# Interior product (contraction) symbol

In differential topology and linear algebra, there's an operator called the interior product, denoted $\iota_X(\omega)$ or alternatively with some other "half box" like operator $X_|\omega$. Does anyone know how to markup that operator in LaTeX?

Google has turned up nothing except for this thread: Symbol for contraction / interior product?

That thread did receive an accepted answer, which was \invneg from the MnSymbol package, but the suggestion given there does not seem correct to me. Or at least, it does not match what I'm familiar with. That answer results in an inverted negation symbol, whereas the contraction operator should have a stroke down at the floor of the line, and a long stroke going up almost the full height of the line. It can be found in many texts, but why can I not find the correct LaTeX markup?

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– Joseph Wright Dec 19 '11 at 21:44
Is the following link a good reference that shows the notation you're after: The Interior Product? We're after an image to see whether this could be contained within an existing font or command (and therefore perhaps be solved by @JosephWright's link), or perhaps requires a larger construct. – Werner Dec 19 '11 at 21:45
The rendering of the character in Asana Math and in the STIX fonts is just like a "reversed \lnot". – egreg Dec 19 '11 at 21:50
Detexify lets you draw the symbol and shows you matches from all the various LaTeX packages. Pretty awesome: detexify.kirelabs.org/classify.html. – Justin Bailey Dec 20 '11 at 0:00
detexify doesn't recognize it – ziggurism Dec 20 '11 at 10:46

I stumbled upon the correct markup used in Wikipedia's article on geometric algebra. I looked at the code and found the symbol is given by \lrcorner. \llcorner is the same thing but flipped horizontally.

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You can import the symbol from MnSymbol by saying

\DeclareFontFamily{U}{MnSymbolC}{}
\DeclareSymbolFont{MnSyC}{U}{MnSymbolC}{m}{n}
\DeclareFontShape{U}{MnSymbolC}{m}{n}{
<-6>  MnSymbolC5
<6-7>  MnSymbolC6
<7-8>  MnSymbolC7
<8-9>  MnSymbolC8
<9-10> MnSymbolC9
<10-12> MnSymbolC10
<12->   MnSymbolC12}{}
\DeclareMathSymbol{\intprod}{\mathbin}{MnSyC}{'270}


This way you won't override your math fonts with MnSymbol.

The alternative way with reversing the \lnot symbol is

\usepackage{graphicx}
\newcommand{\intprod}{\mathbin{\raisebox{\depth}{\scalebox{1}[-1]{$\lnot$}}}}


If the symbol is needed also in other sizes, then

\newcommand{\intprod}{\mathbin{\mathpalette\dointprod\relax}}
\newcommand{\dointprod}[2]{%
\raisebox{\depth}{\scalebox{1}[-1]{$#1\lnot$}}}

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