constraints.tex

Paper VII: Quantum Seed Calculus

constraints.tex

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Stealth,line cap=round,line join=round]
2 \path[use as bounding box] (0,-.6) rectangle (14,4.8);
3 \node[font=\small,align=center,font=\small] at (2.05,4.45) {$[C_1,C_2]$};
4 \path[draw=black!30,fill=white] (0.7,2.85) rectangle (1.6,3.75);
5 \node[font=\small,align=center,font=\small] at (1.15,3.3) {$0$};
6 \path[draw=black!30,fill=white] (1.6,2.85) rectangle (2.5,3.75);
7 \node[font=\small,align=center,font=\small] at (2.05,3.3) {$0$};
8 \path[draw=black!30,fill=white] (2.5,2.85) rectangle (3.4,3.75);
9 \node[font=\small,align=center,font=\small] at (2.95,3.3) {$0$};
10 \path[draw=black!30,fill=white] (0.7,1.95) rectangle (1.6,2.85);
11 \node[font=\small,align=center,font=\small] at (1.15,2.4) {$0$};
12 \path[draw=black!30,fill=white] (1.6,1.95) rectangle (2.5,2.85);
13 \node[font=\small,align=center,font=\small] at (2.05,2.4) {$0$};
14 \path[draw=black!30,fill=black!8] (2.5,1.95) rectangle (3.4,2.85);
15 \node[font=\small,align=center,font=\small] at (2.95,2.4) {$2$};
16 \path[draw=black!30,fill=white] (0.7,1.05) rectangle (1.6,1.95);
17 \node[font=\small,align=center,font=\small] at (1.15,1.5) {$0$};
18 \path[draw=black!30,fill=black!8] (1.6,1.05) rectangle (2.5,1.95);
19 \node[font=\small,align=center,font=\small] at (2.05,1.5) {$-2$};
20 \path[draw=black!30,fill=white] (2.5,1.05) rectangle (3.4,1.95);
21 \node[font=\small,align=center,font=\small] at (2.95,1.5) {$0$};
22 \node[font=\small,align=center,font=\small] at (11.15,4.45) {$P[C_1,C_2]P$};
23 \path[draw=black!30,fill=white] (9.8,2.85) rectangle (10.7,3.75);
24 \node[font=\small,align=center,font=\small] at (10.25,3.3) {$0$};
25 \path[draw=black!30,fill=white] (10.7,2.85) rectangle (11.6,3.75);
26 \node[font=\small,align=center,font=\small] at (11.15,3.3) {$0$};
27 \path[draw=black!30,fill=white] (11.6,2.85) rectangle (12.5,3.75);
28 \node[font=\small,align=center,font=\small] at (12.05,3.3) {$0$};
29 \path[draw=black!30,fill=white] (9.8,1.95) rectangle (10.7,2.85);
30 \node[font=\small,align=center,font=\small] at (10.25,2.4) {$0$};
31 \path[draw=black!30,fill=white] (10.7,1.95) rectangle (11.6,2.85);
32 \node[font=\small,align=center,font=\small] at (11.15,2.4) {$0$};
33 \path[draw=black!30,fill=white] (11.6,1.95) rectangle (12.5,2.85);
34 \node[font=\small,align=center,font=\small] at (12.05,2.4) {$0$};
35 \path[draw=black!30,fill=white] (9.8,1.05) rectangle (10.7,1.95);
36 \node[font=\small,align=center,font=\small] at (10.25,1.5) {$0$};
37 \path[draw=black!30,fill=white] (10.7,1.05) rectangle (11.6,1.95);
38 \node[font=\small,align=center,font=\small] at (11.15,1.5) {$0$};
39 \path[draw=black!30,fill=white] (11.6,1.05) rectangle (12.5,1.95);
40 \node[font=\small,align=center,font=\small] at (12.05,1.5) {$0$};
41 \node[font=\small,align=center] at (6.9,2.7) {$P=\diag(1,0,0)$};
42 \node[font=\small,align=center,font=\small] at (6.9,1.4) {$C_1P=C_2P=0$};
43 \node[font=\small,align=center,font=\scriptsize] at (7,0.3) {The right matrix is zero by the common-kernel choice, not by operator closure.};
44 \end{tikzpicture}

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