summaryrefslogtreecommitdiff
path: root/graphics/pgf/contrib/spectralsequences/examples/SSS-KZ3.tex
blob: 25c7143378789fd6b8ad750367886a3a2ae061a5 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
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}