Paper I: Typed Operator Systems, Seed Rank, and Exact Packet Coordinates

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,
2  every node/.style={font=\sffamily\small},line cap=round,line join=round]
3 \filldraw[fill=black!8,draw=white] (0.0,0.0) rectangle ++(1.15,-.63);
4 \node[] at (0.5750,-0.3150) {$1$};
5 \filldraw[fill=black!8,draw=white] (1.3,0.0) rectangle ++(1.15,-.63);
6 \node[] at (1.8750,-0.3150) {$x$};
7 \filldraw[fill=black!8,draw=white] (2.6,0.0) rectangle ++(1.15,-.63);
8 \node[] at (3.1750,-0.3150) {$x^2$};
9 \filldraw[fill=black!8,draw=white] (3.9000000000000004,0.0) rectangle ++(1.15,-.63);
10 \node[] at (4.4750,-0.3150) {$x^3$};
11 \filldraw[fill=black!8,draw=white] (5.2,0.0) rectangle ++(1.15,-.63);
12 \node[] at (5.7750,-0.3150) {$x^4$};
13 \node[] at (6.9500,-0.3150) {$\cdots$};
14 \filldraw[fill=black!18,draw=white] (0.0,-0.8) rectangle ++(1.15,-.63);
15 \node[] at (0.5750,-1.1150) {$y$};
16 \filldraw[fill=black!18,draw=white] (1.3,-0.8) rectangle ++(1.15,-.63);
17 \node[] at (1.8750,-1.1150) {$xy$};
18 \filldraw[fill=black!18,draw=white] (2.6,-0.8) rectangle ++(1.15,-.63);
19 \node[] at (3.1750,-1.1150) {$x^2y$};
20 \filldraw[fill=black!18,draw=white] (3.9000000000000004,-0.8) rectangle ++(1.15,-.63);
21 \node[] at (4.4750,-1.1150) {$x^3y$};
22 \filldraw[fill=black!18,draw=white] (5.2,-0.8) rectangle ++(1.15,-.63);
23 \node[] at (5.7750,-1.1150) {$x^4y$};
24 \node[] at (6.9500,-1.1150) {$\cdots$};
25 \node[] at (3.2000,0.5200) {Independent coefficient slots: $a(x)$ and $b(x)$};
26 \node[] at (3.2000,-2.1800) {$y^2=x^3-x\quad\Longrightarrow\quad y^3=(x^3-x)y$};
27 \end{tikzpicture}

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