%% %% Description: The Adams Novikov Spectral Sequence for $S_3$, styled to superimpose on ANSS-S_3 %% %% The Adams spectral sequence at the prime 3 through the 45 stem. %% Compare page 5 to example_ass3 %% Copied from page 11 of the green book. %% \documentclass[tooltips]{spectralsequence-example} \begin{document} \NewSseqCommand\tower {d()m} { \IfNoValueF{#1}{\class(#1)} \savestack \Do { #2 } { \class(\lastx, \lasty+1) \structline(\lastclass1)(\lastclass) } \restorestack } \NewSseqCommand\hclass {d()}{ \IfNoValueF{#1}{\pushstack(#1)} \class(\lastx+3,\lasty+1) \structline(\lastclass1)(\lastclass) } \NewSseqCommand\bclass {d()}{ \IfNoValueF{#1}{\pushstack(#1)} \class(\lastx+7,\lasty+1) \structline(\lastclass1)(\lastclass) } \NewSseqCommand\hbachair {d()}{ \IfNoValueF{#1}{\pushstack(#1)} \nameclass{tempclass}(\lastclass) \bclass(\lastx,\lasty+1) \hclass \hclass(tempclass) \bclass \structline(\lastclass3)(\lastclass) } \NewSseqCommand\bahclaw { r() } { \class(#1) \bclass \class(\lastx,\lasty+1) \structline(\lastclass1)(\lastclass) \class(\lastx-3,\lasty-1) \structline(\lastclass1)(\lastclass) \pushstack(\lastclass2) } \begin{sseqdata}[ name=ass3, Adams grading, classes={fill, inner sep=1.2pt, tooltip={(\xcoord,\ycoord)}}, class labels={below,black}, differentials=blue, grid = go, x tick step = 5, x range={0}{45}, y range={0}{11}, xscale=0.7, yscale=1.2, y axis gap=2em ] \tower(0,0){\ymax+1} \classoptions["a_0" {left=0pt}](0,1) \hbachair \classoptions["h_0"](3,1) \classoptions["b_0"](\lastclass) \classoptions[purple,page=3](7,2) \DoUntilOutOfBounds{\hbachair} \begin{scope}[sseq=purple] \class["h_1"](11,1) \tower{2} \d2(\lastclass) \DoUntilOutOfBounds{ \bclass\d2(\lastclass) \hclass\d2(\lastclass) } \end{scope} \begin{scope}[orange] \class["k_0"](26,2) \DoUntilOutOfBounds{ \hclass\bclass } \end{scope} \begin{scope}[sseq=purple] \bahclaw(15,4) \DoUntilOutOfBounds{\hbachair} \bahclaw(27,7) \DoUntilOutOfBounds{\hbachair} \bahclaw(39,10) \DoUntilOutOfBounds{\hbachair} \bahclaw(38,7) \d2(\lastclass1)\d2(\lastclass2)\d2(\lastclass3)\d2(\lastclass4) \DoUntilOutOfBounds{ \hbachair \d2(\lastclass)\d2(\lastclass1) \d2(\lastclass3)\d2(\lastclass4) } \end{scope} \begin{scope}[sseq=purple] \class[](23,3) % label me \tower{3} \d2(\lastclass)\d2(\lastx,\lasty+1) \DoUntilOutOfBounds{ \hbachair \d2(\lastclass)\d2(\lastclass1) \d2(\lastclass3)\d2(\lastclass4) } \end{scope} \class["h_2"](35,1) \tower{8} \DoUntilOutOfBounds{\hbachair} \begin{scope}[sseq=orange] \class["b_{11}"](34,2) \tower{4} \DoUntilOutOfBounds{ \hclass\bclass } \d5(34,2) \d5(44,4) \end{scope} \foreach \y in {1,...,4}{ \d2(35,\y) } \d3(35,5)\d3(35,6) \foreach \y in {7,...,9}{ \classoptions[purple,page=4](35,\y,-1) } \end{sseqdata} \centering \printpage[name=ass3,page=1] \newpage \printpage[name=ass3,page=2] \newpage \printpage[name=ass3,page=3] \newpage \printpage[name=ass3,page=5] \end{document}