Remarks in equations with arrows

Question

In huge calculations it's often very helpful as reader to have nice remarks about which manipulation was made. Also, other remarks in equations can help alot, e.g., this one

which I like more than the ^-convention.
I am generating the above with the following code
vertarrowbox{e_j}{$i$textsuperscript{th} spot}

where
newcommandvertarrowbox[3][2ex]{%
    begin{array}[t]{@{}c@{}} #2 [-0.7ex]
        leftuparrowvcenter{hrule height #1}right.kern-nulldelimiterspace[-1.2ex]
        makebox[0pt]{scriptsize#3}
    end{array}%
}

My goal now is to achieve something similar. I am looking for something like this

to denote that the exchange of the two variables gives a minus sign.
I wonder how I could implement this. I am not sure if tikz-cd is the way to go (I don't have experience with tikz-cd in equations like this and don't know if it is even possible to use it this way).
Thank you for your ideas!

Mathy · Answer

After @daleif gave me the tip to use tikz and tikzmark I found how to do it with some trial and error (tikz seems super complex and powerful). Please correct or improve this solution (I am not fully aware of every comment and if this could be done more nicely of if I am doing something very stupid here).
usepackage{tikz}
usetikzlibrary{tikzmark}

begin{equation*}
    f(tikzmarknode{a}a,b,c,d,tikzmarknode{e}e) = -f(e,b,c,d,a)
end{equation*}

begin{tikzpicture}[overlay,remember picture]
    draw [>=latex,<->]
    (a.south) to[out=-90,in=-90,looseness=1] node [below,sloped] (TextNode1) 
    {scriptsize$cdot (-1)$} (e.south);
end{tikzpicture}

yields

However two problems remain:

I want to apply this in an align environment. But then the spacing is messed up:
 begin{align*}
      f(a,b,c,d,e) &= f(tikzmarknode{a}a,b,c,d,tikzmarknode{e}e) 
                   &= -f(e,b,c,d,a)
 end{align*}

As I will use this very often in the document, I want to write a command for it. But how could I implement that? The obvious problem is that the begin{tikzpicture}[overlay,remember picture] thing has to come after the whole align environment and I have only ever worked with commands which "replace in place".

Any help is very much appreciated!
EDIT:
I added a brace underneath to better symbolize what term exactly is moved. Also read my comment under this answer.

Remarks in equations with arrows

One Answer

Add your own answers!

Ask a Question