Make \mathrm produce upright greek

Question

I need to distinguish between italic and upright greek letters. I use the alphabeta package for that. This allows me to write e.g. an upright \mu in mathmode by typing $\text\mu$. Can I extend this in such a way that also \mathrm produces the upright \mu?

\documentclass{article}
\usepackage{amsmath}
\usepackage{alphabeta}
\begin{document}
\begin{align}
\text{is italic mu: } & \mu \mathit \mu\
\text{should be upright mu: } & \text \mu \mathrm \mu
\end{align}
\end{document}

Answer 1

This is easiest with unicode-math and lualatex or xelatex as a Unicode math font already contains both styles of mu:

\documentclass{article}
\usepackage{amsmath}
\usepackage{unicode-math}
\begin{document}
\begin{align}
\text{is italic mu: } & \mu \
\text{should be upright mu: } & \symup{\mu}
\end{align}
\end{document}

Answer 2

Since you appear to use Greek letters mainly (exclusively?) in math mode, you may want to acquaint yourself with the upgreek package, which offers macros called \upalpha, \upbeta, etc.

\documentclass{article}
\usepackage{upgreek}
\begin{document}
\begin{tabular}{ll}
slanted greek math-mode letters: & $\alpha\beta\gamma\dots\mu\nu\dots\omega$ \\
upright greek math-mode letters: & $\upalpha\upbeta\upgamma\dots\upmu\upnu\dots\upomega$
\end{tabular}
\end{document}

Answer 3

A solution for pdftex. Wildly untested, so there might be issues I haven't thought of. Note that alphabeta cannot be loaded, but its basic functionality is provided.

\documentclass{article}
\usepackage{amsmath}% for \text
\usepackage{bm}
\usepackage{textalpha}
\makeatletter
\def@tempa#1#2#3{%
   \let#2=#1
   \def#1{\TextOrMath{#3}{\ifnum\fam=0 \text{#3}\else#2\fi}}%
}
@tempa\alpha\mathalpha\textalpha
@tempa\beta\mathbeta\textbeta
@tempa\gamma\mathgamma\textgamma
@tempa\delta\mathdelta\textdelta
@tempa\epsilon\mathepsilon\textepsilon
@tempa\zeta\mathzeta\textzeta
@tempa\eta\matheta\texteta
@tempa\theta\maththeta\texttheta
@tempa\vartheta\mathvartheta\texttheta
@tempa\iota\mathiota\textiota
@tempa\kappa\mathkappa\textkappa
@tempa\lambda\mathlambda\textlambda
@tempa\mu\mathmu\textmu
@tempa\mnu\mathmnu\textmnu
@tempa\xi\mathxi\textxi
@tempa\rho\mathrho\textrho
@tempa\varrho\mathvarrho\textrho
@tempa\sigma\mathsigma\textsigma
@tempa\tau\mathtau\texttau
@tempa\upsilon\mathupsilon\textupsilon
@tempa\phi\mathphi\textphi
@tempa\chi\mathchi\textchi
@tempa\psi\mathpsi\textpsi
@tempa\omega\mathomega\textomega
\makeatother
\begin{document}
See \alpha\beta\gamma, but \theta\vartheta\ or \rho\varrho.\par
Normal: $a\alpha l\lambda r\rho\varrho x_{\mu}$\par
With \verb+\mathrm+: $\mathrm{a\alpha l\lambda r\rho\varrho x_{\mu}}$\par
With \verb+\bm+: $\bm{\alpha}$, but $\bm{\mathrm{\alpha}} $
\end{document}

Answer 4

In a comment, I had mentioned the possibility of using \unslant on the Greeks, as done here: Upright Greek font fitting to Computer Modern. However, the OP wants a macro that does it automatically.

Here, I create a macro \mathgr{} that employs a token cycle to check each token in the argument...if they are \up<greek> able, it uses the \unslant upon them (i.e., it only uses upgreek to determine the token's greek-ness).

Because tokcycle collects the tokens before typesetting them, things like macros and grouped arguments pose no difficulty. For example, in the MWE, in the \mathgr argument, I use non-greek macros, I use groupings around an exponent, I use non greek characters, I use an active ~ token, as well as a nested \textrm.

The \ThisStyle{...\SavedStyle...} syntax of the scalerel package is used to preserve smaller math styles for the unslanted characters.

This approach only works in pdflatex.

\documentclass{article}
\usepackage{upgreek}% ONLY USED TO DEFINE NAMES \up...
\usepackage{tokcycle,scalerel}
\newsavebox{\foobox}
\newcommand{\slantbox}[2][0]{\mbox{%
        \sbox{\foobox}{#2}%
        \hskip\wd\foobox
        \pdfsave
        \pdfsetmatrix{1 0 #1 1}%
        \llap{\usebox{\foobox}}%
        \pdfrestore
}}
\newcommand\unslant[2][-.25]{\ThisStyle{\slantbox[#1]{$\SavedStyle#2$}}}
\makeatletter
\newcommand\mathgr[1]{\tokcycle
  {\addcytoks{##1}}
  {\processtoks{##1}}
  {\ifcsname up\expandafter@gobble\string##1\endcsname
   \addcytoks{\unslant{##1}}%
    \else\addcytoks{##1}\fi}
  {\addcytoks{##1}}{#1}%
  \expandafter\mathrm\expandafter{\the\cytoks}%
}
\makeatother
\begin{document}
\begin{tabular}{ll}
slanted greek math-mode letters: & 
  $ab c \alpha\beta\gamma^{\pi+1}\dots\mu~\nu\dots\omega\textrm{a b c}$ \
tokcycle + unslant & 
  $\mathgr{ab c \alpha\beta\gamma^{\pi+1}\dots\mu~\nu\dots\omega\textrm{a b c}}$
\end{tabular}
\end{document}

If one was happy with the look of upgreek and wanted to avoid the vagaries of \unslant, then the token cycle can be adjusted to do so:

\documentclass{article}
\usepackage{upgreek}%
\usepackage{tokcycle}
\makeatletter
\newcommand\mathgr[1]{\tokcycle
  {\addcytoks{##1}}
  {\processtoks{##1}}
  {\ifcsname up\expandafter@gobble\string##1\endcsname
   \addcytoks[1]{\csname up\expandafter@gobble\string##1\endcsname}%
    \else\addcytoks{##1}\fi}
  {\addcytoks{##1}}{#1}%
  \expandafter\mathrm\expandafter{\the\cytoks}%
}
\makeatother
\begin{document}
\begin{tabular}{ll}
slanted greek math-mode letters: & 
  $ab c \alpha\beta\gamma^{\pi+1}\dots\mu~\nu\dots\omega\textrm{a b c}$ \
tokcycle + unslant & 
  $\mathgr{ab c \alpha\beta\gamma^{\pi+1}\dots\mu~\nu\dots\omega\textrm{a b c}}$
\end{tabular}
\end{document}

---

SUPPLEMENT

The OP seems determined to "override" \mathrm. While I don't recommend replacing it, nonetheless, it can be done to automatically include the token cycle with

\documentclass{article}
\usepackage{upgreek}% ONLY USED TO DEFINE NAMES \up...
\usepackage{tokcycle,scalerel}
\newsavebox{\foobox}
\newcommand{\slantbox}[2][0]{\mbox{%
        \sbox{\foobox}{#2}%
        \hskip\wd\foobox
        \pdfsave
        \pdfsetmatrix{1 0 #1 1}%
        \llap{\usebox{\foobox}}%
        \pdfrestore
}}
\newcommand\unslant[2][-.25]{\ThisStyle{\slantbox[#1]{$\SavedStyle#2$}}}
\makeatletter
\newcommand\mathgr[1]{\tokcycle
  {\addcytoks{##1}}
  {\processtoks{##1}}
  {\ifcsname up\expandafter@gobble\string##1\endcsname
   \addcytoks{\unslant{##1}}%
    \else\addcytoks{##1}\fi}
  {\addcytoks{##1}}{#1}%
  \expandafter\svmathrm\expandafter{\the\cytoks}%
}
\let\svmathrm\mathrm
\renewcommand\mathrm[1]{\mathgr{#1}}
\makeatother
\begin{document}
\begin{tabular}{ll}
slanted greek math-mode letters: & 
  $ab c \alpha\beta\gamma^{\pi+1}\dots\mu~\nu\dots\omega\textrm{a b c}$ \
mathrm (tokcycle + unslant) & 
  $\mathrm{ab c \alpha\beta\gamma^{\pi+1}\dots\mu~\nu\dots\omega\textrm{a b c}}$
\end{tabular}
\end{document}