Add exam template
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4
.gitignore
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4
.gitignore
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@ -8,4 +8,6 @@ _region_.tex
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*.log
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*.out
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*.synctex.gz
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.projectile
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.projectile
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__pycache__
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270
exam_template/.vscode/latex.code-snippets
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270
exam_template/.vscode/latex.code-snippets
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{
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"exc": {
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"scope": "latex",
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"prefix": ["\\exc"],
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"body":
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[
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"\\exc{}",
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"\\begin{subexcs}",
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" \\subexc{}",
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" $0",
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"\\end{subexcs}"
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],
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"description": "Adds new exc with subexcs",
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},
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"subexc": {
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"scope": "latex",
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"prefix": ["\\subexc"],
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"body":
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[
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"\\subexc{}",
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"\\begin{ssubexcs}",
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" \\ssubexc{}",
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" $0",
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"\\end{ssubexcs}"
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],
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"description": "Adds new subexc with ssubexcs",
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},
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"graph-table": {
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"scope": "latex",
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"prefix": ["graph-table"],
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"body":
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[
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"\\begin{figure}[H]",
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" \\center",
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" \\begin{tabular}{c|cc}",
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" $A$ & \\multicolumn{2}{c}{$v$} \\\\",
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" \\hline",
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" & $a$ & $b$ \\\\",
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" \\hline",
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" $s_0$ & $s_$ & $s_$ \\\\",
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" $s_1$ & $s_$ & $s_$ \\\\",
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" $s_2$ & $s_$ & $s_$ \\\\",
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" \\end{tabular}",
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"\\end{figure}"
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],
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"description": "Adds graph-table",
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},
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"graph-table-double": {
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"scope": "latex",
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"prefix": ["graph-dtable"],
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"body":
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[
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"\\begin{figure}[H]",
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" \\center",
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" \\begin{tabular}{c|cc}",
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" $A$ & \\multicolumn{2}{c}{$v$} \\\\",
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" \\hline",
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" & $a$ & $b$ \\\\",
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" \\hline",
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" $s_0$ & $s_$ & $s_$ \\\\",
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" $s_1$ & $s_$ & $s_$ \\\\",
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" $s_2$ & $s_$ & $s_$ \\\\",
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" \\end{tabular}",
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"\\end{figure}"
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],
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"description": "Adds graph-table",
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},
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"graph-table-line": {
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"scope": "latex",
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"prefix": ["gtl"],
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"body": " $s_$ & $s_$ & $s_$ \\\\",
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"description": "Adds line inside graph-table",
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},
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"graph-table-double-line": {
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"scope": "latex",
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"prefix": ["gtdl"],
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"body": " $s_$ & $s_$ & $s_$ & $s_$ & $s_$ \\\\",
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"description": "Adds line inside a double graph-table",
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},
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"induction-proof": {
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"scope": "latex",
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"prefix": ["prove-induction"],
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"body": [
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"Base case:",
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"",
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"\\begin{align*}",
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"",
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"\\end{align*}",
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"",
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"Assume that",
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"",
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"\\[ $1 \\]",
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"",
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"Then",
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"",
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"\begin{align*}",
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" &= $1 + \\\\",
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" &=",
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"\\end{align*}",
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"",
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"\\qed"
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],
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"description": "Template for induction proof",
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},
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"injective-proof": {
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"scope": "latex",
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"prefix": ["prove-injective"],
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"body": [
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"In order for $f(x)$ to be injective, it has to hold that",
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"",
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"\\[ f(a) = f(b) \\Rightarrow a = b \\]",
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"",
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"\\begin{align*}",
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" f(a) &= f(b) \\\\",
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" $0",
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"\\end{align*}",
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"",
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"Hence $f(x)$ is injective."
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],
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"description": "Template for injective proof",
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},
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"surjective-proof": {
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"scope": "latex",
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"prefix": ["prove-surjective"],
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"body": [
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"In order for $f(x)$ to be surjective, it has to hold that",
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"",
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"\\[ \\forall x \\in SET \\exists y \\in SET [f(x) = y] \\]",
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"",
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"\\begin{align*}",
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" y &= $1 \\\\",
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"",
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" x &= \\\\" ,
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"\\end{align*}",
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"",
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"$ $ makes up all the elements in SET",
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"",
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"\\begin{align*}",
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" f(y) &= \\\\",
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"",
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"\\end{align*}",
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"",
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"Hence $f(x)$ is surjective"
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],
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"description": "Template for surjective proof",
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},
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"bijective-proof": {
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"scope": "latex",
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"prefix": ["prove-bijective"],
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"body": [
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"\\textbf{Injective:}",
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"",
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"In order for $f(x)$ to be injective, it has to hold that",
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"",
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"\\[ f(a) = f(b) \\Rightarrow a = b \\]",
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"",
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"\\begin{align*}",
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" f(a) &= f(b) \\\\",
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" $0",
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"\\end{align*}",
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"",
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"Hence $f(x)$ is injective.",
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"",
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"",
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"\\textbf{Surjective:}",
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"",
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"In order for $f(x)$ to be surjective, it has to hold that",
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"",
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"\\[ \\forall x \\in SET \\exists y \\in SET [f(x) = y] \\]",
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"",
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"\\begin{align*}",
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" y &= $1 \\\\",
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"",
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" x &= \\\\" ,
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"\\end{align*}",
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"",
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"$ $ makes up all the elements in SET",
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"",
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"\\begin{align*}",
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" f(y) &= \\\\",
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"",
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"\\end{align*}",
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"",
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"Hence $f(x)$ is surjective",
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"",
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"",
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"\\textbf{Inverse:}",
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"",
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"The inverse is the same as the expression which makes up $x$ which we used to prove that $f(x)$ is surjective. Hence",
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"",
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"\\[ f^{-1}(x) = \\]",
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],
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"description": "Template for bijective proof",
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},
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"equivalence-relation-proof": {
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"scope": "latex",
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"prefix": ["prove-eq-rel"],
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"body": [
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"In order for this relation to be an equivalence equation, it has to be reflexive, symmetric and transitive.",
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"",
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"\\textbf{Reflexive:}",
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"",
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"\\[ \\]",
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"",
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"\\textbf{Symmetric:}",
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"",
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"\\[ \\]",
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"",
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"\\textbf{Transitive:}",
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"",
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"\\[ \\]",
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"",
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"Hence the relation is an equivalence relation",
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],
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"description": "Template for equivalence relation proof",
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},
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"partial order-proof": {
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"scope": "latex",
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"prefix": ["prove-poset"],
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"body": [
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"In order for this relation to be a partial order, it has to be reflexive, antisymmetric and transitive.",
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"",
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"\\textbf{Reflexive:}",
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"",
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"\\[ \\]",
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"",
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"\\textbf{Antisymmetric:}",
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"",
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"\\[ \\]",
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"",
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"\\textbf{Transitive:}",
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"",
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"\\[ \\]",
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"",
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"Hence the relation is a partial order",
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],
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"description": "Template for poset proof",
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},
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"poset minmax": {
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"scope": "latex",
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"prefix": ["minmax-poset"],
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"body": [
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"Minimal elements:",
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" \\[ \\{ $0 \\} \\]",
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"Maximal elements:",
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" \\[ \\{ \\} \\]"
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],
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"description": "Minimal maximal elements for poset",
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},
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"Diagram": {
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"scope": "latex",
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"prefix": ["dia"],
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"body": "\\includeDiagram[caption={}, width=1\\linewidth]{graphics/$0.tex}",
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"description": "Include a diagram",
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},
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}
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16
exam_template/.vscode/makefile.code-snippets
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exam_template/.vscode/makefile.code-snippets
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{
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"hasse": {
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"scope": "makefile",
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"prefix": ["hasse"],
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"body": "python ../../python/Hasse.py graphics/src/$1.txt graphics/$1.tex",
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"description": "Add hasse diagram",
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},
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"FSA": {
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"scope": "makefile",
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"prefix": ["fsa"],
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"body": "python ../../python/FSA.py graphics/src/$1.txt graphics/$1.tex",
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"description": "Add FSA diagram",
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}
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}
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9
exam_template/Makefile
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exam_template/Makefile
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.DEFAULT_GOAL := default
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.PHONY: default python
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default: python
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pdflatex main.tex
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python:
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python python/Hasse.py graphics/src/example1.txt graphics/example1.tex
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python python/FSA.py graphics/src/example2.txt graphics/example2.tex
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16
exam_template/graphics/example1.tex
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16
exam_template/graphics/example1.tex
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\begin{tikzpicture}
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\tikzset{every node/.style={shape=circle,draw,inner sep=2pt}}
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\node (a) at (-0.5, 0) {$a$};
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\node (e) at (-1.0, 1) {$e$};
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\node (b) at (0.0, 1) {$b$};
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\node (d) at (-1.0, 2) {$d$};
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\node (c) at (0.0, 2) {$c$};
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\draw (a) -- (e);
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\draw (b) -- (c);
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\draw (e) -- (d);
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\draw (a) -- (b);
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\draw (e) -- (c);
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\end{tikzpicture}
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23
exam_template/graphics/example2.tex
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exam_template/graphics/example2.tex
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\begin{tikzpicture}
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\tikzset{
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->, % makes the edges directed
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>=Stealth, % makes the arrow heads bold
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node distance=5cm, % specifies the minimum distance between two nodes. Change if necessary.
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every state/.style={thick, fill=white}, % sets the properties for each ’state’ node
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initial text=$ $, % sets the text that appears on the start arrow
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}
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\node[state, initial] (s0) {$s_0$};
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\node[state, right of=s0] (s1) {$s_1$};
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\node[state, accepting, right of=s1] (s2) {$s_2$};
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\node[state, right of=s2] (s3) {$s_3$};
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\draw (s0) edge[above] node{$a$} (s1);
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\draw (s0) edge[bend left, above] node{$b$} (s3);
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\draw (s1) edge[loop,below] node{a} (s1);
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\draw (s1) edge[above] node{$b$} (s2);
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\draw (s2) edge[loop,below] node{b} (s2);
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\draw (s2) edge[above] node{$a$} (s3);
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\draw (s3) edge[loop,above] node{a,b} (s3);
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\end{tikzpicture}
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1
exam_template/graphics/src/example1.txt
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1
exam_template/graphics/src/example1.txt
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ab ac ad ae bc ed ec
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12
exam_template/graphics/src/example2.txt
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12
exam_template/graphics/src/example2.txt
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0 s
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1 r0
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2 fr1
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3 r2
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0 a u 1
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0 b u( 3
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o a d 1
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1 b u 2
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o b d 2
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2 a u 3
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o a,b u 3
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33
exam_template/main.tex
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33
exam_template/main.tex
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\documentclass[12pt]{article}
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\usepackage{ntnu}
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\usepackage{ntnu-math}
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\author{TODO: STUDENTNUMMER}
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\title{Exam v2021}
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\usetikzlibrary{automata, positioning, arrows.meta}
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\newcommand{\I}{Option 1 is correct}
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\newcommand{\II}{Option 2 is correct}
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\newcommand{\III}{Option 3 is correct}
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\renewcommand{\theenumi}{\arabic{enumi}}
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\renewcommand{\theenumii}{(\arabic{enumii})}
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\renewcommand{\theenumiii}{\alph{enumiii})}
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\begin{document}
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\ntnuTitle{}
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\break{}
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\tableofcontents
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\begin{excs}
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\exc{}
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\begin{subexcs}
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\subexc{}
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\end{subexcs}
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\end{excs}
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\end{document}
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74
exam_template/python/FSA.py
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74
exam_template/python/FSA.py
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from sys import argv
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from pathlib import Path
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import re
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placementChart = {
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'a': 'above',
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'b': 'below',
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'l': 'left',
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'r': 'right'
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}
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def generateEdge(inputLine):
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s_src, msg, opts, s_dest = inputLine.split(' ')
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out_options = []
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if '(' in opts or ')' in opts:
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out_options.append('bend left' if '(' in opts else 'bend right')
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if any(x in opts for x in 'udlr'):
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out_options.append(
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'above' if 'u' in opts else \
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'below' if 'd' in opts else \
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'left' if 'l' in opts else \
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'right' if 'r' in opts else ''
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)
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if s_src == 'o':
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return f'\draw (s{s_dest}) edge[loop,{",".join(out_options)}] node{{{msg}}} (s{s_dest});'
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else:
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return f'\draw (s{s_src}) edge[{", ".join(out_options)}] node{{${msg}$}} (s{s_dest});'
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def generateNode(inputLine):
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s_src, opts = inputLine.split(' ')
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out_opts = []
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if 's' in opts:
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out_opts.append('initial')
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if 'f' in opts:
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out_opts.append('accepting')
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if place := re.search('[udlr]\d+', opts):
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out_opts.append(placementChart[place.group()[0]] + ' of=s' + place.group()[1])
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return f'\\node[state, {", ".join(out_opts)}] (s{s_src}) {{$s_{s_src}$}};'
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def generate_latex(inputLines):
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nodes, edges = inputLines.split('\n\n')
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output=[]
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for node in nodes.split('\n'):
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output.append(generateNode(node))
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output.append('')
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for edge in edges.split('\n'):
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output.append(generateEdge(edge))
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return '\n'.join(output)
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if __name__ == '__main__':
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filename = argv[1]
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with open(filename) as file:
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content = generate_latex(file.read())
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with open(str(Path(__file__).parent.absolute()) + '/tex_templates/FSA.tex') as template:
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with open(argv[2], 'w') as destination_file:
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destination_file.write(template.read().replace('%CONTENT', content))
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82
exam_template/python/Hasse.py
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82
exam_template/python/Hasse.py
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from sys import argv
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from pathlib import Path
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# Increase if the diagram becomes too clobbered
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HEIGHT_SEPARATOR = 1
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def printred(text):
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print(f'\033[31m{text}\033[0m')
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# For manual usage via stdin
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def getRels(relations=None):
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if relations == None:
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relations = input("Write the relations in the following format: ab ac ad bc cd ...\n")
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relations = (tuple(list(x)) for x in relations.split(' '))
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return set(relations)
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# Generate divisibility graph by range
|
||||
def divisibility_graph(n):
|
||||
E = set()
|
||||
for dst in range(n):
|
||||
for src in range( 1, dst ):
|
||||
if dst % src == 0:
|
||||
E.add( ( src, dst ) )
|
||||
return E
|
||||
|
||||
def hasse_diagram(E):
|
||||
E2 = set()
|
||||
for e0 in E:
|
||||
for e1 in E:
|
||||
if e0[1] == e1[0]:
|
||||
E2.add( ( e0[0], e1[1] ) )
|
||||
return E - E2
|
||||
|
||||
def latex_hasse(hasse):
|
||||
min_el = set(a for a,b in hasse if a not in list(zip(*hasse))[1])
|
||||
keys = set(item for tup in hasse for item in tup)
|
||||
y_pos = dict.fromkeys(keys, 0)
|
||||
|
||||
i = 0
|
||||
while len(next_row := [val for key,val in hasse if key in [x for x,y in y_pos.items() if y == i] ]) != 0:
|
||||
for item in next_row:
|
||||
y_pos[item] = i + 1
|
||||
i += 1
|
||||
|
||||
inv_ypos = dict()
|
||||
for key in set(y_pos.values()):
|
||||
inv_ypos[key] = [x for x,y in y_pos.items() if y == key]
|
||||
|
||||
output = []
|
||||
|
||||
for y in inv_ypos.keys():
|
||||
for i, n in enumerate(inv_ypos[y]):
|
||||
output.append(f'\\node ({n}) at ({i - len(inv_ypos[y])/2}, {y * HEIGHT_SEPARATOR}) {{${n}$}};')
|
||||
|
||||
output.append('')
|
||||
|
||||
for x,y in hasse:
|
||||
output.append(f'\\draw ({x}) -- ({y});')
|
||||
|
||||
|
||||
printred(f"Minimal elements: $\{{ {', '.join(str(e) for e in min_el)} \}}$ \\\\")
|
||||
|
||||
max_el = set(v for k,v in hasse if v not in (x for x,_ in hasse))
|
||||
printred(f"Maximal elements: $\{{ {', '.join(str(e) for e in max_el)} \}}$" )
|
||||
|
||||
return '\n'.join(output)
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
filename = argv[1]
|
||||
|
||||
with open(filename) as file:
|
||||
rels = getRels(file.read())
|
||||
|
||||
# rels = getRels()
|
||||
# rels = divisibility_graph(30)
|
||||
|
||||
content = latex_hasse(hasse_diagram(rels))
|
||||
|
||||
with open(str(Path(__file__).parent.absolute()) + '/tex_templates/Hasse.tex') as template:
|
||||
with open(argv[2], 'w') as destination_file:
|
||||
destination_file.write(template.read().replace('%CONTENT', content))
|
||||
12
exam_template/python/tex_templates/FSA.tex
Normal file
12
exam_template/python/tex_templates/FSA.tex
Normal file
@ -0,0 +1,12 @@
|
||||
\begin{tikzpicture}
|
||||
\tikzset{
|
||||
->, % makes the edges directed
|
||||
>=Stealth, % makes the arrow heads bold
|
||||
node distance=5cm, % specifies the minimum distance between two nodes. Change if necessary.
|
||||
every state/.style={thick, fill=white}, % sets the properties for each ’state’ node
|
||||
initial text=$ $, % sets the text that appears on the start arrow
|
||||
}
|
||||
|
||||
%CONTENT
|
||||
|
||||
\end{tikzpicture}
|
||||
6
exam_template/python/tex_templates/Hasse.tex
Normal file
6
exam_template/python/tex_templates/Hasse.tex
Normal file
@ -0,0 +1,6 @@
|
||||
\begin{tikzpicture}
|
||||
\tikzset{every node/.style={shape=circle,draw,inner sep=2pt}}
|
||||
|
||||
%CONTENT
|
||||
|
||||
\end{tikzpicture}
|
||||
Loading…
Reference in New Issue
Block a user