How to use both Computer Modern and Latin Modern's Calligraphic \mathcal at the same time in LuaTeX with unicode-math

Question

Here's my MWE:

% !TEX program = lualatex
% DOCUMENT CLASS
\documentclass[11pt,preview,varwidth,%
border={5pt 5pt 5pt 5pt}% left bottom right top
]{standalone}
% PACKAGES
\usepackage{mathtools, amssymb} % Math packages
\let\oldmathbb\mathbb % Computer Modern blackboard bold
\let\oldmathcal\mathcal % Computer Modern calligraphic
\AtBeginDocument{\def\mathbb{\oldmathbb}} % Redefine \mathbb to use Computer Modern
\AtBeginDocument{\def\mathcal{\oldmathcal}} % Redefine \mathcal to use Computer Modern
\usepackage[warnings-off={mathtools-colon,mathtools-overbracket}]{unicode-math} % Math fonts
\setmathfont{Latin Modern Math}
\let\newmathbb\mathbb % Latin Modern blackboard bold
\let\newmathcal\mathcal % Latin Modern calligraphic
\newcommand{\AtoZ}{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
% START OF DOCUMENT
\begin{document}
    Computer Modern's \verb|\mathbb|: (\mathbb{\AtoZ})
Latin Modern's \verb|\mathbb|: \(\newmathbb{\AtoZ}\)

Computer Modern's \verb|\mathcal|: \(\mathcal{\AtoZ}\)

Latin  Modern's \verb|\mathcal|: \(\newmathcal{\AtoZ}\)

\end{document}
% END OF DOCUMENT

I am trying to mainly use Computer Modern's blackboard bold (\mathbb) and calligraphic (\mathcal) fonts in LuaTeX with the unicode-math package simply because I prefer them over Latin Modern's (in those particular cases) but I would still want to be able to access Latin Modern's blackboard bold and calligraphic fonts, hence the \newmathbb and \newmathcal macros.

As seen from my MWE, I seem to have a problem accessing Computer Modern's calligraphic font for some reason.

I've read this TeX.SX answer but when I used \setmathfont[range={cal}]{cmsy10}, I ended up not being able to access Latin Modern's calligraphic font instead as it seems to globally change every calligraphic font to cmsy10:

% !TEX program = lualatex
% DOCUMENT CLASS
\documentclass[11pt,preview,varwidth,%
border={5pt 5pt 20pt 5pt}% left bottom right top
]{standalone}
% PACKAGES
\usepackage{mathtools, amssymb} % Math packages
\let\oldmathbb\mathbb % Computer Modern blackboard bold
\AtBeginDocument{\def\mathbb{\oldmathbb}} % Redefine \mathbb to use Computer Modern
\usepackage[warnings-off={mathtools-colon,mathtools-overbracket}]{unicode-math} % Math fonts
\setmathfont{Latin Modern Math}
\let\newmathbb\mathbb % Latin Modern blackboard bold
\let\newmathcal\mathcal % Latin Modern calligraphic
\setmathfont[range={cal}]{cmsy10} % Computer Modern calligraphic
\newcommand{\AtoZ}{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
% START OF DOCUMENT
\begin{document}
    Computer Modern's \verb|\mathbb|: (\mathbb{\AtoZ})
Latin Modern's \verb|\mathbb|: \(\newmathbb{\AtoZ}\)

Computer Modern's \verb|\mathcal|: \(\mathcal{\AtoZ}\)

Latin  Modern's \verb|\mathcal|: \(\newmathcal{\AtoZ}\)

\end{document}
% END OF DOCUMENT

(I received the warnings Package fontspec Warning: Font "cmsy10" does not contain requested Script "Math"., Package fontspec Warning: OpenType feature 'Style=MathScript' (ssty) not available for font 'cmsy10' with script '' and language 'Default'., and Package fontspec Warning: OpenType feature 'Style=MathScriptScript' (ssty) not available for font 'cmsy10' with script '' and language 'Default'.)

I've also read another TeX.SX answer but when I tried its approach I still couldn't use both Computer Modern and Latin Modern's calligraphic fonts at the same time:

% !TEX program = lualatex
% DOCUMENT CLASS
\documentclass[11pt,preview,varwidth,%
border={5pt 5pt 20pt 5pt}% left bottom right top
]{standalone}
% PACKAGES
\usepackage{mathtools, amssymb} % Math packages
\let\oldmathbb\mathbb % Computer Modern blackboard bold
\AtBeginDocument{\def\mathbb{\oldmathbb}} % Redefine \mathcal to use Computer Modern
\usepackage[warnings-off={mathtools-colon,mathtools-overbracket}]{unicode-math} % Math fonts
\setmathfont{Latin Modern Math}
\let\newmathbb\mathbb % Latin Modern blackboard bold
\ExplSyntaxOn
\makeatletter
\cs_new:Npn\definemathgroup#1#2#3#4{
  \fontspec_set_family:Nnn\l_my_math_font_family{SmallCapsFont={},ItalicFont={},BoldFont={},Script=Math,#3}{#4}
  \exp_args:Nc\new@mathgroup{\string#1}
  ::c::n::f:::\new@symbolfont{\string#1}{TU}{\l_my_math_font_family}{\seriesdefault}{\shapedefault}
  \cs_new:Npn#1##1{#2{\fam\use:c{\string#1}##1}}
}
\makeatother
\ExplSyntaxOff
\definemathgroup{\oldmathcal}{\symcal}{}{cmsy10} % Computer Modern calligraphic
\AtBeginDocument{\def\mathcal{\oldmathcal}} % Redefine \mathcal to use Computer Modern
\definemathgroup{\newmathcal}{\symcal}{}{Latin Modern Math} % Latin Modern calligraphic
\newcommand{\AtoZ}{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
% START OF DOCUMENT
\begin{document}
    Computer Modern's \verb|\mathbb|: (\mathbb{\AtoZ})
Latin Modern's \verb|\mathbb|: \(\newmathbb{\AtoZ}\)

Computer Modern's \verb|\mathcal|: \(\mathcal{\AtoZ}\)

Latin  Modern's \verb|\mathcal|: \(\newmathcal{\AtoZ}\)

\end{document}
% END OF DOCUMENT

(I also received the warning Package fontspec Warning: Font "cmsy10" does not contain requested Script "Math".)

What went wrong and how do I fix this issue?

Thank you.

Answer 1

Your question is not so clear but this shows Latin Modern Math OpenType Blackboard bold and Calligraphic alongside type 1 AMS Blackboard bold and Computer Modern Calligraphic.

\documentclass{article}
\usepackage{unicode-math}
\setmathfont{LatinModern Math}
\DeclareMathAlphabet\amsmathbb{U}{msb}{m}{n}
\DeclareMathAlphabet\cmmathcal{OMS}{cmsy}{m}{n}
\begin{document}
$ABC \symbb{ABC} \amsmathbb{ABC}$
$ABC \symcal{ABC} \cmmathcal{ABC}$
$\bar{\cmmathcal{A}} +
 \dot{\cmmathcal{A}}$
$\bar{{\mkern-1.5mu}\cmmathcal{A}{\mkern1.5mu}} + 
 \dot{{\mkern-1.5mu}\cmmathcal{A}{\mkern1.5mu}}$
\end{document}