# How to reproduce vertical bars with trangles on the side, used for the r.o.c. of the Laplace transform?

what is the command for this symbol? this symbol is to represent the bounds of ROC of laplace transform. looked up online latex documents, still couldn't find this symbol.

• Can you choose a better title for your question?
– Werner
Feb 18 '21 at 3:35
• What is this symbol for? Feb 18 '21 at 18:18
• @vinny, can you tell us what books or papers you have found this symbol used in? If you can find any papers on the arXiv using this symbol, then you can download the LaTeX source from the arXiv and find the code the author(s) used. Feb 18 '21 at 22:48

## 2 Answers

A version that differentiates between display and text style (don't try it in subscripts)

\documentclass[twocolumn]{article} % twocolumn just for a smaller picture
\usepackage{amsmath,amssymb}

\makeatletter
\newcommand{\rocl}[3]{%
% #1 = left bound, #2 = function, #3 = right bound
\mathopen{}
\mathpalette\rocl@{{#1}{#2}{#3}}%
\mathclose{}
}
\newcommand{\rocl@}[2]{\rocl@@{#1}#2}
\newcommand{\rocl@@}[4]{%
\ifx#1\displaystyle
{\vphantom{\Big|}}_{#2}\kern-\scriptspace
\Big|%
\mspace{-4.5mu}
\vcenter{\hbox{$\scriptstyle\blacktriangleright$}}%
\,{#3}\,
\vcenter{\hbox{$\scriptstyle\blacktriangleleft$}}%
\mspace{-4.5mu}
{\Big|}_{#4}%
\else
{\vphantom{\big|}}_{#2}\kern-\scriptspace
\big|%
\mspace{-4.5mu}
\vcenter{\hbox{$\scriptscriptstyle\blacktriangleright$}}%
\,{#3}\,
\vcenter{\hbox{$\scriptscriptstyle\blacktriangleleft$}}%
\mspace{-4.5mu}
{\big|}_{#4}%
\fi
}
\makeatother

\begin{document}

This $\rocl{\sigma_{\mathrm{L}}}{X(s)}{\sigma_{\mathrm{H}}}$
in text, next in a display
$\rocl{\sigma_{\mathrm{L}}}{X(s)}{\sigma_{\mathrm{H}}}$
with some text following.

\end{document}



Actually, the hardest part of this formulation was the prescript on the left. I discovered if you use _ following a \vphantom it does not work right, so I invented \subdepth{} to push a subscript to the right depth.

\documentclass{article}
\usepackage{amssymb}
\newcommand\subdepth[1]{\raisebox{-6pt}{${}_{#1}$}}
\newcommand\midscript[1]{\vcenter{\hbox{$\scriptstyle#1$}}}
\newcommand\ROCl{\Bigl|\mkern-4mu\midscript{\blacktriangleright}}
\newcommand\ROCr{\midscript{\blacktriangleleft}\mkern-4mu\Bigr|}
\begin{document}
$\subdepth{\sigma_L}\ROCl X(s)\ROCr\subdepth{\sigma_H}$
\end{document}


Here, I automate it to switch from displaystyle to textstyle, and simplify the invocation to a three-argument \ROC macro.

\documentclass{article}
\usepackage{amssymb,amsmath,scalerel}
\makeatletter
\newcommand\subdepth[1]{\ThisStyle{\if D\m@switch
\raisebox{-6pt}{${}_{#1}$}\else{}_{#1}\fi}}
\newcommand\midscript[1]{\vcenter{\hbox{$\scriptstyle#1$}}}
\newcommand\ROCl{\ThisStyle{\if D\m@switch
\Bigl|\mkern-4mu\midscript{\blacktriangleright}\else
|\mkern-4mu\midscript{\blacktriangleright}\fi}}
\newcommand\ROCr{\ThisStyle{\if D\m@switch
\midscript{\blacktriangleleft}\mkern-4mu\Bigr|\else
\midscript{\blacktriangleleft}\mkern-4mu|\fi}}
\makeatother
\newcommand\ROC[3]{\subdepth{#1}\ROCl #2\ROCr\subdepth{#3}}
\begin{document}
$\ROC{\sigma_L}{X(s)}{\sigma_H}$
\centering
$\ROC{\sigma_L}{X(s)}{\sigma_H}$
\end{document}