Bold dot and plus operator for math

Question

I'm rewriting some math equation in LaTeX, and I came across something like this:

Where apparently there is something like a bullet dot operator, probably used for dot product. It's different than a regular \cdot. But, also the plus is different than a regular plus, it's a bit bolder and smaller. Any ideas how to write them in LaTeX?

Answer 1

For the fat dot you can use \bullet the plus might be \textadvanced or a \textsubplus

For future reference use How to look up a symbol or identify a math symbol or character?

Now if you some day, even through the above question/answer set, cannot find the symbol in any existing LaTeX, you can always draw it yourself. I don't know if this is the proper way to do it, but here's what I came up with:

\documentclass[border=5pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}

\usepackage{tikz}

\newcommand{\fatterdot}{\raisebox{0.25ex}{\tikz\filldraw[black,x=2pt,y=2pt] (0,0) circle (1);}}
\newcommand{\fatplus}{\raisebox{0ex}{\tikz\filldraw[black,x=2pt,y=2pt] (0,0) -- ++(1,0) -- ++(0,1) -- ++(1,0) -- ++(0,-1) -- ++(1,0) -- ++(0,-1) -- ++(-1,0) -- ++(0,-1) -- ++(-1,0) -- ++(0,1) -- ++(-1,0) -- cycle;}}
\begin{document}
$\Gamma\fatterdot \Delta' = \Theta \fatplus \theta \fatterdot \beta^T$
\end{document}

Which produces:

As you can see this is much fatter plus's and dots. They are however not nice to use with different fonts and fontsizes.

Answer 2

Here I introduce \boldify which works across math styles and uses pdf literals to achieve the graduated bolding (thus, only works in pdflatex). It can be used on anything in math mode.

Syntax is \boldify[<boldness-factor>]{<argument-to-be-math-bolded>}. A boldness factor of 0 is no boldness. I have set the default to .2. For this MWE, I have defined also \bcdot and \bplus to define bolded \cdot and + with appropriate spacing.

\documentclass{article}
\usepackage{xcolor,amsmath,scalerel}
\input pdf-trans
\newbox\qbox
\def\usecolor#1{\csname\string\color@#1\endcsname\space}
\newcommand\outline[1]{\leavevmode%
  \def\maltext{#1}%
  \setbox\qbox=\hbox{\maltext}%
  \boxgs{Q q 2 Tr \thickness\space w 0 0 0 rg 0 G}{}%
  \copy\qbox%
}
\newcommand\boldify[2][.2]{%
  \def\thickness{#1}%
  \ThisStyle{\outline{$\SavedStyle#2$}}%
}
\def\bcdot{\mathbin{\boldify[1]{\cdot}}}
\def\bplus{\mathbin{\boldify[.6]{+}}}
\begin{document}
$y \boldify[0]{y} \boldify{y} \boldify[.3]{y}$

$\scriptscriptstyle y \boldify[0]{y} \boldify{y} \boldify[.3]{y}$

$\Gamma\bcdot \Lambda = \Theta \bplus \theta \bcdot \beta^T$

$\Gamma\cdot \Lambda = \Theta + \theta \cdot \beta^T$
\end{document}

I should add that it automaTeXly works with any font. Thus, if I add newtxmath to the preamble, the result changes to