Custom \sqcap operators

Question

I want to ask for something similar to Horizontal lines in \sqcup and \sqcap

But instead of the alignment asked in that question, I want the horizontal line to align vertically to a minus sign and the new symbol's spacing equal to a regular \sqcap's spacing, like this

.

And if possible, I would also like to ask for a big version of this operator whose dimensions are the same as the dimensions of \bigsqcup.

Answer 1

You can overlap the \sqcap and minus with \ooalign. The mismatch in width can be cured by shrinking the minus sign only in the horizontal direction. For the “big” version, the same idea is used, but the minus sign is also stretched vertically to match the thickness (it maybe requires a different factor in scriptstyle, though).

\documentclass{article}
\usepackage{amsmath,stmaryrd,graphicx}
\makeatletter
\newcommand{\semisqcap}{\mathbin{\mathpalette\semisqcap@\relax}}
\newcommand{\semisqcap@}[2]{%
  \begingroup\m@th
  \sbox\z@{$#1\sqcap$}%
  \ooalign{\hidewidth\resizebox{\wd\z@}{\height}{$#1-$}\hidewidth\cr$#1\sqcap$\cr}%
  \endgroup
}
\newcommand{\bigsemisqcap}{\DOTSB\mathop{\mathpalette\bigsemisqcap@\relax}\slimits@}
\newcommand{\bigsemisqcap@}[2]{%
  \begingroup\m@th
  \sbox\z@{$#1\bigsqcap$}%
  \ooalign{\hidewidth\semisqbar@{#1}\hidewidth\cr$#1\bigsqcap$\cr}%
  \vphantom{\box\z@}%
  \endgroup
}
\newcommand{\semisqbar@}[1]{%
  \raisebox{-0.25\height}{\resizebox{\wd\z@}{2\height}{$#1-$}}%
}
\makeatother
\begin{document}
\begin{gather}
a\semisqcap b
\quad\scriptstyle a\semisqcap b
\
a\sqcap b
\quad\scriptstyle a\sqcap b
\
\bigsemisqcap_{i=1}^n a_i \bigsqcap_{i=1}^n a_i
\
\bigsemisqcap_{i=1}^n a_i \bigsqcap_{i=1}^n a_i
\
\textstyle\bigsemisqcap_{i=1}^n a_i \bigsqcap_{i=1}^n a_i
\
\scriptstyle\bigsemisqcap_{i=1}^n a_i \bigsqcap_{i=1}^n a_i
\end{gather}
\end{document}

Answer 2

You can literally take the answer you link to, and change a few values.

\documentclass{article}
\usepackage{amsmath}
\usepackage{scalerel}
\def\widen{\mathrel{\ThisStyle{\stretchrel*{\ooalign{%
  \raise0.45\LMex\hbox{$\SavedStyle\sqcup$}\cr%
  \raise-0.45\LMex\hbox{$\SavedStyle\sqcup$}}}{\sqcup}}}}
\def\narrow{\mathrel{\ThisStyle{\stretchrel*{\ooalign{%
  \raise0.75\LMex\hbox{$\SavedStyle\sqcap$}\cr%
  \raise-0.75\LMex\hbox{$\SavedStyle\sqcap$}}}{\sqcap}}}}
\def\Widen{\mathrel{\ThisStyle{\stretchrel*{\ooalign{%
  \raise0.6\LMex\hbox{$\SavedStyle\sqcup$}\cr%
  \raise-0.6\LMex\hbox{$\SavedStyle\sqcup$}}}{\bigsqcup}}}}
\begin{document}
$a -\widen b \quad\scriptstyle a -\widen b \quad\scriptscriptstyle a -\widen b$
$a -\narrow b \quad\scriptstyle a -\narrow b \quad\scriptscriptstyle a -\narrow b$
$a -\Widen b \quad\scriptstyle a -\Widen b \quad\scriptscriptstyle a -\Widen b$
\end{document}