\magnification \magstep2
\nopagenumbers

%%%% The 5-term relation, also known as Viereridentit\"at.

$$
%% x(y,z,t) + (x,y,z)t = (xy,z,t) - (x,yz,t) + (x,y,zt)
%% (x,y,z)t + (x,yz,t) + x(y,z,t) = (x,y,zt) + (xy,z,t)
(x,y,z)t + (x,yz,t) + x(y,z,t) = (xy,z,t) + (x,y,zt)
$$

\bye

((xy)z)t - (x(yz))t
         + (x(yz))t - x((yz)t)
                    + x((yz)t) - x(y(zt)) =
((xy)z)t - (xy)(zt) + (xy)(zt) - x(y(zt))

%%%%%%%%

%% html tag

%%%% <img src="images/assoc1.png"
%%%%      alt="(x,y,z)t + (x,yz,t) + x(y,z,t) = (xy,z,t) + (x,y,zt)"
%%%%      width="826" height="36">

%%%%%%%%

%% png creation (normal size, transparent)

%%% pdftex assoc1.tex
%%% pdftocairo -png -singlefile -transp -r 180 assoc1.pdf tmp
%%% magick -define png:exclude-chunk=date,time tmp.png -trim +repage assoc1.png
%%% optipng assoc1.png %% no effect

%%%% magick adds white (fallback) background to the transparent image
%%%% and has the convenient option -trim.

%%%% Image size is 826x36.

%% program versions

%%% This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019/Debian) (preloaded format=pdftex 2024.3.16)

%%% pdftocairo version 0.86.1
%%% ImageMagick 7.1.1-43 Q16-HDRI x86_64 22550 https://imagemagick.org
%%% OptiPNG version 0.7.7

%%%%%%%%

%%%% First versions (using tex, dvipng):
%%% 2024-05-17, 2024-11-04

%%%% Recompiled:
%%% 2025-08-09

%%%%%%%%
