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%%
%% Package: spectralsequences.sty version 1.0
%% Author: Hood Chatham
%% Email: hood@mit.edu
%% Date: 2017-06-18
%% License: Latex Project Public License
%%
%% File: example_bo_May_SS.tex
%%
%% Draws the May spectral sequence computing Ext_{A(1)} ( F_2, F_2 ), which by a change of rings and a simple argument that the ASS has to collapse,
%% is telling us pi_* bo. See the Green Book for reference.
%% The main purpose of this example from my perspective is to illustrate the utility of class "tags".
%%
\documentclass{article}
\usepackage{spectralsequences}
\NewSseqGroup\tower {} {
\class(0,0)
\foreach\i in {1,...,11}{
\class(0,\i)
\structline(0,\i-1,-1)(0,\i,-1)
}
}
\NewSseqGroup\hvee {} {
\tower(0,0)
\foreach\i in {1,...,11}{
\class(\i,\i)
\structline(\i-1,\i-1,-1)(\i,\i,-1)
}
}
\begin{document}
\begin{sseqdata}[
name=A1 May,
x range={0}{10}, y range={0}{10},
degree={-1}{1},
classes={fill, tooltip = {(\xcoord,\ycoord)}},
class labels={below=3pt},
run off differentials= ->,
no orphan edges,
]
\foreach\i in {0,1,2}{
\begin{scope}[xshift=4*\i,yshift=2*\i,tag prefix=\i.]
\hvee[tag=id](0,0)
\hvee[tag=h0h1](1,2)
\hvee[tag=h20](2,1)
\foreach\j in {1,...,10}{
\d1(2,\j,h20,h0h1)
}
\foreach\j in {1,...,10}{
\d1(2+\j,1+\j,h20,h0h1)
}
\end{scope}
}
\foreach\i in {0,...,7}{
\d2(4+\i,2+\i,1.id,0.id)
}
\class(12,6)
\d2(12,6,,1)
%\classoptions["h_0"](0,1)
\classoptions["h_1"](1,1)
\classoptions["h_{20}"](2,1)
\classoptions["h_{20}^2"](4,2)
\classoptions["h_{20}^3"](6,3)
\classoptions["h_{20}^4"](8,4)
\classoptions["h_{20}^5"](10,5)
\doptions[shorten >=3pt]1(10,10,2.h20,2.h0h1)
\end{sseqdata}
\printpage[name=A1 May,page=1]
\newpage
\printpage[name=A1 May,page=2]
\newpage
\begin{sseqpage}[name=A1 May,page=3]
\classoptions["h_0h_{20}^2"](4,3,1.id)
\end{sseqpage}
\end{document}
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