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diff --git a/Master/texmf-dist/doc/latex/spectralsequences/examples/SSS-KZ3.tex b/Master/texmf-dist/doc/latex/spectralsequences/examples/SSS-KZ3.tex new file mode 100644 index 00000000000..25c71433787 --- /dev/null +++ b/Master/texmf-dist/doc/latex/spectralsequences/examples/SSS-KZ3.tex @@ -0,0 +1,133 @@ +%% +%% Description: The Serre spectral sequence for $\HZ$ cohomology of $\CP^\infty \to pt \to K(\Z,3)$ +%% +%% File: example_KZ3.tex +%% +%% This was one of the first spectral sequences I ever worked out (probably after the one for loops S^n), in the summer of 2013 with Kevin Donoghue. +%% + +\documentclass{article} +\usepackage[landscape,margin=0.5cm,top=2cm]{geometry} +\usepackage{spectralsequences} +\usepackage{amssymb} +\def\Z{\mathbb{Z}} +% Last time test: 1.1 sec +\begin{document} +\def\column#1[#2]{\foreach \y in {0,...,6} {\class[#2](#1,2*\y)}} +\sseqset{classes={draw=none}} +\begin{sseqdata}[ + name={K(Z,3)}, + x range={0}{12}, + y range={0}{10}, + cohomological Serre grading, + differentials={->}, + xscale=1.8, + y axis gap=0.7cm, + math nodes, + x axis extend end=0.8cm, + this page cycles=red, + title=\textup{Serre SS Page \page{}}, + x label = {$H^*(K(\Z,3))$}, + y label = {$H^*(K(\Z,2))$} +] + +\column0["\Z\{\ifnum\y>0\relax x\ifnum\y>1\relax ^{\y}\fi\else1\fi\}"] +\column3["\Z\{a\ifnum\y>0x\ifnum\y>1 ^{\y}\fi\fi\}"] + + +\foreach\y in {1,...,6} {\d["\cdot \y"']3(0,2*\y)} +\replaceclass["\Z/3"](3,4) +\replaceclass["\Z/5"](3,8) + + +\column6["\Z/2"] +\d3(3,2) +\d3(3,6) +\d3(3,10) +\replaceclass["\Z/2"](3,6) +\replaceclass["\Z/3"](3,10) +\column8["\Z/3"] +\d5(3,4) +\d5(3,10) +\column9["\Z/2"] +\d3(6,2) +\d3(6,6) +\d3(6,10) +\column10["\Z/2"] +\d7(3,6) +\column11["\Z/3"] +\d3(8,2) +\d3(8,4) +\d3(8,8) +\d3(8,10) +\column12["\Z/2\oplus\Z/5"] +\column13["\Z/2"] +\column15["\Z/2\oplus\Z/2\oplus\Z/5"] +\d3(9,2) +\d3(9,6) +\d3(9,10) +\d3(10,2) +\d3(10,6) +\d3(10,10) +\d3(10,12) +\d3(12,2) +\d3(12,4) +\d3(12,6) +\d3(12,8) +\d3(12,10) +\d3(12,4) +\replaceclass["\Z/5"](12,0) +\replaceclass["\Z/5"](12,4) +\replaceclass["\Z/5"](12,8) +\d9(3,8) + + +\replaceclass["\Z/5"](12,10) +\replaceclass["\Z/2"](15,0) +\replaceclass["\Z/2\oplus\Z/2"](15,4) + +\d5(10,4) + +\class["\Z/3"](16,0) +\class["\Z/3"](16,6) +\d5(11,4) +\d5(11,10) + +\class["\Z/2"] (17,0) + +\class["\Z/2"](17,8) + +\d5(12,12) + +\class["\Z/2"](19,0) +\d9(10,8) + +\class["\Z/5"](23,0) +\d11(12,10) + +\replaceclass["\Z/6"](16,0) +\d13(3,12) + +%\replaceclass["\Z/6"](21,0) +%\d13(8,12) +\class["\Z/3"](24,0) +\d13(11,12) +\end{sseqdata} + + +\printpage[name={K(Z,3)}, page=0,no differentials] +\newpage +\printpage[name={K(Z,3)}, page=0] +\newpage +\printpage[name={K(Z,3)}, page=3] +\newpage +\printpage[name={K(Z,3)}, page=5] +\newpage +\printpage[name={K(Z,3)}, page=7] +\newpage +\printpage[name={K(Z,3)}, page=9] +\newpage +\printpage[name={K(Z,3)}, page=11] +\newpage +\printpage[name={K(Z,3)}, page=12] +\end{document} |