextFontCommand{\textsup}{\sufigures}\def\destyle{\addfontfeature{RawFeature=+subs}}
  \let\infstyle\destyle
  \let\infigures\destyle
  \DeclareTextFontCommand{\textinf}{\destyle}
  \newcommand{\textfrac}[3][]{%
	\mbox{%
    \ifthenelse{\not\equal{#1}{}}%Test for integer portion [optional #1]
      {\textlf{#1}\kern.1em}{}\Lfrac{#2/#3}}}

\else % type1
	\let\sustyle\sufigures
	\let\nustyle\sufigures
	\let\textnu\textsup
	\let\textsu\textsup
 
	\def\minlibfamily{MinLibertinusSerif-Inf}
		\def\infigures{\@nomath\infigures\fontfamily{\minlibfamily}\selectfont}

	\let\instyle\infigures
	\let\destyle\infigures
	\let\defigures\infigures
	\DeclareTextFontCommand{\textinf}{\infigures}
	\let\textde\textinf
	\def\textlf#1{{\LibertinusSerifLF#1}}

  \let\textfrac\lbtntextfrac
\fi
%      \fa@naming@exception{figures}{{inferior}{proportional}}{Inf}
%      \fa@naming@exception{figures}{{inferior}{tabular}}{Inf}
%      \def\infigures{\@nomath\infigures\fontfigurestyle{inferior}\selectfont}
%      \DeclareTextFontCommand{\textinf}{\infigures}
%      \let\destyle\infigures
%      \let\textde\textinf
	% \sufigures and \textsup from libertinus-type1.sty

\or % 11, erewhon
\or % 12, XCharter
\or % 13, stickstoo
\or % 14, scholax
\or % 15, scholax/fourier
\or % 16, gelasio
\fi
% galasio.sty does not offer macros for numerators, denominators or inferiors
%\ifgelasio@otf
%  \providecommand\nufigures{%
%  \addfontfeatures{VerticalPosition=Numerator}}
%  \providecommand\defigures{%
%  \addfontfeatures{VerticalPosition=Denominator}}
%  \providecommand\infigures{%
%  \addfontfeatures{VerticalPosition=Inferior}}
%  
%  \DeclareTextFontCommand{\textnum}{\nufigures}
%  \DeclareTextFontCommand{\textde}{\defigures}
%  \DeclareTextFontCommand{\textinf}{\infigures}
%  \@ifundefined{tx@sfrSC}{}{%
%  \newcommand*{\textsmde}[1]{%
%  \setbox0=\hbox{\scalebox\tx@sfrSC{\textde{#1}}}\box0}}
%
%\else % type1  --we define \text.. by lowering \textsu
%  \newbox\tx@box
%  \newcommand*{\textde}[1]{{\setbox0=\hbox{\textsu{#1}}\setbox1=\hbox{\raise -.763ex \box0}\dp1=0pt\ht1=.977ex\box1\relax}}
% 
%  \providecommand*\textnum[1]{\raisebox{.507ex}{\textde{#1}}}
%  \let\textnu\textnum
%%  \providecommand*\textde[1]{{\setbox0=\hbox{\textsu{#1}}%
%%  \setbox1=\hbox{\lower.763ex\box0}\dp0=0pt\relax\box1\relax}}
%  %\raisebox{-.763ex}{\textsu{#1}}}
%   % the following will be used only by \textsfrac
%  \@ifundefined{tx@sfrSC}{}{%
%  \newcommand*{\textsmde}[1]{%
%  \setbox0=\hbox{\scalebox\tx@sfrSC{\textde{#1}}}\box0}%
%    }
%\fi
%\DeclareTextFontCommand{\textlf}{\liningnums}
%\fi % end ifcase
\ifnum\ntx@id=16\relax
\else % create \textsmsmde for other than minion and gelasio
% We move the small font to the text baseline and scale it by \tx@sfrSC, for use only in the \textsfrac macro.
\ifnum\ntx@id=4\relax
\else
  \ifnum\tx@debase=0
    \newcommand*{\textsmde}[1]{%
    \setbox0=\hbox{\scalebox\tx@sfrSC{\textde{#1}}}\box0}
  \else
    \newdimen\tx@u \newdimen\tx@v
    \tx@u=-\tx@debase pt
    \tx@toex{\strip@pt\tx@u}\tx@y=\tx@x
    %\showthe\tx@y
    \tx@v=\strip@pt\tx@y ex
    \newcommand*{\textsmde}[1]{%
    \setbox2=\hbox{\textde{#1}}%
    \setbox1=\hbox{\raise \tx@v \box2}%
    \setbox0=\hbox{\scalebox{\tx@sfrSC}{\box1}}\box0}
  \fi %\ifnum\tx@debase=0
\fi %\ifnum\ntx@id=4
\fi %\ifnum\ntx@id=16
\endinput
</pre></body></html>