Is there anyway to apply different color for different parameters within the same formula (especially for background presentation)?

Question

The photo is from Prof Alfredo Canziani from NYU, who manage to create presentation with formulas which parameters using different colour regarding to a same formula.

I wonder is there any editors or tricks in Latex to achieve this especially for blackground presentation.

Link of reference to Professor Alfredo's photo

What I have tried?

I have tried to use draw.io for this code

$$x \text { in }\left(Z_{p}\right)^{*} \text { is a Q.R. } \Leftrightarrow x^{(p-1) / 2}=1 \text { in } Z_{p}$$

The Latex become uncompilable after only assign colors to a certain parameters in the formula

Answer 1

hm, it may serve as starting point:

\documentclass[border=3.141592,varwidth]{standalone}
\usepackage{xcolor}
\usepackage{amsmath}

\begin{document}
\[
{\color{orange}L}
    \left[ 
{\color{orange}L}({\color{pink}x},{\color{cyan}\mathcal{Y}}),{\color{cyan}y}
    \right]
\]
\end{document}

Addendum: You should use editor by which is the most familiar. Some of them enable to define shortcuts. However on the LaTeX side you can define abbreviations for colored variables. For example, for above MWE is sufficient to define five of them:

\documentclass[border=3.141592,varwidth]{standalone}
\usepackage{xcolor}
\usepackage{amsmath}
    \newcommand\cF{{\color{orange}F}}
    \newcommand\cL{{\color{orange}L}}
    \newcommand\cx{{\color{pink}x}}
    \newcommand\cy{{\color{cyan}y}}
    \newcommand\cmY{{\color{cyan}\mathcal{Y}}}

\begin{document}
\[
\cL
    \left[
\cF(\cx,\cmY),\cy
    \right]
\]
\end{document}

Result of compilation is the same as before, but code is significant shorter. Since the all possible colored variables are unknown to us, is hard to say if this approach is suitable.

Answer 2

Partial solution:

unicode-math package calls fontspec package, which has a [Color=...] option, at font-level; different colors can be applied to different alphabet ranges.

MWE

\documentclass[border=3.141592,varwidth]{standalone}
\usepackage{xcolor}
\usepackage{unicode-math}

\pagecolor{black}
\setmathfont{TexGyreTermesMath}[Colour=white]
\setmathfont{TexGyreTermesMath}[range=it/{latin},Colour=cyan]
\setmathfont{TexGyreTermesMath}[range=it/{Latin},Colour=pink]
\setmathfont{TexGyreTermesMath}[range={"0079,"1D466},Colour=brown]%y
\setmathfont{TexGyreTermesMath}[range=cal,Colour=yellow]

\begin{document}
\[
L
    \left[ 
L(x,\mathcal{Y}),y
    \right]
\]
\end{document}

In the OP image, the 𝑦 looks hand-coloured (otherwise 𝑦' would be the same colour, not white). Which means 𝑥 must be hand-coloured too.