summaryrefslogtreecommitdiff
path: root/graphics/pgf/contrib/spectralsequences/examples/MaySS-tmf-A(2).tex
blob: c2ce0a1d55397742f6ea5041bb5d13902bd65a57 (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
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
%%
%% Description: The May spectral sequence for $Ext(\HF_{2*}\tmf)$
%%
%%    I got this from Mike Hill's note: https://pdfs.semanticscholar.org/ddbb/8d584e4e81a71400088117b16cd241238c6c.pdf
%%


\documentclass[tooltips]{spectralsequence-example}
\begin{document}
\sseqset{htwostructstyle/.sseq style = {gray,very thin, run off=-}}


\NewSseqCommand\twods{ O{} U( r() m m }{
    \def\temp{#1,#2,#3,#4,#5}
    \getdtarget\target#2{#3}             % Store the target position in \target
    \nameclass{source}(#3)               % naming the classes gives us a speed boost
    \nameclass{target1}(\target,#4)      % by preventing sseqpages from reparsing the coordinate
    \nameclass{target2}(\target,#5)      % it also makes the code easier to read
%
    \circleclasses[ differential style, #1,
           name path = circ, page = #2--#2 ]
                (target1)(target2)            % Circle the classes, use differential style
%
    \d[invisible]#2(source)(target1)     % don't draw anything, but record source and targets as hit.
    \d[invisible]#2(source)(target2)
%
    \path(target1)--(target2)
                coordinate[midway](midpt);% put a coordinate in the center of the two classes
    \path[name path = lin] (source) -- (midpt);% save path from start to midpoint
%
    % draw line in "differential style" from start to intersection point of circ and lin
    \draw[ differential style, #1, page constraint= { \page == #2 },
           name intersections = { of = circ and lin } ]
                (source) -- (intersection-1);
}


\NewSseqCommand \tower { O{} d() } {
    \IfNoValueF{#2}{
        \pushstack(#2)
    }
    \savestack
    \begin{scope}[#1]
    \DoUntilOutOfBounds{
        \class(\lastx,\lasty+1)
        \structline(\lastclass1)(\lastclass)
    }
    \end{scope}
    \restorestack
}

\NewSseqCommand\honetower {O{}} {
    \savestack
    \begin{scope}[#1]
    \DoUntilOutOfBounds{
        \class(\lastx+1,\lasty+1)
        \structline(\lastclass1)(\lastclass)
    }
    \end{scope}
    \restorestack
}

\NewSseqCommand\htwo { O{} d()  } {
    \IfNoValueF{#2}{
        \pushstack(#2)
    }
    \class[#1](\lastx+3,\lasty+1)
    \structline[htwostructstyle](\lastclass1)(\lastclass)
}

\NewSseqCommand \htwotower { O{} d() } {
    \IfNoValueF{#2}{
        \pushstack(#2)
    }
    \begin{scope}[#1]
    \gettag\thetag(\lastclass)
    \class(\lastx+3,\lasty+1)
    \structline[htwostructstyle](\lastclass)(\lastclass1)
    \savestack
    \DoUntilOutOfBounds{
        \class(\lastx,\lasty+1)
        \structline(\lastclass1)(\lastclass)
        \structline[htwostructstyle](\lastx-3,\lasty-1,\thetag)(\lastclass)
    }
    \restorestack
    \end{scope}
}


\NewSseqCommand\dtower {u(u)} {
    \foreach\i in {0,...,10}{
        \d[yshift=\i]#1(#2)
    }
}

\begin{sseqdata}[name=tmfmayss,y range={0}{8}, x range={0}{25}, degree={-1}{1},
    classes=fill,
    class labels={below=3pt},differentials=blue,
    class pattern=linear, classes={ tooltip = {(\xcoord,\ycoord)} },
    xscale=1.48,
    yscale=2.2,
    title = {Page \page},
    run off differentials = ->
]
\class[tag= h0^i](0,0) \tower[tag=h0^i]
\honetower \classoptions["h_1"](1,1)

\htwotower[tag=h0^i h2]
\classoptions["h_2"](3,1)
\htwotower[tag=h0^i h2^2]
\htwotower[tag=h0^i h2^3]
\htwotower[tag=h0^i h2^4]
\htwotower[tag=h0^i h2^5]
\htwotower[tag=h0^i h2^6]
\htwotower[tag=h0^i h2^7]
\htwotower[tag=h0^i h2^8]
\htwo%\htwotower[tag=h0^i h2^9]


\class["b_{20}",name=b20,tag=h1^i b20](4,2)
\tagclass{h0^i b20}(4,2)
\honetower[tag=h1^i b20]
\tower[tag=h0^i b20]
\class["x_7",tag=h0^i x7,name=x7](7,2) \honetower
\htwotower[tag=h0^i x7](b20)
\structline(\lastclass)(x7) % h0 x7 = h2 b20


\class["b_{21}", tag=h0^i b21,name=b21](10,2)
\honetower[tag=h1^i b21]
%\structline(\lastclass)(h2^2 b20) % h2 (h0 x7) = h2 (h2 b20)

\htwotower[tag=h0^i b21](x7)
\structline(b21)(\lastclass)



\htwotower[tag=h0^i h2 b21](b21)
\htwotower[tag=h0^i h2^2 b21]
\htwotower[tag=h0^i h2^3 b21]
\htwotower[tag=h0^i h2^4 b21]
\htwotower[tag=h0^i h2^5 b21]
\htwotower[tag=h0^i h2^6 b21]

\class["b_{30}",tag=h1^i b30](12,2)
\tagclass{h0^i b30}(12,2)
\tower[tag=h0^i b30]\honetower[tag=h1^i b30]
\htwotower[tag=h0^i h2 b30]
\htwotower[tag=h0^i h2^2 b30]
\htwotower[tag=h0^i h2^3 b30]
\htwotower[tag=h0^i h2^4 b30]
\htwotower[tag=h0^i h2^5 b30]



%

\class[tag=h0^i x7^2](14,4)
\classoptions["x_7^2",page=0--3](\lastclass)
\classoptions["d",page=4--100](\lastclass)
\tower[tag=h0^i x7^2] \honetower

\htwotower[tag=h0^i h2 x7^2]
\htwotower[tag=h0^i h2^2 x7^2]
\htwotower[tag=h0^i h2^3 x7^2]
\htwotower[tag=h0^i h2^4 x7^2]
\htwo%\htwotower[tag=h0^i h2^5 x7^2]


\class["b_{20}^2",tag=h0^i b_{20}^2](8,4)
\tower[tag=h0^i b_{20}^2]
\honetower
\htwotower[tag=h0^i h2 b_{20}^2]
\htwotower[tag=h0^i h2^2 b_{20}^2]
\htwotower[tag=h0^i h2^3 b_{20}^2]
\htwotower[tag=h0^i h2^4 b_{20}^2]
\htwo%\htwotower[tag=h0^i h2^5, b_{20}^2]

\class[tag=h0^i b21^2](20,4)
\classoptions["b_{21}^2",page=0--3](\lastclass)
\classoptions["g",page=4--100](\lastclass)
\honetower
\tower[tag=h0^i b21^2]

\htwotower[tag=h0^i h2 b21^2]
\htwotower[tag=h0^i h2^2 b21^2]

\class["b_{30}^2",tag=h0^i b30^2](24,4)
\tower[tag=h0^i b30^2]
\honetower
\htwotower
%\htwotower[tag=h0^i h2^3 b21^2]



\twods3(4,2,-1){1}{2} % d3(b20) = h1^3 + h0^2 h2
\replaceclass[offset={(0,0)}](3,3)
\structline(3,2)(3,3)
\structline(2,2)(3,3)
\structline[htwostructstyle](0,2)(3,3)

\foreach\y in {3,...,8} {\d3(4,\y,-1,-1)} % d3( h0^i b20 ) = h0^{2+i} h2
\foreach\n in {3,...,8} {\d3(2+\n,\n,h1^i b20,1)} % d3(h1^i b20) = h1^{3+i}
\foreach \y in {2,...,8} {\d3(7,\y,h0^i x7,h0^i h2^2)}

\foreach \y in {2,...,8} {\d3(10,\y,h0^i b21,h0^i h2^3)}

\foreach \y in {3,...,8} {\d3(13,\y,  h0^i h2 b21  ,h0^i h2^4)}
\foreach \y in {3,...,7} {\d3(16,\y+1,h0^i h2^2 b21,h0^i h2^5)}
\foreach \y in {3,...,6} {\d3(19,\y+2,h0^i h2^3 b21,h0^i h2^6)}
\foreach \y in {3,...,5} {\d3(22,\y+3,h0^i h2^4 b21,h0^i h2^7)}
\foreach \y in {3,...,4} {\d3(25,\y+4,h0^i h2^5 b21,h0^i h2^8)}

\foreach \n in {0,...,6} {\d3(12+\n,2+\n,h1^i b30,h1^i b21)}

\foreach \n in {0,...,4} {\d5(24,4+\n,-1,-1)}


\classoptions[page=4--100,"c_0"](8,3)
\classoptions[page=4--100,"a"](12,3)
\classoptions[page=4--100,"b"](15,3)



\end{sseqdata}
\printpage[name=tmfmayss,page=2]
\newpage
\printpage[name=tmfmayss,page=3]
\newpage
\printpage[name=tmfmayss,page=5]
\newpage
\printpage[name=tmfmayss,page=8,title={Page $\infty$}]
\end{document}