Looking for delimiters similar to ceil

Question

I want to use brackets similar to lceil, rceil and lfoor, rfloor, but with the vertical lines on both sides at an angle. Does anything like this already exist? If not, would it be difficult to create them?

Answer 1

If you don't need them to auto-scale, here is a pdflatex solution. See ADDENDUM for scalable version.

\documentclass[12pt]{article}
\usepackage{scalerel,mathtools}
\newsavebox{\foobox}
\newcommand{\slantbox}[2][.5]
  {%
    \mbox
      {%
        \sbox{\foobox}{#2}%
        \hskip\wd\foobox
        \pdfsave
        \pdfsetmatrix{1 0 #1 1}%
        \llap{\usebox{\foobox}}%
        \pdfrestore
      }%
  }
\newcommand\lsceil{\ThisStyle{\slantbox[.2]{$\SavedStyle\lceil$}}}
\newcommand\rsceil{\ThisStyle{\slantbox[-.2]{$\,\SavedStyle\rceil$}}}
\newcommand\lsfloor{\ThisStyle{\slantbox[-.2]{$\,\SavedStyle\lfloor$}}}
\newcommand\rsfloor{\ThisStyle{\slantbox[+.2]{$\SavedStyle\rfloor\,$}}}
\usepackage{amsmath}
\DeclarePairedDelimiter{\sceils}{\lsceil}{\rsceil}
\DeclarePairedDelimiter{\sfloors}{\lsfloor}{\rsfloor}
\begin{document}
\begin{equation*}
x\sceils{A}y \quad x\sfloors{A}y 
\end{equation*}
\end{document}

ADDENDUM

\documentclass[12pt]{article}
\usepackage{scalerel,mathtools}
\newsavebox{\foobox}
\newcommand{\slantbox}[2][.5]
  {%
    \mbox
      {%
        \sbox{\foobox}{#2}%
        \hskip\wd\foobox
        \pdfsave
        \pdfsetmatrix{1 0 #1 1}%
        \llap{\usebox{\foobox}}%
        \pdfrestore
      }%
  }
%\newcommand\lsceil{\ThisStyle{\slantbox[.2]{$\SavedStyle\lceil$}}}
%\newcommand\rsceil{\ThisStyle{\slantbox[-.2]{$\,\SavedStyle\rceil$}}}
%\newcommand\lsfloor{\ThisStyle{\slantbox[-.2]{$\,\SavedStyle\lfloor$}}}
%\newcommand\rsfloor{\ThisStyle{\slantbox[+.2]{$\SavedStyle\rfloor\,$}}}
\newsavebox\tmpbox
\newcommand\sceils[1]{\ThisStyle{\savebox\tmpbox{$\SavedStyle\mkern-1mu#1$}%
  \slantbox[.2]{$\SavedStyle\left\lceil\vphantom{\usebox{\tmpbox}}\right.$}%
  \usebox{\tmpbox}%
  \slantbox[-.2]{$\SavedStyle\left.\vphantom{\usebox{\tmpbox}}\right\rceil$}%
}}
\newcommand\sfloors[1]{\ThisStyle{\savebox\tmpbox{$\SavedStyle#1$}\mkern1mu%
  \slantbox[-.2]{$\SavedStyle\left\lfloor\vphantom{\usebox{\tmpbox}}\right.$}%
  \usebox{\tmpbox}%
  \slantbox[.2]{$\SavedStyle\left.\vphantom{\usebox{\tmpbox}}\right\rfloor$}%
}}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
x\sceils{A}y \quad x\sfloors{A}y 
\end{equation*}
\begin{equation*}
\frac{x}{y}\sceils{\frac{x}{y}}\frac{x}{y} \quad 
x\sfloors{\frac{x}{y}}y 
\end{equation*}
\end{document}