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Latex labels for Graphviz (work in progress)
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| """ Latex labels for Graphviz """ | |
| import html | |
| import re | |
| import subprocess | |
| from pylatexenc.latex2text import ( | |
| LatexNodes2Text, | |
| MacroTextSpec, | |
| get_default_latex_context_db as get_default_l2t_context_db, | |
| ) | |
| from pylatexenc.latexwalker import ( | |
| LatexMacroNode, | |
| LatexEnvironmentNode, | |
| LatexWalker, | |
| get_default_latex_context_db as get_default_walker_context_db, | |
| ) | |
| from pylatexenc.macrospec import EnvironmentSpec, MacroSpec | |
| BLACKBOARD_MAP = {"Z": "ℤ", "N": "ℕ", "C": "ℂ", "R": "ℝ", "Q": "ℚ"} | |
| def custom_mathbb(node, l2tobj): | |
| """ foobar """ | |
| arg_nodes = getattr( | |
| node.nodeargd, "argnlist", getattr(node.nodeargd, "argnodelist", []) | |
| ) | |
| arg = l2tobj.nodelist_to_text(arg_nodes) | |
| return BLACKBOARD_MAP.get(arg, arg) | |
| EXTRA_WALKER_MACROS = [ | |
| MacroSpec("textbf", "{"), | |
| MacroSpec("cong"), | |
| MacroSpec("mathbb", "{"), | |
| MacroSpec("text", "{"), | |
| MacroSpec("longrightarrow"), | |
| MacroSpec("Longrightarrow"), | |
| MacroSpec("iff"), | |
| MacroSpec("implies"), | |
| MacroSpec("sim"), | |
| MacroSpec("approx"), | |
| MacroSpec("equiv"), | |
| MacroSpec("lcm"), | |
| MacroSpec("lbr"), | |
| MacroSpec("bar", "{"), | |
| MacroSpec("vspace", "{"), | |
| MacroSpec("ord"), | |
| MacroSpec("gcd"), | |
| MacroSpec("mod"), | |
| ] | |
| walker_ctx = get_default_walker_context_db() | |
| walker_ctx.add_context_category( | |
| "math-extra", macros=EXTRA_WALKER_MACROS, prepend=True | |
| ) | |
| walker_ctx.add_context_category( | |
| "env-extra", environments=[EnvironmentSpec("cases")], prepend=True | |
| ) | |
| l2t_ctx = get_default_l2t_context_db() | |
| l2t_ctx.add_context_category( | |
| "math-extra-override", | |
| macros=[ | |
| MacroTextSpec("textbf", "@@@BOLDSTART@@@%(1)s@@@BOLDEND@@@"), | |
| MacroTextSpec("cong", " ≅ "), | |
| MacroTextSpec("mathbb", custom_mathbb), | |
| MacroTextSpec("text", "%(1)s"), | |
| MacroTextSpec("vert", "|"), | |
| MacroTextSpec("longrightarrow", "⟶"), | |
| MacroTextSpec("Longrightarrow", "⟹"), | |
| MacroTextSpec("iff", "⇔ "), | |
| MacroTextSpec("implies", "⇒"), | |
| MacroTextSpec("sim", "~"), | |
| MacroTextSpec("approx", "≈"), | |
| MacroTextSpec("equiv", "≡"), | |
| MacroTextSpec("Z", "ℤ"), | |
| MacroTextSpec("N", "ℕ"), | |
| MacroTextSpec("lcm", "lcm"), | |
| MacroTextSpec("lbr", "@@@BRLEFT@@@"), | |
| MacroTextSpec("bar", "@@@BARSTART@@@%(1)s@@@BAREND@@@"), | |
| MacroTextSpec("vspace", "@@@VSPACESTART@@@%(1)s@@@VSPACEEND@@@"), | |
| MacroTextSpec("ord", "ord"), | |
| MacroTextSpec("gcd", "gcd"), | |
| MacroTextSpec("mod", "mod"), | |
| ], | |
| prepend=True, | |
| ) | |
| def preprocess_sub_super_scripts(text): | |
| """Replaces superscripts/subscripts with safe placeholder tags free of underscores.""" | |
| text = re.sub(r"\^\{([^}]+)\}", r"@@@SUPSTART@@@\1@@@SUPEND@@@", text) | |
| text = re.sub( | |
| r"\^([a-zA-Z0-9\+\-]|\\iota)", r"@@@SUPSTART@@@\1@@@SUPEND@@@", text | |
| ) | |
| text = re.sub(r"_\{([^}]+)\}", r"@@@SUBSTART@@@\1@@@SUBEND@@@", text) | |
| text = re.sub(r"_([a-zA-Z0-9\+\-])", r"@@@SUBSTART@@@\1@@@SUBEND@@@", text) | |
| return text | |
| def postprocess_html_tags(text): | |
| """Converts safe tokens to valid Graphviz HTML labels.""" | |
| # Convert \vspace{N} to a small empty break tag | |
| text = re.sub( | |
| r"@@@VSPACESTART@@@(\d+)@@@VSPACEEND@@@", | |
| r'<BR ALIGN="LEFT"/><FONT POINT-SIZE="\1"> </FONT><BR ALIGN="LEFT"/>', | |
| text | |
| ) | |
| return ( | |
| text.replace("@@@BOLDSTART@@@", "<B>") | |
| .replace("@@@BOLDEND@@@", "</B>") | |
| .replace("@@@SUPSTART@@@", "<SUP>") | |
| .replace("@@@SUPEND@@@", "</SUP>") | |
| .replace("@@@SUBSTART@@@", "<SUB>") | |
| .replace("@@@SUBEND@@@", "</SUB>") | |
| .replace("@@@BRLEFT@@@", '<BR ALIGN="LEFT"/>') | |
| .replace("@@@BARSTART@@@", "<O>") | |
| .replace("@@@BAREND@@@", "</O>") | |
| ) | |
| def find_unknown_macro(node, ctx): | |
| """ foobar """ | |
| if node is None: | |
| return None | |
| if isinstance(node, LatexMacroNode): | |
| if ctx.get_macro_spec(node.macroname) is None: | |
| return node | |
| if hasattr(node, "nodeargd") and node.nodeargd: | |
| arg_list = getattr( | |
| node.nodeargd, | |
| "argnlist", | |
| getattr(node.nodeargd, "argnodelist", []), | |
| ) | |
| for child in arg_list: | |
| err_node = find_unknown_macro(child, ctx) | |
| if err_node: | |
| return err_node | |
| elif hasattr(node, "nodelist") and node.nodelist: | |
| for child in node.nodelist: | |
| err_node = find_unknown_macro(child, ctx) | |
| if err_node: | |
| return err_node | |
| return None | |
| # pylint: disable=too-many-locals | |
| def process_cases_environment(env_node, converter, full_latex_str): | |
| """ foobar """ | |
| rows = [[]] | |
| for child in env_node.nodelist: | |
| if isinstance(child, LatexMacroNode) and child.macroname == "\\": | |
| rows.append([]) | |
| else: | |
| rows[-1].append(child) | |
| table_rows = [] | |
| num_rows = len([r for r in rows if r]) | |
| for row_nodes in rows: | |
| if not row_nodes: | |
| continue | |
| first_pos = row_nodes[0].pos | |
| last_node = row_nodes[-1] | |
| last_pos = last_node.pos + last_node.len | |
| row_str = full_latex_str[first_pos:last_pos] | |
| if "&" in row_str: | |
| expr_str, cond_str = row_str.split("&", 1) | |
| else: | |
| expr_str, cond_str = row_str, "" | |
| w_expr = LatexWalker(expr_str, latex_context=walker_ctx) | |
| n_expr, _, _ = w_expr.get_latex_nodes() | |
| expr = converter.nodelist_to_text(n_expr).strip() | |
| w_cond = LatexWalker(cond_str, latex_context=walker_ctx) | |
| n_cond, _, _ = w_cond.get_latex_nodes() | |
| cond = converter.nodelist_to_text(n_cond).strip() | |
| expr = postprocess_html_tags(html.escape(expr)) | |
| cond = postprocess_html_tags(html.escape(cond)) | |
| if len(table_rows) == 0: | |
| table_rows.append( | |
| f"<TR>" | |
| f'<TD ROWSPAN="{num_rows}" VALIGN="MIDDLE" ALIGN="RIGHT" BORDER="0">' | |
| f'<FONT POINT-SIZE="22">{</FONT></TD>' | |
| f'<TD ALIGN="LEFT" VALIGN="MIDDLE" BORDER="0">{expr}</TD>' | |
| f'<TD ALIGN="LEFT" VALIGN="MIDDLE" BORDER="0"> {cond}</TD>' | |
| f"</TR>" | |
| ) | |
| else: | |
| table_rows.append( | |
| f"<TR>" | |
| f'<TD ALIGN="LEFT" VALIGN="MIDDLE" BORDER="0">{expr}</TD>' | |
| f'<TD ALIGN="LEFT" VALIGN="MIDDLE" BORDER="0"> {cond}</TD>' | |
| f"</TR>" | |
| ) | |
| return ( | |
| '<TABLE BORDER="0" CELLBORDER="0" CELLSPACING="0" CELLPADDING="1">' | |
| + "".join(table_rows) | |
| + "</TABLE>" | |
| ) | |
| def latex_to_graphviz_html(latex_str): | |
| """ foobar """ | |
| latex_str = preprocess_sub_super_scripts(latex_str) | |
| walker = LatexWalker(latex_str, latex_context=walker_ctx) | |
| nodes, _, _ = walker.get_latex_nodes() | |
| for node in nodes: | |
| missing_node = find_unknown_macro(node, l2t_ctx) | |
| if missing_node: | |
| raise ValueError(f"Unknown macro \\{missing_node.macroname}") | |
| converter = LatexNodes2Text(latex_context=l2t_ctx) | |
| if r"\begin{cases}" in latex_str: | |
| for node in nodes: | |
| if ( | |
| isinstance(node, LatexEnvironmentNode) | |
| and node.environmentname == "cases" | |
| ): | |
| cases_table = process_cases_environment( | |
| node, converter, latex_str | |
| ) | |
| prefix_str = latex_str[: node.pos] | |
| suffix_str = latex_str[node.pos + node.len :] | |
| if r"\\" in prefix_str: | |
| lines = prefix_str.split(r"\\") | |
| line1_html = latex_to_graphviz_html(lines[0])[1:-1] | |
| line2_html = latex_to_graphviz_html(lines[1])[1:-1] | |
| suffix_html = latex_to_graphviz_html(suffix_str)[1:-1] | |
| full_html = ( | |
| '<TABLE BORDER="0" CELLBORDER="0" CELLSPACING="0" CELLPADDING="0">' | |
| f'<TR><TD BORDER="0" ALIGN="LEFT" COLSPAN="2">{line1_html}</TD></TR>' | |
| f'<TR><TD BORDER="0" VALIGN="MIDDLE" ALIGN="LEFT">{line2_html}</TD>' | |
| f'<TD BORDER="0" VALIGN="MIDDLE" ALIGN="LEFT">{cases_table}</TD>' | |
| f'<TD BORDER="0" VALIGN="MIDDLE" ALIGN="LEFT">{suffix_html}</TD></TR>' | |
| "</TABLE>" | |
| ) | |
| return f"<{full_html}>" | |
| prefix_html = latex_to_graphviz_html(prefix_str)[1:-1] | |
| suffix_html = latex_to_graphviz_html(suffix_str)[1:-1] | |
| full_html = ( | |
| '<TABLE BORDER="0" CELLBORDER="0" CELLSPACING="0" CELLPADDING="0"><TR>' | |
| f'<TD BORDER="0" VALIGN="MIDDLE">{prefix_html}</TD>' | |
| f'<TD BORDER="0" VALIGN="MIDDLE">{cases_table}</TD>' | |
| f'<TD BORDER="0" VALIGN="MIDDLE">{suffix_html}</TD>' | |
| "</TR></TABLE>" | |
| ) | |
| return f"<{full_html}>" | |
| plain_text = converter.nodelist_to_text(nodes) | |
| escaped_text = html.escape(plain_text) | |
| # Convert placeholders to Graphviz HTML tags for standard nodes | |
| html_label_body = postprocess_html_tags(escaped_text.replace("\n", "<BR/>")) | |
| return f"<{html_label_body}>" | |
| def_label = latex_to_graphviz_html( | |
| r"""\textbf{Def 2.1 }Number-theoretic function:\\""" | |
| r"""a: \mathbb{N}\to \mathbb{C}""" | |
| ) | |
| ex_label = latex_to_graphviz_html( | |
| r"""\textbf{Ex 2.2a }for s\in\mathbb{C}: \iota^{s}(n) := n^s \forall n \in | |
| \mathbb{N} is s-th power\\function (s=0 constant one function, identity \iota^1 =: \iota)""" | |
| ) | |
| def_3_13_label = latex_to_graphviz_html( | |
| r"""\textbf{Def 3.13 } Ring R, x\in R: if \exists y\in R\setminus \{0\}: xy=0, | |
| then x is called zero divisor""" | |
| ) | |
| ex_3_14_label = latex_to_graphviz_html( | |
| r"""\textbf{Ex 3.14 } zero divisors in \Z/3\Z: \bar{0}, so has no zero divisors\vspace{3}""" | |
| r"""zero divisors in \Z/4\Z: \bar{0},\bar{2}, so has zero divisor\\""" | |
| ) | |
| def_3_15_label = latex_to_graphviz_html( | |
| r"""\textbf{Def 3.15 } Ring R, x\in R: if \exists y\in R: xy=1,\\then x is called a unit""" | |
| ) | |
| ex_3_16_label = latex_to_graphviz_html( | |
| r"""\textbf{Ex 3.16 } units in \Z/3\Z: \bar{1},\bar{2}\vspace{3}""" | |
| r"""units in \Z/4\Z: \bar{1},\bar{3}""" | |
| ) | |
| prop_3_17_label = latex_to_graphviz_html( | |
| r"""\textbf{Prop 3.17 } R ring\lbr""" | |
| r"""(a) R^{\times}:=\{x\in R: x is unit\} with \cdot\ is (abelian) group of units\lbr""" | |
| r"""(b) x\in R^{\times} \implies\ x no zero divisor\lbr""" | |
| r"""(c) R finite, then also: x\in R no zero divisor \implies\ x is unit\lbr""" | |
| ) | |
| ex_3_18_label = latex_to_graphviz_html( | |
| r"""\textbf{Ex 3.18 } Finite ring R=\Z/n\Z, n\in \N, x\in R:\vspace{5}""" | |
| r"""\bar{x} unit \iff \bar{x} no zero divisor\lbr """ | |
| r"""Units in R are called coprime residue classes modulo n\lbr """ | |
| r"""(\Z/n\Z)^{\times} is called multiplicative group of integers modulo n""" | |
| ) | |
| def_3_19_label = latex_to_graphviz_html( | |
| r"""\textbf{Def 3.19 } (Commutative) ring R | |
| with R^{\times} = R \setminus \{0\} is called field""" | |
| ) | |
| ex_3_20_label = latex_to_graphviz_html( | |
| r"""\textbf{Ex 3.20 } \Z/3\Z\ is field, \Z/4\Z\ and zero ring are no fields.""" | |
| ) | |
| thm_3_21_label = latex_to_graphviz_html( | |
| r"""\textbf{Thm 3.21 } n\in \N, these are equivalent\lbr""" | |
| r"""(i) n is prime\lbr""" | |
| r"""(ii) \Z/n\Z\ is field\lbr""" | |
| r"""(iii) \Z/n\Z\ has no zero divisors\lbr""" | |
| ) | |
| prop_3_22_label = latex_to_graphviz_html( | |
| r"""\textbf{Prop 3.22 } a\in \mathbb{N}, \bar{a}\in \Z/n\Z:\vspace{3}""" | |
| r"""\bar{a}\in (\Z/n\Z)^{\times} \iff \gcd(a,n)=1""" | |
| ) | |
| cor_3_23_label = latex_to_graphviz_html( | |
| r"""\textbf{Cor 3.23 } n\in \mathbb{N}, a\in \Z:\vspace{3}""" | |
| r"""(\exists x\in \Z: ax\equiv 1 (\mod\ n)) \iff \gcd(a,n)=1""" | |
| ) | |
| ex_3_24_label = latex_to_graphviz_html( | |
| r"""\textbf{Ex 3.24 } Solutions for\\""" | |
| r"""3x\equiv 1 (\mod\ 37): L=25+37\Z""" | |
| ) | |
| prop_3_25_label = latex_to_graphviz_html( | |
| r"""\textbf{Prop 3.25 } a,b\in \Z, n\in\N\\""" | |
| r"""(\exists x\in\Z: ax\equiv b (\mod\ n)) \iff \gcd(a,n)\vert b""" | |
| ) | |
| ex_3_26_label = latex_to_graphviz_html( | |
| r"""\textbf{Ex 3.26 } (a) \nexists x\in \Z: 15x\equiv 7 (\mod\ 21)\lbr""" | |
| r"""(b) \exists x\in\Z: 15x\equiv 6 (\mod\ 21)\lbr""" | |
| ) | |
| def_3_27_label = latex_to_graphviz_html( | |
| r"""\textbf{Def 3.27 } Order \vert G\vert\ of group\\""" | |
| r"""is number of its elements""" | |
| ) | |
| ex_3_28_label = latex_to_graphviz_html( | |
| r"""\textbf{Ex 3.28 }\vert(\Z/n\Z)^{\times}\vert=\phi(n)""" | |
| ) | |
| prop_3_29_label = latex_to_graphviz_html( | |
| r"""\textbf{Prop 3.29 } G finite abelian group.\lbr | |
| \forall g\in G: g^{\vert G\vert} =1 """ | |
| ) | |
| thm_3_30_label = latex_to_graphviz_html( | |
| r"""\textbf{Thm 3.30 } (Fermat-Euler theorem) \vspace{5}""" | |
| r"""n\in \mathbb{N}. """ | |
| r"""\forall \bar{a}\in (\Z/n\Z)^{\times}:\ \bar{a}^{\phi(n)} =\bar{1} """ | |
| ) | |
| ex_3_31_label = latex_to_graphviz_html( | |
| r"""\textbf{Ex 3.31 } 3^{19}\equiv 10 (\mod\ 17)""" | |
| ) | |
| cor_3_32_label = latex_to_graphviz_html( | |
| r"""\textbf{Cor 3.32 } (Fermat's little theorem) p prime:\vspace{3}""" | |
| r"""(a) \forall \bar{a}\in \mathbb{F}_p^{\times}: \bar{a}^{p-1}=\bar{1}\vspace{5}""" | |
| r"""(b) \forall \bar{a}\in \mathbb{F}_p: \bar{a}^p=\bar{a}\lbr""" | |
| ) | |
| def_3_33_label = latex_to_graphviz_html( | |
| r"""\textbf{Def 3.33 } Group G is cyclic:\lbr | |
| \exists g\in G generator with\lbr | |
| G = \{g^n: n\in \Z\}=:<g>\lbr""" | |
| ) | |
| rem_3_34_label = latex_to_graphviz_html( | |
| r"""\textbf{Rem 3.34 } Every cyclic group is abelian.""" | |
| ) | |
| ex_3_35_label = latex_to_graphviz_html( | |
| r"""\textbf{Ex 3.35 }(a) group (\Z/5\Z)^{\times} = \{\bar{1},\bar{2},""" | |
| r"""\bar{3},\bar{4}\} is cyclic\vspace{3}""" | |
| r"""(b) group (\Z/8\Z)^{\times} = \{\bar{1},\bar{3},\bar{5},\bar{7}\} is not cyclic\lbr""" | |
| r"""(c) additive group \Z\ is cyclic\vspace{3}""" | |
| r"""(d) additive group \Z/m\Z =\{\bar{0},\bar{1},\dots,\bar{m-1}\}\ is cyclic\lbr""" | |
| ) | |
| def_3_36_label = latex_to_graphviz_html( | |
| r"""\textbf{Def 3.36 } G finite abelian group.\lbr | |
| Order \ord(G):=\min\{n\in \mathbb{N}: g^n=1\}\lbr """ | |
| ) | |
| ex_3_37_label = latex_to_graphviz_html( | |
| r"""\textbf{Ex 3.37 }For G=(\Z/5\Z)^{\times}:\vspace{3}""" | |
| r"""(a) ord(\bar{2})=4\vspace{3}""" | |
| r"""(b) ord(\bar{4})=2\lbr""" | |
| ) | |
| prop_3_38_label = latex_to_graphviz_html( | |
| r"""\textbf{Prop 3.38 }G finite abelian group: | |
| G is cyclic \iff \exists g\in G with ord(g)=\vert G\vert""" | |
| ) | |
| prop_3_39_label = latex_to_graphviz_html( | |
| r"""\textbf{Prop 3.39 }G finite abelian group,\\g\in G, m\in \Z: ord(g)\vert m \iff g^m=1""" | |
| ) | |
| cor_3_40_label = latex_to_graphviz_html( | |
| r"""\textbf{Cor 3.40 } G finite abelian group.\lbr | |
| \forall g\in G: ord(g) \vert\ \vert G\vert """ | |
| ) | |
| def_3_41_label = latex_to_graphviz_html( | |
| r"""\textbf{Def 3.41 } G finite abelian group.\lbr | |
| Exponent \exp(G):=\min\{n\in \mathbb{N}: g^n=1 \forall g\in G\}\lbr """ | |
| ) | |
| ex_3_42_label = latex_to_graphviz_html( | |
| r"""\textbf{Ex 3.42 }(a) exp((\Z/5\Z)^{\times})=4\lbr | |
| (b) exp((\Z/8\Z)^{\times})=2\lbr""" | |
| ) | |
| prop_3_43_label = latex_to_graphviz_html( | |
| r"""\textbf{Prop 3.43 }G finite abelian group G:\lbr """ | |
| r"""(a) \exp(G) \vert\ \vert G\vert\ \lbr """ | |
| r"""(b) \exp(G)= \lcm(\{ord(g): g\in G\})\lbr""" | |
| ) | |
| def_3_44_label = latex_to_graphviz_html( | |
| r"""\textbf{Def 3.44 } homomorphism\\ isomorphism, \cong """ | |
| ) | |
| ex_3_45_label = latex_to_graphviz_html( | |
| r"""\textbf{Ex 3.45 }K field implies\lbr | |
| det:GL_n(K)\to K^{\times} homomorphism""" | |
| ) | |
| prop_3_46_label = latex_to_graphviz_html( | |
| r"""\textbf{Prop 3.46 }G, H groups, \psi: G\to\ H homomorphism:\lbr """ | |
| r"""(a) \psi \text{ injective} \iff \text{ker}(\psi):=\{g\in G: \psi(g)=1\}=\{1\}\lbr """ | |
| r"""(b) \psi \text{ isomorphism} \text{implies} \psi^{-1}: H\to G isomorphism\lbr""" | |
| ) | |
| thm_3_47_label = latex_to_graphviz_html( | |
| r"""\textbf{Thm 3.47 }For cyclic group G:\\ G \cong \begin{cases} | |
| \mathbb{Z} & \text{for }G\text{ infinite,}\\ | |
| \Z /|G|\mathbb{Z} & \text{for }G\text{ finite.} \end{cases}""" | |
| ) | |
| ex_3_48_label = latex_to_graphviz_html( | |
| r"""\textbf{Ex 3.48 } (\Z/5\Z)^{\times} \cong \Z/4\Z\\ \psi: \begin{cases} | |
| \Z/4\Z &\to\ (\Z/5\Z)^{\times}\\ | |
| a &\mapsto\ \bar{2}^a \end{cases}\lbr""" | |
| ) | |
| thm_3_49_label = latex_to_graphviz_html( | |
| r"""\textbf{Thm 3.49 }G finite abelian group: | |
| G is cyclic \iff \exp(G) = \vert G\vert""" | |
| ) | |
| dot_content = f"""digraph G {{ | |
| layout=neato; | |
| overlap="false"; | |
| sep="+15"; | |
| node [shape=box, fontsize=12, margin="0.15,0.1"]; | |
| labelloc=t | |
| label="3.3 prime residue classes and Fermat-Euler theorem (Def 3.13 — Cor 3.32)\n3.4 cyclic groups (Def 3.33 — Thm 3.49)\n\n " | |
| # def_2_1 [label={def_label}]; | |
| # ex_2_2a [label={ex_label}]; | |
| def_3_13 [label={def_3_13_label}]; | |
| ex_3_14 [label={ex_3_14_label}]; | |
| def_3_15 [label={def_3_15_label}]; | |
| ex_3_16 [label={ex_3_16_label}]; | |
| prop_3_17 [label={prop_3_17_label}]; | |
| ex_3_18 [label={ex_3_18_label}]; | |
| def_3_19 [label={def_3_19_label}]; | |
| ex_3_20 [label={ex_3_20_label}]; | |
| thm_3_21 [label={thm_3_21_label}]; | |
| prop_3_22 [label={prop_3_22_label}]; | |
| cor_3_23 [label={cor_3_23_label}]; | |
| ex_3_24 [label={ex_3_24_label}]; | |
| prop_3_25 [label={prop_3_25_label}]; | |
| ex_3_26 [label={ex_3_26_label}]; | |
| def_3_27 [label={def_3_27_label}]; | |
| ex_3_28 [label={ex_3_28_label}]; | |
| prop_3_29 [label={prop_3_29_label}]; | |
| thm_3_30 [label={thm_3_30_label}]; | |
| ex_3_31 [label={ex_3_31_label}]; | |
| cor_3_32 [label={cor_3_32_label}]; | |
| def_3_33 [label={def_3_33_label}]; | |
| rem_3_34 [label={rem_3_34_label}]; | |
| ex_3_35 [label={ex_3_35_label}]; | |
| def_3_36 [label={def_3_36_label}]; | |
| ex_3_37 [label={ex_3_37_label}]; | |
| prop_3_38 [label={prop_3_38_label}]; | |
| prop_3_39 [label={prop_3_39_label}]; | |
| cor_3_40 [label={cor_3_40_label}]; | |
| def_3_41 [label={def_3_41_label}]; | |
| ex_3_42 [label={ex_3_42_label}]; | |
| prop_3_43 [label={prop_3_43_label}]; | |
| def_3_44 [label={def_3_44_label}]; | |
| ex_3_45 [label={ex_3_45_label}]; | |
| prop_3_46 [label={prop_3_46_label}]; | |
| thm_3_47 [label={thm_3_47_label}]; | |
| ex_3_48 [label={ex_3_48_label}]; | |
| thm_3_49 [label={thm_3_49_label}]; | |
| def_3_13 -> ex_3_14 [style=dotted]; | |
| def_3_15 -> ex_3_16 [style=dotted]; | |
| {{ def_3_13 def_3_15 }} -> prop_3_17 [style=dotted]; | |
| ex_3_14 -> ex_3_16 [style=invis,arrowhead=none]; | |
| prop_3_17 -> ex_3_18 [style=dotted]; | |
| prop_3_17 -> thm_3_21; | |
| {{ ex_3_16 def_3_19 }} -> ex_3_20 [style=dotted]; | |
| ex_3_20 -> thm_3_21; | |
| prop_3_29 -> def_3_36; | |
| thm_3_21 -> prop_3_22 [style=dotted]; | |
| prop_3_22 -> cor_3_23 [style=dotted]; | |
| def_3_19 -> thm_3_21; | |
| cor_3_23 -> ex_3_24 [style=dotted]; | |
| cor_3_23 -> prop_3_25 [style=dotted]; | |
| prop_3_25 -> ex_3_26 [style=dotted]; | |
| ex_3_24 -> def_3_27 [style=invis,arrowhead=none]; | |
| prop_3_22 -> ex_3_28; | |
| def_3_27 -> ex_3_28 [style=dotted]; | |
| def_3_33 -> ex_3_35 [style=dotted]; | |
| def_3_36 -> ex_3_37 [style=dotted]; | |
| thm_3_30 -> {{ ex_3_31 cor_3_32 }}; | |
| {{ ex_3_28 prop_3_29 }} -> thm_3_30; | |
| ex_3_31 -> cor_3_32 [style=invis,arrowhead=none]; | |
| def_3_33 -> rem_3_34 [style=dotted label="https://gist.github.com/Hermann-SW/12c7644ac0c75b4eb019f76c3f023fe5 " | |
| URL="https://gist.github.com/Hermann-SW/12c7644ac0c75b4eb019f76c3f023fe5"] | |
| def_3_41 -> prop_3_43 [style=dotted]; | |
| prop_3_39 -> cor_3_40; | |
| prop_3_39 -> prop_3_43; | |
| def_3_44 -> {{ ex_3_45 prop_3_46 }} [style=dotted]; | |
| prop_3_38 -> thm_3_47; | |
| prop_3_39 -> thm_3_47; | |
| def_3_36 -> prop_3_38 [style=dotted]; | |
| prop_3_46 -> thm_3_47 [style=dotted]; | |
| prop_3_29 -> cor_3_40; | |
| def_3_41 -> ex_3_42 [style=dotted]; | |
| {{ ex_3_35 thm_3_47 }} -> ex_3_48; | |
| {{ prop_3_39 prop_3_43 }} -> thm_3_49; | |
| prop_3_38 -> thm_3_49; | |
| }}""" | |
| DOTFILENAME = "graph_unicode.dot" | |
| with open(DOTFILENAME, "w", encoding="utf-8") as f: | |
| f.write(dot_content) | |
| print("Generated .dot file:\n") | |
| print(dot_content) | |
| subprocess.run( | |
| ["dot", "-Tpdf", DOTFILENAME, "-o", "graph_output.pdf"], check=True | |
| ) |
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Added sections 3.3 “prime residue classes and Fermat-Euler theorem” and 3.4 “cyclic groups” of (German language) lecture script sitting behind Heidelberg University VPN. From definition 3.13 until theorem 3.49. More:
https://forum.graphviz.org/t/latex-labels-for-graphviz-work-in-progress/3402/3
Latest 10% screenshot below, full PDF for browser view:
https://stamm-wilbrandt.de/prime_residue_classess_and_Fermat-Euler_theorem.cyclic_groups.pdf