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diff --git a/Master/texmf-dist/doc/latex/spectralsequences/examples/example_mayss.tex b/Master/texmf-dist/doc/latex/spectralsequences/examples/example_mayss.tex new file mode 100644 index 00000000000..fd48445ca0c --- /dev/null +++ b/Master/texmf-dist/doc/latex/spectralsequences/examples/example_mayss.tex @@ -0,0 +1,129 @@ +%% +%% Package: spectralsequences.sty version 1.0 +%% Author: Hood Chatham +%% Email: hood@mit.edu +%% Date: 2017-06-18 +%% License: Latex Project Public License +%% +%% File: example_mayss.tex +%% +%% I think this is the May SS for the sphere. May spectral sequences are annoying to draw neatly it turns out -- there's too much stuff in them. +%% It helps a lot if you start at E_2 though, since E_1 is polynomial. They also have the problem with their crappy grading that makes all +%% differentials the same length. I seem to have graded this weirdly, probably because the normal grading looked too bad. +%% + +\documentclass{article} +\usepackage{fullpage} +\usepackage{spectralsequences} + +\begin{document} +\NewSseqGroup\tower {m} { + \class["#1"](0,0) + \foreach\i in {1,...,14}{ + \class(0,\i) + \structline(0,\i-1,-1)(0,\i,-1) + } +} + +\NewSseqGroup\hone {m} { + \foreach\i in {1,...,#1}{ + \class(\i,\i) + \structline(\i-1,\i-1,-1)(\i,\i,-1) + } +} + +\NewSseqCommand\dtower {u(u)} { + \foreach\i in {0,...,10}{ + \d[yshift=\i]#1(#2) + } +} + + +\def\single(#1)#2{\class["#2"](#1)} + +\NewSseqGroup\htwo {m} { + \foreach \n in {0,...,5}{ + \tower(3*\n,\n){\sseqifempty{#1}{}{#1}\sseqpowerempty{h_2}{\n}} + \ifnum\n>0\relax + \structline(3*\n-3,\n-1,-1)(3*\n,\n,-1) + \fi + } +} + +\NewSseqGroup\htwosinglejoin {mm} { + \foreach \n in {0,...,5}{ + \single(3*\n,\n){\sseqifempty{#1}{}{#1}\sseqpowerempty{h_2}{\n}} + \ifnum\n>0\relax + \structline(3*\n-3,\n-1,-1)(3*\n,\n,-1) + \fi + } + \foreach \n in {0,...,#2}{ + \structline(3*\n,\n,-1)(3*\n,\n+1,-1) + } +} + + + +\begin{sseqdata}[name=may, degree={-1}{1-#1},x range={0}{13}, y range={0}{13},class labels=below right,differentials=blue,x axis extend end=23pt,draw] +\tower(7,1){h_3} +\htwo(0,0){} +\classoptions[label position=above left](9,3) +\hone(0,0){3} +\htwo[label position={xshift=3pt,yshift=2pt}](4,4){b_{2,0}} +\dtower2(4,4,-1,-1) % d2(b_{2,0}h_0^n) = h_2h_0^{n+2} +\d2(4,4,-1,1) % d2(b_{2,0})= h_2h0^2 + h1^3 + +%\hone(4,4){3} +\htwo(8,8){b_{2,0}^2} +\hone(8,8){3} +\dtower4(8,8,,1) % d4(b_{2,0}^2) = h3 h0^4 +%\hone(8,8){3} +\hone(7,1){2} + + +\htwosinglejoin(7,4){x_7}{4} +\dtower2(7,4,2,-1) +\hone(7,4){2} +\htwosinglejoin(11,8){x_7b_{2,0}}{4} +\htwosinglejoin(10,4){b_{2,1}}{3} +%\hone(10,4){1} +\d2(10,4,-1,2) % d2(b21)=h2^3+h3h1^2 +\dtower2(10,4,1,1) % d2(b21 h0^n) = h2^3 h0^n + + +\tower(11,5){h_3b_{2,0}} +\tower(12,6){b_{3,0}} +\dtower2(12,6,-1,-1) + +\htwo(12,12){b_{2,0}^3} +\dtower2(12,12,-1,1) % d2(b20^3 h_0^n) = h0^n b20^2 d2(b20) = h0^{n+2} h2 b20^2 +\d2(12,12,-1,2) % d2(b_{2,0}^3)= b20^2 d2(b20) = h_2 h0^2 b20^2 + h1^3 b20^2 +\hone(12,12){3} +\replaceclass(11,11) + +\structline(11,10)(11,11) +\structline(10,10,2)(11,11) + +\replaceclass(3,3) + +\structline(2,2)(3,3) +\structline(3,2)(3,3) + + + + + +\replaceclass(9,3) +\structline(6,2)(9,3) +\structline(8,2)(9,3) + + + +%\dtower2(12,6,2,-1) +\end{sseqdata} +\printpage[name=may] +\newpage +\printpage[name=may, page=4] +\newpage +\printpage[name=may, page=5] +\end{document}
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