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\preamble
  ______________________________________________________
  The PM-ISOmath bundle 
  Copyright (C) 2017 Claudio Beccari 
  All rights reserved

  License information appended

\endpreamble
\postamble

Copyright 2017 Claudio Beccari

Distributable under the LaTeX Project Public License,
version 1.3c or higher (your choice). The latest version of
this license is at: http://www.latex-project.org/lppl.txt

This work is "author-maintained"

This work consists of this file pm-isomath.dtx, a README file
the manifest.txt file, and the derived files: 
    pm-isomath.sty, pm-isomath.pdf.
 
\endpostamble

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%</internal>
%
% Copyright 2017 Claudio Beccari
%
% This file is part of the PM-ISOmath bundle
% -------------------------------------------
%
% It may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3
% of this license or (at your option) any later version.
% The latest version of this license is in
%    http://www.latex-project.org/lppl.txt
% and version 1.3 or later is part of all distributions of LaTeX
% version 2003/12/01 or later.
%
% This file has the LPPL maintenance status "author-maintained".
%
% The list of all files belonging to the PM-ISOmath bundle is
% given in the file `manifest.txt'.
%
% The set of derived (unpacked) files belonging to the distribution
% and covered by LPPL is created by the self unpacking file
% pm-isomath.dtx which is the principal part of the distribution.
%
% \fi
%
% \iffalse
%^^A The following trick uses the same date for every file header.
%<style>\NeedsTeXFormat{LaTeX2e}[2017/01/01]
%<*driver>
\ProvidesFile{pm-isomath.dtx}[%
%</driver>
%<style>\ProvidesPackage{pm-isomath}[%
%<*driver,style>
2017/08/22 v.1.0.00 
%<style>Poor man package for typesetting ISO compliant math when using pdfLaTeX]
%</driver,style>
%<*driver>
]
%</driver>
%<*driver>
\documentclass{ltxdoc}
\GetFileInfo{pm-isomath.dtx}
\title{\texttt{PM-ISOmath}\\The Poor Man ISO math bundle}
\date{\fileversion\space--- \filedate}
 \author{Claudio Beccari\thanks{E-mail: \texttt{claudio dot beccari at gmail dot com}}}
 
\usepackage{metalogo,multicol,enumitem,url,booktabs}
\usepackage[utf8]{inputenc}
\usepackage[LGR,T1]{fontenc}
\usepackage{lmodern}
\usepackage{pm-isomath}
\let\originalmeta\meta
\renewcommand\meta[1]{{\normalfont\originalmeta{#1}}}
\def\prog#1{\textsf{#1}}
\def\pack#1{\textsf{\slshape#1}}
\def\env#1{\textit{#1}}\let\amb\env
\def\file#1{\texttt{#1}}
\def\marg#1{{\normalfont\texttt{\{}\meta{#1}\texttt{\}}}}
\def\Marg#1{{\texttt{\{#1\}}}}
\def\opz#1{{normalfont\textsl{#1}}}
\def\oarg#1{{\normalfont\texttt{[\meta{#1}]}}}
\def\Oarg#1{{\normalfont\texttt{[#1]}}}
\def\parg#1{{\normalfont\texttt{(\meta{#1})}}}
\def\Parg#1{{\normalfont\texttt{(#1)}}}
\providecommand\pdfLaTeX{pdf\/\LaTeX}
\providecommand\pdfTeX{pdf\/\TeX}
\newenvironment{ttsintassi}{\flushleft\ttfamily\obeylines}{\endflushleft}
\begin{document}\errorcontextlines=9
\maketitle
\begin{multicols}{2}
\tableofcontents
\end{multicols}
 \setlength\hfuzz{20pt}
 \DocInput{pm-isomath.dtx}
\end{document}
%</driver>
% \fi
%
% ^^A \CheckSum{}%
% \begin{abstract}
% The ISO regulation for typesetting math in the field of physics
% and technology are pretty stringent and imply legal questions
% that we do not treat here; It suffices to say the an
% ``Expertise'' for a Legal Court that does not fulfil such
% regulations in certain countries may be rejected by the Court,
% independently from its expert contents.
%
% Authors may not like them, but in the filed of \emph{applied
% sciences}, or better, of \emph{experimental sciences} that
% use measured quantities and units of measure, they are compulsory.
%
% With \LuaLaTeX\ and \XeLaTeX, while using OpenType math fonts
% there should not be any difficulty in fulfilling the regulations,
% but with \pdfLaTeX; things are not so simple. There exist some
% facilities, but sometimes they do not work.
%
% This package provides some robust work-arounds to bypass the
% difficulties experienced by some \pdfLaTeX\ users.
% \end{abstract}

% \section{Introduction}
% The ISO regulations (formerly ISO\,31/XI, now ISO\,80000) are
% stringent rules to typeset mathematics in the domains of physics
% and applied sciences; their title explicitly mentions ``physics
% and technology'', but their careful reading let understand that
% they apply to alla sciences that use the ``mathematics of
% quantities''. Such entities form a special group or space,
% where the elements are couples of two ordered elements $(x, y)$,
% where $y$ represents the unit of measure and $x$ represents the
% ratio of the quantity to the unit of measure. Such paired
% elements may not e separated, therefore some special
% mathematical rules are established in order to operate on
% such entities.
%
% Add to these special mathematical bases the facto that the
% measure component of the quantity is pretty fuzzy and it
% is always accompanied by a certain degree of uncertainty;
% metrologists are the the masters in measuring quantities
% and handling their measures and uncertainties, but although
% for simplicity measures are handled by lay people as rational
% numbers (after all aren't the the ratio of something to be
% measured and the unit of measure?) we are facing the domain
% of fuzzy sets.
%
% Furthermore quantities are so many that any work in applied
% sciences should contain a nomenclature list in order to
% explain which symbol is used for which quantity. This is
% where the ISO regulations set some order and they published
% a long list of named quantities with their preferred symbols
% and their ``normal'' units according to the prescriptions
% of the Comité International des Pois et Mésures, that
% established the the International System of measures 
% (Systhème International, SI).
% 
% This ISO nomenclature is used uniformly by most, if not all,
% people involved in applied sciences; therefore among the few
% letters of the Latin and Greek alphabets almost none is free
% to be used for other purposes.
%
% This means that the usual math italic alphabet can be used for
% very few symbols if confusion is to be avoided. Other series
% and shapes must be judiciously used and the ISO regulations
% say how.
%
% There are no problems when typesetting applied science
% documents with \LuaLaTeX\ or \XeLaTeX, at least if the
% proper OpenType math fonts are used; Such fonts have
% available so mani slots (code points) that may contain
% any variation of any glyph; it suffices to specify the
% option |math style = ISO| to the math handling package
% |unicode-math| and to select an OpenType math font. The
% only problem, if any, is to know which font series and
% shapes should be used according to the ISO regulations.
%
% These regulations can be purchased from the ISO site in
% Switzerland; they are quite expensive and the cost is
% affordable by associated professional studios or large
% academic and/or research institutions.
%
% For private users I'd suggest to download the PDF document
% \url{https://www.nist.gov/pml/special-publication-811-extended-%contents}. This document has been produced by the National
% Institute for Science and Technology, the Institutions that
% several years ago was appointed to replace the United States
% National Bureau of Standards. Thei staff is made essentially
% by metrologists and this guide is written to give precise
% instructions for handling the applied science mathematics
% according to the ISO Regulations; Is establishes also several
% rules for writing text about mathematics and metrology. It
% is extremely valuable for anglophones, but, with the due
% differences concerning the mother languages, it is extremely
% useful also for people using other languages than English.
%
% \section{The \pdfLaTeX\ handicaps}
% Users of \pdfLaTeX, on the opposite are in trouble. In facts
% this typesetting program suffers from an inherited limitation:
% math fonts are encoded with the old 128 glyph encodings; this
% is not a limitation  set forth by the underlying interpreter
% \pdfTeX. Matter of fact there exist the quite recent
% LibertinusT1math fonts for \pdfLaTeX, created by Michal Sharpe,
% that to my best knowledge are the only ones with 256 glyph
% encodings. Package |libertinust1math| accepts the |ISO| option
% that allows to fulfil the ISO regulations; it accepts other
% options depending on which the number of math groups, beyond
% the essential first four ones, increases by three to six units,
% reaching a maximum of ten; there remains enough free math
% groups to satisfy any user requirement.
%
% But even while using such LibertinusT1math fonts, \pdfTeX\ 
% suffers from another handicap derived from the knuthian
% original \TeX-the-program and by the NFSS (New FonT Selection
% Scheme, which is not new any more, because it dates back to
% 1994, when \LaTeX\,209 became obsolete and was substituted
% by \LaTeXe.). I am not complaining about these \pdfTeX\ and
% \LaTeX\ limitations; for decades people have been happily
% typesetting math with results that are much superior to any
% other typesetting program if it does not use some \TeX\ software.
%
% The handicap I am talking about is the way math alphabets are
% handled at the moment by \pdfTeX and \LaTeX; such alphabets
% are loaded in the form of math groups, the number of which
% cannot exceed 16 (numbered from 0 to 15); each group loads
% three sizes for normal math style, for script style and for
% script-script style. 
%
% By default four groups are always loaded; group~0 for
% operators; group~1 for letters; group~2 for symbols;
% group~3 for large operators and delimiters; users very
% often load also the two symbol-fonts provided by the
% American Mathematical Society, and this means two more
% math groups. Apparently there are ten more groups for
% other math groups. It seems that this number is abundantly
% sufficient to handle any situation, but it is not so. The
% author of this extension already reached the limit of~16
% without doing anything special -- at least he thought so,
% but he was evidently wrong. Users who use packages such
% as the Fourier or the KPfonts have to pay special attention
% to their documentation because they might specify options
% that imply loading up to 14 math groups.
%
% Several authors provided packages to help users produce
% perfect documents that fulfil the ISO regulations; I would
% like to cite the excellent Package|ISOmath| by Günter Milde,
% entitled ``Mathematical style for science and  technology''.
% It should be the perfect package to use in order to fulfil
% the ISO regulations; sometimes it succeeds with excellent
% results, but more often than not the results are just partial,
% because of the limitations of the math fonts available to
% \pdfLaTeX\ that are in contrast with the requirements of
% the ISO regulations.
%
% Therefore, dear reader, before using the poor man solutions
% of this package, try |ISOmath|, if your font set passes all
% the requirements described in this package documentation,
% you don't need the poor man patches offered by this package.
%
% \section{ISO rules summary}
% This summary does not replace the original ISO document nor
% what is written in the instructions published by NIST. It
% simply recalls those rules that this package tries to implement.
% In the following the word ``quantity'' is used to represent
% any physical entity that may be measured according to the
% metrological standards; the word ``variable'' is used to
% represent a mathematical entity that represents variable data.
%\begin{enumerate}[noitemsep]
% \item 
%   All quantity and variable symbols are represented by one
%   letter (with as many appositions are needed); but no acronyms
%   are allowed; in computer science programming many strings 
%   are called variables, in the sense that they may represent 
%   variable data; but computer programs are not mathematics, 
%   rather they are a special language that tells the computer 
%   what to do, even mathematics, but the language is not the 
%   one that represents math. Unfortunately som acronyms have 
%   gained strong popularity and wide usage, but they are 
%   forbidden by the ISO rules; example: \emph{CMRR} is often 
%   used to mean ``common mode rejection ratio'', but this is 
%   an improper usage of mathematics. Obviously this rule 
%   must be applied by the user, because \LaTeX\ is a 
%   typesetting language and does not understand the real 
%   meaning of what it typesets.
% \item
%   All quantity symbols must be set in italics, slanted type
%   is allowed, but serifed italics should be referred, unless 
%   the ISO rules prescribe a sans serif font. This implies that
% the differential symbol be in upright font to avoid confusion
% with the physical quantity $d$; the Napier number `e' must be
% set in upright font to avoid confusion with the elementary
% electric charge $e$; the imaginary unit j in electrical
% engineering, i in other applied sciences) be in upright font
% in order to avoid confusion with the electric current density
% $j$ or the electric current $i$; more difficult: the
% transcendental number $\ISOpi=3.14159\dots$ be distinguished 
% from the plane angle $\pi$; and similar other numerical constants represented by Latin or Greek letters.
% \item
%   All symbols that do not represent quantities should be 
%   typeset in an upright font, preferably a serifed font, 
%   except when the ISO rules require a sans serif font.
%   This rule include numbers and their digits, symbols that 
%   represent constant numeric values, all appositions both 
%   in subscript and superscript position. Appositions are not 
%   quantities or variables: for example in $V_i$, the 
%   subscript $i$ is a variable because it represents the $i$-th 
%   element in a sequence, such as $V_0, V_1, V_2, \dots$; on 
%   the opposite $V_{\mathrm{i}}$ is an apposition because `i' 
%   means, say, `input'.
% \item
%   Upright bold roman or black board bold symbols represent sets.
% \item
%   Italic bold symbols represent matrices; une column matrices
%   may represent vectors in an algebraic way and should be 
%   treated as any other matrix; generally multirow and multicolumn 
%   matrices are typeset with uppercase letters, while lowercase 
%   ones are reserved for vectors; but in some sciences also vectors 
%   may have uppercase letters. Geometrical vectors that might be 
%   typeset wit a medium series upper o lowercase italic letter 
%   with an arrow on top of it are nor treated by the ISO 
%   regulations that speak of vectors irrespective if they are 
%   considered as one column matrices od oriented segments; 
%   apparently oriented segments should be treated the same as 
%   one column matrices.
% \item
%   Labels to geometrical entities, such as points, segments,
%    angles (not their measures) should be set in upright 
%    medium series sans serif fonts; the same rule applies 
%    to labels used in sketches and drawings representing 
%    machinery, electric circuitry, and the like when the label 
%    refers to an object and not to its measure: ``the lens 
%    $\mathsf{L}_1$'', ``the switch $\mathsf{S}_2$'', ``the 
%    planetary gear $\mathsf{G}_3$'', and so on.
% \item
%   Tensors should be set in slanted bold sans serif font.
% \item 
%   The above rules apply to both Latin and Greek 
%   letters.\label{enum:latin-greek}
%\end{enumerate}
%
% Such font rules  for families, series and shapes are difficult
% to implement with \pdfLaTeX\ for many reasons that do not imply
% only the limited number of math groups, but also the categories
% of symbols; Greek letters in particular are troublesome for a
% couple of reasons connected with rule~\ref{enum:latin-greek}:
%\begin{itemize}[noitemsep]
%\item
%   Uppercase greek letters are taken from the ``operators'' 
%   alphabet and are letter symbols; therefore they are upright; 
%   but if they represent quantities they must be in italics, 
%   or at least slanted;
%\item
%   Lowercase Greek letters are taken from the ``letters'' alphabet
%   and are ordinary symbols; they are slanted, and this is fine, 
%   but as ordinary symbols they cannot be modified by commands 
%   such as |\mathrm|; furthermore upright lowercase Greek letters
%   are not available.
%\end{itemize}
%
% \section{Some existing solutions}
% Several packages to be used with \pdfLaTeX\ allow for upright
% Greek letters, especially those packages for French typography,
% where the national rules (in contrst with the ISO regulations)
% require that all math entities typeset with Greek letters be
% upright. Among these the |fourier| and the |kpfont|. Other
% packages such as |newpxmath| and |newtxmath| are intended for
% general use, but with suitable options and extra math groups
% let the user employ upright lowercase letters as well as
% slanted uppercase ones.
%
% Package |libertinust1math| allows the use of the 256~glyph
% encoded fonts and are less sensitive to the limit of 16~math
% groups, Is many options allow to use the various font styles
% without requiring the |\boldmath| declaration; this implies
% that medium and bold series are both preloaded without
% actually using extra math alphabets beyond the small number
% it uses for its full functionality. An option |ISO| is
% already available to fulfill the ISO regulations. Maybe
% the only drawback of the fonts used is that they match text
% fonts that are blacker than the standard Computer or Latin
% Modern fonts. The auxiliary font selection commands used in
% the |ISOmath| package are already implemented with this
% |libertinust1math| one.
%
% Of course the |ISOmath| package might solve all problems if the
% user math environment has the necessary functionalities, in
% particular all the math alphabets needed for the task and
% there are no difficulties with the number of math groups.
%
% \section{The poor man solution}
% The poor man solution is  very simple in theory; it handles
% text fonts in math expressions through the |\text| command
% of the |amsmath| package; of course there are functionalities
% to chose families series and shapes in a comfortable way
% by means of the powerful command definition commands provided
% by the |xparse| package; for Greek letters it uses the
% functionalities of the |alphabeta| package, that allows to use
% in text mode the same control sequences that are used
% in math mode. The default families for Latin and Greek letters
% are the Latin Modern ones that allow a piecewise continuous
% scaling of any available particular font of the collection.
%
% Needless to say, this poor man solution has advantages and
% disadvantages over the other indicated solutions.
%
% The main advantage is that no math groups are involved,
% therefore the user may couple any font family with any
% series and shape that family allows; the default
% family for Greek fonts are the Latin Modern compliant
% LGR encoded collection of CBfonts; they are always
% available with any updated and complete \TeX\ system
% installation.
%
% This is also a disadvantage, in the sense that Latin Modern
% fonts might not be the best ones to use with any specific
% text font; for example they have an x-height smaller than
% the Palatino ones, and a larger `em' unit compared to the
% Times ones; they have also a slightly lighter `color'
% than most other fonts.
%
% Nevertheless they work very well with the ISO regulations
% and in spite of the disadvantages listed above, they are
% usable without problems. 'This documentation is typeset
% with Latin Modern fonts and this very package. The examples
% shown in a following chapter show the ease with which the
% ISO regulations may be fulfilled.
%
% There are other Greek fonts that may be used in place if
% those of the CBfonts collection, especially those distributed
% by the Greek Font Society (GFS) that are already part of the
% \TeX\ system distribution; they are LGR encoded and have their
% specific |.fd| files. They are not so rich in series and shapes
% (some of them may lack the bold extended series and sometimes
% lack also the bold series); I would say the the GFS Bodoni
% family is sufficiently rich of series and shapes, and may be used
% also for the Latin fonts. 
%
% There are also the Greek fonts that are ``companions'' to the
% Times fonts. So the user is not limited to the Latin Modern
% fonts, but admittedly there is not a great choice and, if it
% is necessary, the disadvantage of an unmatching Greek font is
% the price to pay if the user has to use \pdfLaTeX.
%
% \section{Usage}
% The usage of the package is very simple; in your preamble 
% add the line
%\begin{ttsintassi}
%\cs{usebackage}\Oarg{engineer}\Marg{pm-isomath}
%\end{ttsintassi}
% The |engineer| option is used to set the imaginary unit the
% way electrical engineers usually do.
%
% The main macros that support the whole package, and that may
% be used also by the end user, are:
%\begin{ttsintassi}
%\cs{MathLatin}\marg{letter}\marg{family}\oarg{series}\parg{shape}
%\end{ttsintassi}
%and
%\begin{ttsintassi}
%\cs{MathGreek}\marg{letter}\marg{family}\oarg{series}\parg{shape}
%\end{ttsintassi}
% where \cs{MathLatin} sets the text encoding to |T1|, while
% \cs{MathGreek} set it to |LGR|. In both commands the arguments
% specified with \marg{family}\oarg{series}\parg{shape} are all
% optional, including the first one in spite of being surrounded
% by curly braces. In both cases the default values for each
% argument are respectively |lmr|, |m|, and |n| (normal upright).
%
% Such default values, after loading |pm-isomath|, may be globally
% redefined by using in the preamble:
%\begin{ttsintassi}
%\cs{renewcommand}\Marg{ISOfam}\marg{family}
%\cs{renewcommand}\Marg{ISOser}\marg{series}
%\cs{renewcommand}\Marg{ISOsha}\marg{shape}
%\end{ttsintassi}
% We discourage this global redefinitions unless the user really
% knows what s/he is doing; in practice it must be checked  that
% T1 encoded families and LGR encoded ones have the same family
% names. If the encoding+family|.fd| files are not available
% either they have to be created, or  such default values should
% not be redefined.
% 
% For Latin letters to use in the |\MathLatin| command mandatory
% argument there are no problems.
%
% For Greek letters you might use the math commands |\alpha|,
% |\beta|,\dots, |\Omega| commands, but it is much simpler to
% use the package commands |\ISOalpha|, |\ISObeta|,\dots,
% |\ISOOmega|. All these commands follow the syntax:
%\begin{ttsintassi}
%\cs{ISO}\meta{lettername}\marg{family}\oarg{series}\parg{shape}
%\end{ttsintassi}
% where all the arguments are optional, including the first in
% spite of being surrounded by curly braces. Such optional
% arguments must follow that order but all possible combinations
% are usable, for example:
%\begin{ttsintassi}
%\cs{ISOalpha}
%\cs{ISOalpha}\marg{family}
%\cs{ISOalpha}\oarg{series}
%\cs{ISOalpha}\parg{shape}
%\cs{ISOalpha}\marg{family}\oarg{series}
%\cs{ISOalpha}\marg{family}\parg{shape}
%\cs{ISOalpha}\oarg{series}\parg{shape}
%\cs{ISOalpha}\marg{family}\oarg{series}\parg{shape}
%\end{ttsintassi}
% This offers the maximum flexibility in using the necessary
% commands.
%
% The package defines other macros for fulfilling the rules
% relative to the differential symbol and the numerical constants
% represented with letters; Furthermore defines the commands
% for the |\ohm| unit of measure and the |\micro| SI prefix;
% this latter macro uses a special shape of the CBfonts where
% an upright shape with serifed lowercase Greek letters is
% available; if another family lacking this shape is being used,
% then the normal upright shape is used. In typesetting this
% documentation, evidently there are no problems, but with other
% font selections, especially with Greek fonts, there might be
% some mismatching shapes.
% 
% Commands similar to those defined by the |ISOmath| package
% are also defined so as to simplify the font selection for
% vectors, matrices and tensors.
%
% \section{Examples}
% \subparagraph{ISO Greek letters}
% In this example we typeset an array in math mode, where
% we show all the Greek letters that can be typeset with
% the \cs{ISO}\meta{letter} macros; the array is typeset
% in normal math style, but the ISO letters are in bold
% style so that there is no confusion with a normal
% bold math setting; some letters, equal to
% the Latin ones, are also defined because some users have
% experienced difficulties in remembering the correct signs
% especially while labelling diagrams. The
% array may be a useful reference, \ref{tab:isoletters}.
%\begin{table}[!tb]
%\def\T#1{\cs{ISO#1} & \csuse{ISO#1}[bx]}
%\[\begin{array}{lclclclc}
%\T{alpha} 	& \T{beta} 		&
%\T{gamma} 	& \T{delta}  	\\ 
%\T{epsilon} & \T{zeta}  	&
%\T{eta} 	& \T{theta}  	\\ 
%\T{iota} 	& \T{kappa}  	& 
%\T{lambda} & \T{mu}  		\\ 
%\T{nu} 	& \T{xi}  		&
%\T{omicron}& \T{pi}  		\\ 
%\T{rho} 	& \T{sigma}  	& 
%\T{tau} 	& \T{upsilon}  	\\ 
%\T{phi} 	& \T{chi}  		&
%\T{psi} 	& \T{omega}  	\\ 
%\T{Gamma} 	& \T{Delta}  	& 
%\T{Eta} 	& \T{Theta}  	\\ 
%\T{Lambda} & \T{Xi}  		& 
%\T{Pi} 	& \T{Rho}  		\\ 
%\T{Sigma} 	& \T{Upsilon}  	& 
%\T{Phi} 	& \T{Chi}  		\\
%&&\T{Psi} 	& \T{Omega}
%\end{array}\]
%\caption{The \cs{ISO}\meta{letter} macros and their rendering in bold  style}
%\label{tab:isoletters}
%\end{table}
% \subparagraph{A small matrix equation}
%\[ \vectorsymbol{b} = \matrixsymbol{M}\vectorsymbol{a} \] is
% typeset with the following code
%\begin{verbatim}
%\[ \vectorsymbol{b} = \matrixsymbol{M}\vectorsymbol{a} \]
%\end{verbatim}
% \subparagraph{A resistivity value}
% The resistivity of copper is $1.68\,\micro\ohm\,\mathrm{cm}$ (1.68\unit{\micro\ohm\,cm})
% is typeset with the following code
%\begin{verbatim}
%$i.68\,\micro\ohm\,\mathrm{cm}$ (1.68\unit{\micro\ohm\,cm})
%\end{verbatim}
%\subparagraph{A tensor}
%\[ \vectorsymbol{D} =\epsilon_0\vectorsymbol{\epsilon}\ped{r}\vectorsymbol{E}\]
%is typeset with the following code
%\begin{verbatim}
%\[ 
%\vectorsymbol{D} = \epsilon_0\tensorsymbol{\epsilon}\ped{r}\vectorsymbol{E}
%\]
%\end{verbatim}
%\subparagraph{Solid angle}
% An energy flux of light form a isomorph source that irradiates
% the power $P$ through the solid angle $\Omega$ generates
% a flux \[\Phi = \frac{P}{\Omega}\] is typeset with the following
% code
%\begin{verbatim}
%\[\Phi = \frac{P}{\Omega}\]
%\end{verbatim}
% where, as you see the uppercase Greek letters are slanted,
% as the ISO rules require, instead of upright, as \LaTeX\ sets
% them by default.
% \subparagraph{A bold formula}
% This is the very important inverse Laplace transform
%{\boldmath\[
%f(t) = \frac{1}{2\ISOpi\iu} -\mkern-19mu\int_{\sigma-\iu\infty}^{\sigma+\iu\infty}\eu^{pt}\diff p \qquad \text{for } \sigma > \sigma\ped{c}
%\]}
%%typeset with the following code
%\begin{verbatim}
%{\boldmath\[f(t)=
%f(t) = \frac{1}{2\ISOpi\iu} -\mkern-19mu
%   \int_{\sigma-\iu\infty}^{\sigma+\iu\infty}\eu^{pt}\diff p 
%     \qquad \text{for } \sigma > \sigma\ped{c}
%\]}
%\end{verbatim}
% Notice the the use of |\boldmath| does not imply the use
% of new math groups; but the bold upright $\ISOpi$ is rendered
% without any problem.
% \subparagraph{Various styles of Greek fonts} Here are some
% examples of Greek fonts in various styles;  within the same
% table bold and medium series fonts stay side by side, as well
% as font coming from different families.\medskip
%
%\bgroup\begin{lrbox}{0}
%\begin{tabular}{@{}ll@{}}
%\cs{ISOgamma}, \cs{ISOzeta}, \cs{ISOeta}, \cs{ISOOmega}&
%$\ISOgamma, \ISOzeta, \ISOeta, \ISOOmega$\\
%\cs{ISOgamma}[bx], \cs{ISOzeta}[bx], \cs{ISOeta}[bx], \cs{ISOOmega}[bx]&
%$\ISOgamma[bx], \ISOzeta[bx], \ISOeta[bx], \ISOOmega[bx]$\\
%\cs{ISOgamma}\{lmss\}, \cs{ISOzeta}\{lmss\}, \cs{ISOeta}\{lmss\}, \cs{ISOOmega}\{lmss\}&
%$\ISOgamma{lmss}, \ISOzeta{lmss}, \ISOeta{lmss}, \ISOOmega{lmss}$\\
%\cs{ISOgamma}\{artemisia\}, \cs{ISOzeta}\{artemisia\}, \cs{ISOeta}\{artemisia\}, \cs{ISOOmega}\{artemisia\}&
%$\ISOgamma{artemisia}, \ISOzeta{artemisia}, \ISOeta{artemisia}, \ISOOmega{artemisia}$\\
%\cs{ISOgamma}(rs), \cs{ISOzeta}(rs), \cs{ISOeta}(rs), \cs{ISOOmega}(rs)&
%$\ISOgamma(rs), \ISOzeta(rs), \ISOeta(rs), \ISOOmega(rs)$\\
%\end{tabular}\end{lrbox}
%\noindent\resizebox{\textwidth}{!}{\usebox{0}}\egroup
%
%\section{Final remarks}
% This package |pm-isomath| is far from perfect, and its results are
% questionable; of course poor man solutions are just patches;
% incomplete solutions; But the results are not so bad. It has
% the indubitable advantage that is does not use any math group,
% therefore there is no risk to exceed the limit of 16~math groups.
%
% \StopEventually{}
%
% \section{The code}
% This package was loosely inspired by the |ISOmath| package
% by Günter Milde, but tacles the problem of insuffiente maximum
% number of math font groups so as to avoid any problem with such
% groups, and therfore all the caveats in Milde's package. That
% package is much more comfortable to use then this one; but
% it is subject to a number of conditions the, depending on the
% user environment, may even result in a complete failure. This
% package avoids problema with math font groups because it does
% not use any, but it is not so comfortable to use because often
% the user has to specify optional settings.
%
%The preliminary lines have been already defined; therefore we
% start with real code.
%
%The trick of this package is that all fonts different from the
% four or six (including the AMS symbol fonts) are textual fonts
% used in math typesetting through the intermediate action of
% the |\text| command defined by the |amsmath| package.
% Therefore we start by verifying if packages |amsmath|,
% |alphabeta| and |xparse| have already been loaded by in the
% preamble document; this implies a weak loading order, that is this
% package must be loaded after all the above packages are loaded;
% in facts of such packages are not loaded, they are by this
% package, and they are loaded without options. The package
% loading mechanism assures avoiding conflicts if packages are
% loaded without options; this is why if one of the three packages
% is loaded after this one but with some option specified an
% ``Option clash"" error flag is raised; this is where the
% ``weak'' loading error becomes an very ``strong'' one.
 
%\iffalse
%<*style>
%\fi
%    \begin{macrocode}
% The we verify if the document is being typeset with \pdfLaTeX;
% it it is not; and error flag is raised and reading of this
% package is immediately interrupted. For this purpose we need
% an engine-detecting package, and we generally use the |iftex| one.
\@ifpackageloaded{iftex}{}{\RequirePackage{iftex}}
\unless\ifPDFTeX
    \PackageError{ISOrules4pdfLaTeX}{%
       ******************************************\MessageBreak
       This package should be used only when     \MessageBreak
       typesetting with pdfLaTeX.                \MessageBreak
       Skipping loading the package              \MessageBreak
       ******************************************\MessageBreak
    }{%
       ******************************************\MessageBreak
       Press the X key and restart typesetting   \MessageBreak
       while using pdfLaTeX\MessageBreak
       ******************************************\MessageBreak
    }
\expandafeter\@firstoftwo
\else
    \PackageInfo{ISOrules4pdfLaTeX}{%
       ******************************************\MessageBreak
       Typesetting this document with pdfLaTeX!  \MessageBreak
       ******************************************\MessageBreak
    }
\expandafter\@secondoftwo
\fi
{\endinput}{\relax}
%    \end{macrocode}
% Actually this package accepts an option: |engineer|. This
% option is for deciding if the imaginary uit should be
% defined as `i' or `j'. As we have remarked in the previous
% documentation, engineers, especially those who deal with
% electricity and electrical quantities, but also electronics
% and telecommunications engineers, use only `j'; all these
% varieties of engineers could not do anything in their profession
% if they don't use complex  numbers and quantities (the latter
% called phasors). possible they are the applied scientists
% who use complex numbers more than any other scientist.
% This option has not been used to prepare this documented \TeX\ file.
%    \begin{macrocode}
\newif\ifengineer \engineerfalse
\DeclareOption{engineer}{\engineertrue}
\ProcessOptions*\relax
%    \end{macrocode}
% Are the necessary packages already loaded?
%    \begin{macrocode}
\@ifpackageloaded{amsmath}{}{\RequirePackage{amsmath}}
\@ifpackageloaded{etoolbox}{}{\RequirePackage{etoolbox}}
\@ifpackageloaded{xparse}{}{\RequirePackage{xparse}}
%    \end{macrocode}
% Now we have almost alla software instruments available. We
% define a macro to switch the definitions of certain math
% Greek symbols; some of these are defined in the \LaTeX\ 
% kernel: the lowercase Greek variant letters; some others
% are defined in the |amsmath| package: the uppercase slanted
% greek letters. all these variant lettere have a name identical
% to the regular ones but prefixed with the string |var|;
% example |\epsilon| and |\varepsilon|, |\Omega| and |\varOmega|.
% We switch the control sequence definitions between the |var|-less
% ones and the |var|-prefixed ones. The first  group of lowercase
% letters is switched because the glyphs give a better match with
% those produced with the textual Greek glyphs obtained when
% the ISO macros are used.
%    \begin{macrocode}
\newcommand\switchvarsymbols[1]{%
\letcs{\tempA}{#1}\csletcs{#1}{var#1}\cslet{var#1}{\tempA}}
%%%% 
\switchvarsymbols{epsilon}
\switchvarsymbols{theta}
\switchvarsymbols{rho}
\switchvarsymbols{phi}
%%%%%
\switchvarsymbols{Gamma}
\switchvarsymbols{Delta}
\switchvarsymbols{Theta}
\switchvarsymbols{Lambda}
\switchvarsymbols{Xi}
\switchvarsymbols{Pi}
\switchvarsymbols{Sigma}
\switchvarsymbols{Upsilon}
\switchvarsymbols{Phi}
\switchvarsymbols{Psi}
\switchvarsymbols{Omega}
%    \end{macrocode}
% Eventually we load the |alphabeta| package; this package
% allows using the same macros used in math mode while
% typesetting in text mode. We find it very useful in this
% package.
%    \begin{macrocode}
\@ifpackageloaded{alphabeta}{}{\RequirePackage{alphabeta}}
%    \end{macrocode}
% The next line defines the default family, series and shape
% to be used in the macros that follow; as it can be seen
% the default family is the Latin Modern regular (or roman);
% the series i medium and the shape is normal (or upright).
% The codes used are the same used in the font description
% files with extension |.fd|. their name if obtained by merging
% the encoding name with the family name; Therefore the default
% font description  file for Latin Characters is |t1lmr.fd|,
% while the one for Greek characters is |lgrlmr.fd|; these
% files define the series the contains that are identified
% with codes such as |m| (medium); |bx| (bold extended);
% |b| (bold). Other fonts, with different series may have
% also other codes. For each series the |.fd| defines the
% codes for shapes, and for every valid combination of
% series, shape and sizes it defines the specific font file
% to use. 

% We should not care for the font names, but in order to use
% different font families, series, and shapes the user should
% know their codes. this is generally a difficult task, but
% not impossible; is ``suffices'' to open the packages that
% allow to use the desired fonts, read the code and fin out
% the names of the |.fd| files; then search this file on the
% trees of the \TeX\ system, and eventually find out the
% codes for the available series and shapes.
% 
% for the Latin and Greek |.fd| file we havethe series and
% shapes shown in table~\ref{tab:lmr-series-shapes}.
%
%\begin{table}[!tb]\centering
%\begin{tabular}{llllll}
%\toprule
%       &      & \multicolumn2c{Latin (T1)} 
%                      & \multicolumn2c{Greek (LGR)} \\
%\cmidrule(r){3-4} \cmidrule(l){5-6}
%Series & Code & Shape   & Code & Shape     & Code \\
%\midrule
%medium &  m   & normal          &  n   & normal        & n    \\
%       &      & italics         & it   & italics       & it   \\
%       &      & slanted         & sl   & slanted       & sl   \\
%       &      &                 &      & lipsian       & li   \\
%       &      &                 &      & serif         & rs   \\
%       &      &                 &      & serif oblique & ro   \\
%       &      & upright italics &  ui  & upright italics& ui  \\
%       &      & small caps      & sc   & small caps    & sc   \\
%\midrule
% bold  &   b  & 				 &		& lipsian		& li   \\
%		&	   & normal			 & n	&				&      \\
%		%      & slanted		 & sl	&				&	   \\
%\midrule
% bold extended&bx& normal       & n    & normal        & n    \\
%       &      & italics         & it   & italics		& it   \\
%		&	   & slanted         & sl   & slanted       & sl   \\
%       &      &				 &		& lipsian       & li   \\
%		%	   &				 &		& serif         & rs   \\
%		%	   &				 &		& serif oblique & rs   \\
%		&	   &				 %      & upright italics& ui  \\
%		&	   &				 &		& small caps	& sc   \\
%\bottomrule
%\end{tabular}
%\caption{Seres and shapes available with the Latin Modern regular family with Latin and Greek fonts}
%\label{tab:lmr-series-shapes}
%\end{table}
%
%
%
%
%%%%%% Queste sono le impostazioni di default per la famiglia,
%%%%%% la serie e la forma:
%    \begin{macrocode}
\def\ISOfam{lmr}\def\ISOser{m}\def\ISOsha{n}
%    \end{macrocode}
%
% As explained in the initial documentation all fonts changing
% commands are constructed in such a way as to have a default
% family, series and shape common  to both Latin and Greek fonts;
% therefore with thre optional arguments that the user can
% specify with different delimiters but respecting their order,
% the user can get eight different choice combinations that
% allow the selection of an almost limited less number of
% different looks.
%
% We now define the mains macros and service macros that allow
% such font selection; We have ti create similar macros that
% mostly differ in the choice of the encoding for Latin or
%  for Greek letters.
%
% The user macros are defined by meanso of the defining commands
% provided by the |xparse| package, while the service macros use
% normal \LaTeX\ commands. The user commands follow this special
% syntax:
%\begin{ttsintassi}
%\cs{MathLatin}\marg{Latin letter}\marg{family}\oarg{series}\parg{shape}
%\cs{MathGreek}\marg{Greek letter}\marg{family}\oarg{series}\parg{shape}
%\end{ttsintassi}
% where in both cases the last three arguments are differently
% delimited values, even the first one of the three, in spite
% of being delimited by curly braces. In both cases the only
% mandatory argument is the Latin or Greek letter; the latter
% one my be specified by the macros |\alpha|, |\beta|,\dots,
% |\Omega|, the same ones that are normally used in math.
%    \begin{macrocode}
\NewDocumentCommand\MathLatin{m gO{m}D(){it}}{\bgroup
\edef\y{\IfNoValueTF{#2}{\ISOfam}{#2}}%
\edef\x{\noexpand\egroup\noexpand\MLatin{\noexpand#1}{\y}}\x{#3}{#4}}

\providecommand\MLatin[4]{\text{%
\def\ISOfam{#2}\def\ISOser{#3}\def\ISOsha{#4}%
\ifcsstring{math@version}{bold}{\def\ISOser{bx}}{}%
\usefont{T1}{\ISOfam}{\ISOser}{\ISOsha}#1}}

\NewDocumentCommand\MathGreek{ m g O{m} d()}{%
\edef\y{\IfNoValueTF{#2}{\ISOfam}{#2}}%
\edef\x{\IfNoValueTF{#4}{\ISOsha}{#4}}%
\MGreek{#1}{\y}{#3}{\x}}

\newcommand{\MGreek}[4]{\text{%
\def\ISOfam{#2}\def\ISOser{#3}\def\ISOsha{#4}%
\ifcsstring{math@version}{bold}{\def\ISOser{bx}}{}%
{\usefont{LGR}{\ISOfam}{\ISOser}{\ISOsha}#1}}}

%    \end{macrocode}
% We now define the macros for all lowercase Greek letters
% and several Uppercase ones (even some that are identical
% to some Latin Letters) that should save several keystrokes
% when entering Greek letters in the source file. The shorter
% the code to type in, the smaller the the number of typos.
%    \begin{macrocode}
\newcommand\ISOalpha{\MathGreek{\alpha}}
\newcommand\ISObeta{\MathGreek{\beta}}
\newcommand\ISOgamma{\MathGreek{\gamma}}
\newcommand\ISOdelta{\MathGreek{\delta}}
\newcommand\ISOepsilon{\MathGreek{\epsilon}}
\newcommand\ISOzeta{\MathGreek{\zeta}}
\newcommand\ISOeta{\MathGreek{\eta}}
\newcommand\ISOtheta{\MathGreek{\theta}}
\newcommand\ISOiota{\MathGreek{\iota}}
\newcommand\ISOkappa{\MathGreek{\kappa}}
\newcommand\ISOlambda{\MathGreek{\lambda}}
\newcommand\ISOmu{\MathGreek{\mu}}
\newcommand\ISOnu{\MathGreek{\nu}}
\newcommand\ISOxi{\MathGreek{\xi}}
\newcommand\ISOomicron{\MathGreek{\omicron}}
\newcommand\ISOpi{\MathGreek{\pi}}
\newcommand\ISOrho{\MathGreek{\rho}}
\newcommand\ISOsigma{\MathGreek{\sigma}}
\newcommand\ISOtau{\MathGreek{\tau}}
\newcommand\ISOupsilon{\MathGreek{\upsilon}}
\newcommand\ISOphi{\MathGreek{\phi}}
\newcommand\ISOchi{\MathGreek{\chi}}
\newcommand\ISOpsi{\MathGreek{\psi}}
\newcommand\ISOomega{\MathGreek{\omega}}
\newcommand\ISOGamma{\MathGreek{\Gamma}}
\newcommand\ISODelta{\MathGreek{\Delta}}
\newcommand\ISOEta{\MathGreek{\Eta}}
\newcommand\ISOTheta{\MathGreek{\Theta}}
\newcommand\ISOLambda{\MathGreek{\Lambda}}
\newcommand\ISOXi{\MathGreek{\Xi}}
\newcommand\ISOPi{\MathGreek{\Pi}}
\newcommand\ISORho{\MathGreek{\Rho}}
\newcommand\ISOSigma{\MathGreek{\Sigma}}
\newcommand\ISOUpsilon{\MathGreek{\Upsilon}}
\newcommand\ISOPhi{\MathGreek{\Phi}}
\newcommand\ISOChi{\MathGreek{\Chi}}
\newcommand\ISOPsi{\MathGreek{\Psi}}
\newcommand\ISOOmega{\MathGreek{\Omega}}
%    \end{macrocode}
% We redefine also the |\mathrm| and |\mathit| so that if they
% have to contain Greek letters the default shape is set equal
% to that of the enclosing command. Such macros are just those
% defined in the \LaTeX\ kernel where the |\ISOsha| redefinition
% is added.
%    \begin{macrocode}
\DeclareRobustCommand{\mathrm}%
{\relax\ifmmode\else\expandafter\non@alpherr
\csname mathrm \endcsname\fi
\def\ISOsha{n}\expandafter\use@mathgroup
\csname M@OT1\endcsname\symoperators}

\DeclareRobustCommand{\mathit}%
{\relax\ifmmode\expandafter\non@alpherr
\csname mathit \endcsname\fi
\def\ISOsha{it}\expandafter\use@mathgroup
\csname M@OT1\endcsname{9}}
%    \end{macrocode}
% Imitating the |ISOmath| package we define also the macros
% for selecting the bold italics (produces results similar
% to those obtained with package|bm|, but it does not require
% any math group), and sans serif in  both normal and bold
% slanted shape.
%    \begin{macrocode}
\newcommand\mathbfit[1]{\MathLatin{#1}{lmr}[bx](it)}
\newcommand\mathsfit[1]{\MathLatin{#1}{lmss}[m](sl)}
\newcommand\mathsfbfit[1]{\MathLatin{#1}{lmss}[bx](sl)}
%    \end{macrocode}
% Package |ISOmath| defines macros for typesetting vectors,
% matrices and tensors; we do the same, but avoid the
% abbreviation |sym| in place of |symbol|.
%    \begin{macrocode}
\let\vectorsymbol\mathbfit
\let\matrixsymbol\mathbfit
\let\tensorsymbol\mathsfbfit
%    \end{macrocode}
%
% We now define some macros for setting some elements in the
% proper fonts; the ideaa is the same as that for vectors,
% matrices and tensors, except that these macros produce
% directly the desired symbol without using arguments, if
% possible.
%
% The imaginary unit is subject to the state of the |engineer|
% switch, set with the proper option on calling the package.
% If such option has been specifies in calling this package,
% the |\iu| command is let to |\junit|, otherwise it's let
% to |\iunit|. In spite of this option driven aliases, both
% commands |\iunit| and |\junit| are stille available to the
% user.
%
% The Napier number `e' is defined in roman type, but as an
% operator; this number is not an operator in the mathematical
% sense, but it is most often uses as the base of an exponential;
% therefore such mathematica ``atom'' must be treated as an
% operator as well as when the official operator macro |\exp|
% is used.
%
% The transcendental number $\ISOpi$, different from the plane
% angle $\pi$, is defined so as to be typeset in upright
% style; similar definitions may be used for other numerical
% constants; we define just |\uppi| because we think it is the
% most used symbol in any kind of mathematics. The
% $\ISOpi{lmss}(n)$ Greek letter in upright sans serif font
% may indicate the subatomic particle ``pion'' so that a
% similar macro, say, |\sspi| or, more expressively, |\pion|
% may be given a suitable definition.
%
% The differential symbol is not an operator, but it requires
% a special treatment; a macro |\diff| for the differential
% symbol uses an empty`operator' and a negative shift to typeset
% an upright letter `d'  with an operator spacing on its left,
% so that proper spacing is used in math typesetting; Notice
% that the given definition does not perform as the direct
% use of a thin math space before the upright `d', because
% spacing bteween math atoms depends on their category, while
% the thin space |\,| is absolute and does not change depending
% on the preceding math atom.
%
% The command |\unit| for appending the units of measure to
% the numerical value of the measure is added if no packages
% have already defined it; package |siunitx| is a particularly
% recommended one.  Similar considerations hold true for the
% |\ap| and |\ped| (apex and pedex, respectively; i.e\ 
% superscript and subscript); therefore such command definitions
% are deferred to the start of the document so as to be sure
% to avoid damaging other package settings. All these commands
% may be used in both text and math modes; therefore a robust
% macro |\textormath| is (re)defined even if often such command
% is already available; the |\DeclareRobustCommand| unconditionally
% declares and redeclares robust commands even if they are
% already defined; possibly an information line is written in
% the |.log| file in case a redefinition takes palace. These
% commands typeset their arguments in upright math fonts, but
% with the current font in text mode.
%
% The |\ohm| and |\micro| macros produce their symbols in
% upright style while in math mode, and with the current
% font and shape in text mode.
%
%    \begin{macrocode}
\newcommand\iunit{\MathLatin{i}(n)}
\newcommand\junit{\MathLatin{j}(n)}
\ifengineer
   \let\iu\junit
\else
   \let\iu\iunit
\fi
% i
\let\eu\undefined
\DeclareMathOperator\eu{\MathLatin{e}(n)}
\providecommand\uppi{}
\renewcommand\uppi{\ISOpi(n)}
% 
\providecommand*\diff{}
\renewcommand*\diff{\ensuremath{\mathop{}\!\MathLatin{d}(n)}}
% 
\providecommand*\micro{}
\renewcommand*\micro{\textormath{\ifcsdef{textmicro}%
{\textmicro}{\ISOmu(rs)}}{\ISOmu(rs)}}
% 
\providecommand*\ohm{}
\AtBeginDocument{\@ifpackageloaded{textcomp}{%
\renewcommand*\ohm{\textormath{{\textohm}}{\ISOOmega(n)}}}%
{\renewcommand*\ohm{\textormath{\ISOOmega(\f@shape)}{\ISOOmega(n)}}}}
% 
\global\csletcs{bbl@it@ped}{undefined}
\global\csletcs{bbl@it@ap}{undefined}
%
\DeclareRobustCommand\textormath{%
\unless\ifmmode\expandafter\@firstoftwo
\else\expandafter\@secondoftwo\fi}
%
\AfterEndPreamble{\let\ped\undefined\let\ap\endefined
\DeclareRobustCommand*\ped[1]{%
\textormath{\textsubscript{#1}}{_{\mathrm{#1}}}}%
%
\providecommand\ap{}
\DeclareRobustCommand\ap[1]{%
\textormath{\textsuperscript{#1}}{^{\mathrm{#1}}}}%
%
\unless\ifcsname unit\endcsname
\DeclareRobustCommand{\unit}[1]{\,\textormath{#1}{\mathrm{#1}}}
\fi}

\endinput
%    \end{macrocode}
%This is the end
%\begin{center}
%\LARGE HAPPY \TeX{}ing\,!
%\end{center}
%\iffalse
%</style>
%\fi

%\Finale
% \endinput