chore: SAVEPOINT
This commit is contained in:
@@ -1,3 +1,6 @@
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[submodule "ams-latex-template"]
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path = ams-latex-template
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url = ssh://git@gitea.dideric.is/didericis/ams-latex-template.git
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[submodule "plantri"]
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path = plantri
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url = https://github.com/mishun/plantri
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@@ -26,23 +26,55 @@ This creates a new directory (name derived from the title) containing a `paper.t
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## Setup
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The Python library code in `lib/` requires SageMath. To set up the linting environment, run:
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The Python library code in `lib/` requires SageMath. Run setup once per machine:
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```sh
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./run.sh setup
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./run.sh setup <sage_python_path> <sage_site_packages> [system_name]
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```
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This creates a `.venv` using the SageMath Python interpreter and installs `pylint` into it.
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- `sage_python_path` — path to the SageMath Python interpreter (e.g. `/opt/sage/local/bin/python3`)
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- `sage_site_packages` — path to SageMath's site-packages directory
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- `system_name` — optional label for this machine (defaults to `hostname -s`); used to store per-machine env files as `.env.<system_name>`
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On subsequent runs the paths default to whatever was saved in `.env`, so `./run.sh setup` alone re-runs setup with the existing configuration.
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Setup also compiles the [plantri](https://github.com/mishun/plantri) submodule via `make`.
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## Running Sage
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To run a Sage script with `plantri` available on `PATH`:
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```sh
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./run.sh sage <script.py> [args...]
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```
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Or to open an interactive Sage session:
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```sh
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./run.sh sage
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```
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## Linting
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To lint the `lib/` directory:
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```sh
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./run.sh lint
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```
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This runs `pyright` (via `npx`) and `pylint` using the SageMath Python interpreter.
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Runs `pyright` and `pylint` on `lib/` using the SageMath Python interpreter.
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## Shell Completion
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To enable tab-completion for `run.sh` in zsh, add this to your `.zshrc`:
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```sh
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eval "$(path/to/run.sh completion)"
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```
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Or source it once in the current shell session:
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```sh
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eval "$(./run.sh completion)"
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```
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## Building
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@@ -0,0 +1,93 @@
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from sage.all import graphs, Graph
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from collections import defaultdict
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from pathlib import Path
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import base64
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DIR = Path(__file__).parent
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PALETTE = ['red', 'blue', 'green', 'yellow']
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def plot_colored(g, coloring, title, filename):
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g.is_planar(set_embedding=True, set_pos=True)
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vertex_colors = defaultdict(list)
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for v, c in coloring.items():
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vertex_colors[PALETTE[c]].append(v)
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label = base64.urlsafe_b64encode(g.canonical_label().graph6_string().encode()).decode()
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out_dir = DIR / "data" / label
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out_dir.mkdir(exist_ok=True)
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g.plot(vertex_colors=dict(vertex_colors), title=title).save(out_dir / filename)
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def pluck(G: Graph, coloring, v0, kind, step=1):
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# Contract v1 and v2 into v0 to obtain the minor G'.
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# merge_vertices([v0, v1, v2]) folds v1 and v2 into v0.
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G_prime = G.copy()
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G_prime.delete_vertex(v0)
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coloring_prime = coloring.copy()
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del coloring_prime[v0]
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print(f"\nG' (after reduction): {G_prime.order()} vertices, {G_prime.size()} edges")
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# Plot before and after side by side.
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plot_colored(G_prime, coloring_prime, f"G' (after pluck for v0={v0})", f"step_{step:04d}_({kind}).png")
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return reduce(G_prime, coloring_prime, step+1)
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def squish(G: Graph, coloring, v0, kind, step=1):
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# Among v0's neighbors, find two with the same color (v1 and v2).
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neighbor_by_color = defaultdict(list)
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for v in G.neighbors(v0):
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neighbor_by_color[coloring[v]].append(v)
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v1, v2 = next(
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(vs[0], vs[1]) for vs in neighbor_by_color.values() if len(vs) >= 2
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)
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print(f"Shared-color neighbors: v1 = {v1}, v2 = {v2} (color {coloring[v1]})")
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# Contract v1 and v2 into v0 to obtain the minor G'.
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# merge_vertices([v0, v1, v2]) folds v1 and v2 into v0.
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G_prime = G.copy()
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G_prime.merge_vertices([v0, v1, v2])
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coloring_prime = {v: c for v, c in coloring.items() if v not in (v1, v2)}
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coloring_prime[v0] = coloring[v1]
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print(f"\nG' (after reduction): {G_prime.order()} vertices, {G_prime.size()} edges")
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# Plot before and after side by side.
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plot_colored(G_prime, coloring_prime, f"G' (after squish for v0={v0}, v1={v1}, v2={v2})", f"step_{step:04d}_({kind}).png")
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return reduce(G_prime, coloring_prime, step+1)
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def reduce(G, coloring, step=1):
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# 2. Find a proper 4-coloring.
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# G.coloring() returns a partition of vertices into color classes.
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# By pigeonhole (5 neighbors, at most 3 available colors for each
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# degree-5 vertex), the reduction step below always succeeds.
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print(f"Coloring: {coloring}")
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degree_4_candidates = []
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degree_5_candidates = []
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# Pick the first degree 5 vertex where the neighbors form a wheel
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for v in G.vertices():
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if G.degree(v) == 3 and G.subgraph(G.neighbors(v)).is_cycle():
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return pluck(G, coloring, v, 'triangle', step)
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elif G.degree(v) == 4 and G.subgraph(G.neighbors(v)).is_cycle():
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degree_4_candidates.append(v)
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elif G.degree(v) == 5 and G.subgraph(G.neighbors(v)).is_cycle():
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degree_5_candidates.append(v)
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for v in degree_4_candidates:
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return squish(G, coloring, v, 'square', step)
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for v in degree_5_candidates:
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return squish(G, coloring, v, 'triangle', step)
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print("DONE")
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return
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# 1. Generate a maximal planar graph (triangulation) on 14 vertices
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# with minimum degree 5, via plantri.
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G = next(graphs.planar_graphs(20, minimum_degree=5))
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print(f"G: {G.order()} vertices, {G.size()} edges")
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print(f"Degree sequence: {sorted(G.degree_sequence(), reverse=True)}")
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coloring_classes = G.coloring()
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coloring = {v: i for i, cls in enumerate(coloring_classes) for v in cls}
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plot_colored(G, coloring, "Start", f"step_{0:04d}.png")
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reduce(G, coloring)
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@@ -0,0 +1,8 @@
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\relax
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\newlabel{tocindent-1}{0pt}
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\newlabel{tocindent0}{0pt}
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\newlabel{tocindent1}{17.77782pt}
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\newlabel{tocindent2}{0pt}
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\newlabel{tocindent3}{0pt}
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\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Definitions}}{1}{}\protected@file@percent }
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\gdef \@abspage@last{1}
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@@ -0,0 +1,55 @@
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# Fdb version 3
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(generated)
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"paper.aux"
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"paper.log"
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"paper.pdf"
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@@ -0,0 +1,160 @@
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PWD /Users/didericis/Code/math-research/colored_pentagon_reduction
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INPUT /usr/local/texlive/2022/texmf.cnf
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INPUT /usr/local/texlive/2022/texmf-dist/web2c/texmf.cnf
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INPUT /Users/didericis/Code/math-research/colored_pentagon_reduction/paper.tex
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OUTPUT paper.log
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INPUT /usr/local/texlive/2022/texmf-dist/tex/latex/amscls/amsart.cls
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</usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmcsc10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi7.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti8.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb>
|
||||
Output written on paper.pdf (1 page, 148889 bytes).
|
||||
PDF statistics:
|
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73 PDF objects out of 1000 (max. 8388607)
|
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43 compressed objects within 1 object stream
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|
||||
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@@ -0,0 +1,114 @@
|
||||
%% filename: amsart-template.tex
|
||||
%% version: 1.1
|
||||
%% date: 2014/07/24
|
||||
%%
|
||||
%% American Mathematical Society
|
||||
%% Technical Support
|
||||
%% Publications Technical Group
|
||||
%% 201 Charles Street
|
||||
%% Providence, RI 02904
|
||||
%% USA
|
||||
%% tel: (401) 455-4080
|
||||
%% (800) 321-4267 (USA and Canada only)
|
||||
%% fax: (401) 331-3842
|
||||
%% email: tech-support@ams.org
|
||||
%%
|
||||
%% Copyright 2008-2010, 2014 American Mathematical Society.
|
||||
%%
|
||||
%% This work may be distributed and/or modified under the
|
||||
%% conditions of the LaTeX Project Public License, either version 1.3c
|
||||
%% of this license or (at your option) any later version.
|
||||
%% The latest version of this license is in
|
||||
%% http://www.latex-project.org/lppl.txt
|
||||
%% and version 1.3c or later is part of all distributions of LaTeX
|
||||
%% version 2005/12/01 or later.
|
||||
%%
|
||||
%% This work has the LPPL maintenance status `maintained'.
|
||||
%%
|
||||
%% The Current Maintainer of this work is the American Mathematical
|
||||
%% Society.
|
||||
%%
|
||||
%% ====================================================================
|
||||
|
||||
% AMS-LaTeX v.2 template for use with amsart
|
||||
%
|
||||
% Remove any commented or uncommented macros you do not use.
|
||||
|
||||
\documentclass{amsart}
|
||||
|
||||
\newtheorem{theorem}{Theorem}[section]
|
||||
\newtheorem{lemma}[theorem]{Lemma}
|
||||
|
||||
\theoremstyle{definition}
|
||||
\newtheorem{definition}[theorem]{Definition}
|
||||
\newtheorem{example}[theorem]{Example}
|
||||
\newtheorem{xca}[theorem]{Exercise}
|
||||
|
||||
\theoremstyle{remark}
|
||||
\newtheorem{remark}[theorem]{Remark}
|
||||
|
||||
\numberwithin{equation}{section}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\title{Colored Pentagon Reductions}
|
||||
|
||||
% Remove any unused author tags.
|
||||
|
||||
% author one information
|
||||
\author{Eric Bauerfeld}
|
||||
\address{}
|
||||
\curraddr{}
|
||||
\email{}
|
||||
\thanks{}
|
||||
|
||||
|
||||
\subjclass[2010]{Primary }
|
||||
|
||||
\keywords{}
|
||||
|
||||
\date{}
|
||||
|
||||
\dedicatory{}
|
||||
|
||||
\begin{abstract}
|
||||
We investigate specific types of minors we can obtain by a sequence of contractions of two incident to a sequence of vertices of degree 5 relative to a proper coloring.
|
||||
\end{abstract}
|
||||
|
||||
\maketitle
|
||||
|
||||
\section{Definitions}
|
||||
|
||||
\begin{definition}
|
||||
Let $G$ be a maximal planar graph with a proper 4-coloring $c : V(G) \to \{1,2,3,4\}$. A \emph{colored pentagon reduction} is a function
|
||||
\[
|
||||
R : (G, c, v_0, v_1, v_2) \mapsto G / \{v_1 v_0,\, v_2 v_0\}
|
||||
\]
|
||||
where $v_0 \in V(G)$ has degree 5, $v_1$ and $v_2$ are adjacent vertices satisfying $c(v_1) = c(v_2)$, and $G / \{v_1 v_0,\, v_2 v_0\}$ denotes the minor obtained by contracting $v_1$ and $v_2$ each into $v_0$.
|
||||
\end{definition}
|
||||
|
||||
\begin{lemma}
|
||||
If $G' = R(G, c, v_0, v_1, v_2)$, then $G'$ has a proper 4-coloring.
|
||||
\end{lemma}
|
||||
|
||||
\begin{proof}
|
||||
The idea is to recolor $v_0$ with the shared color of $v_1$ and $v_2$, and check that this creates no new conflicts.
|
||||
|
||||
Let $\alpha = c(v_1) = c(v_2)$ and define $c' : V(G') \to \{1,2,3,4\}$ by
|
||||
\[
|
||||
c'(v) = \begin{cases} \alpha & \text{if } v = v_0, \\ c(v) & \text{otherwise.} \end{cases}
|
||||
\]
|
||||
Every edge of $G'$ not incident to $v_0$ is an edge of $G$ between vertices outside $\{v_1, v_2\}$, so those edges are still properly colored. It remains to check edges $v_0 w$ in $G'$, i.e., that no neighbor of $v_0$ in $G'$ also has color $\alpha$.
|
||||
|
||||
Since $c(v_1) = c(v_2)$ and $c$ is proper, $v_1$ and $v_2$ cannot be adjacent in $G$, so they are non-adjacent in the 5-cycle induced by $N_G(v_0)$ (which exists because $G$ is maximal planar). One can check that in any 5-cycle, two non-adjacent vertices together cover every other vertex --- that is, every remaining vertex is adjacent to at least one of them. Therefore every $w \in N_G(v_0) \setminus \{v_1, v_2\}$ is adjacent in $G$ to $v_1$ or $v_2$, so $c(w) \neq \alpha = c'(v_0)$.
|
||||
|
||||
For new neighbors of $v_0$ coming from the contraction, namely $w \in (N_G(v_1) \cup N_G(v_2)) \setminus \{v_0, v_1, v_2\}$, we get $c(w) \neq \alpha = c'(v_0)$ for free since $c$ is proper on $G$.
|
||||
|
||||
Hence $c'$ is a proper 4-coloring of $G'$.
|
||||
\end{proof}
|
||||
|
||||
\end{document}
|
||||
|
||||
%-----------------------------------------------------------------------
|
||||
% End of amsart-template.tex
|
||||
%-----------------------------------------------------------------------
|
||||
Submodule
+1
Submodule plantri added at 09745aeb09
@@ -14,6 +14,10 @@ init_paper() {
|
||||
local name
|
||||
name="$(printf '%s' "$raw" | tr '[:upper:]' '[:lower:]' | tr -d '\\' | tr '[:space:]' '_')"
|
||||
local dest="$SCRIPT_DIR/$name"
|
||||
if [ -d "$dest" ]; then
|
||||
echo "Error: '$dest' already exists" >&2
|
||||
exit 1
|
||||
fi
|
||||
mkdir -p "$dest"
|
||||
cp "$SCRIPT_DIR/ams-latex-template/doc/amsart-template.tex" "$dest/paper.tex"
|
||||
sed -i '' "s|\\\\title{}|\\\\title{$raw}|" "$dest/paper.tex"
|
||||
@@ -23,20 +27,20 @@ init_paper() {
|
||||
}
|
||||
|
||||
setup() {
|
||||
local python_path="${1:?Usage: setup <python_path> <sage_site_packages> <system_name>}"
|
||||
local sage_site_packages="${2:?Usage: setup <python_path> <sage_site_packages> <system_name>}"
|
||||
local system_name="${3:?Usage: setup <python_path> <sage_site_packages> <system_name>}"
|
||||
local sage_python_path="${1:-${SAGE_PYTHON_PATH:?Usage: setup <sage_python_path> <sage_site_packages> <system_name>}}"
|
||||
local sage_site_packages="${2:-${SAGE_SITE_PACKAGES:?Usage: setup <sage_python_path> <sage_site_packages> <system_name>}}"
|
||||
local system_name="${3:-$(hostname -s)}"
|
||||
|
||||
printf 'SAGE_PYTHON_PATH=%s\nSAGE_SITE_PACKAGES=%s\n' "$python_path" "$sage_site_packages" \
|
||||
printf 'SAGE_PYTHON_PATH=%s\nSAGE_SITE_PACKAGES=%s\n' "$sage_python_path" "$sage_site_packages" \
|
||||
>"$SCRIPT_DIR/.env.$system_name"
|
||||
ln -sf ".env.$system_name" "$SCRIPT_DIR/.env"
|
||||
source "$SCRIPT_DIR/.env"
|
||||
|
||||
mkdir -p "$SCRIPT_DIR/.vscode"
|
||||
"$python_path" - <<EOF
|
||||
"$sage_python_path" - <<EOF
|
||||
import json
|
||||
settings = {
|
||||
"python.defaultInterpreterPath": "$python_path",
|
||||
"python.defaultInterpreterPath": "$sage_python_path",
|
||||
"python.analysis.extraPaths": ["$sage_site_packages"],
|
||||
"python.analysis.diagnosticSeverityOverrides": {
|
||||
"reportUnknownMemberType": "warning",
|
||||
@@ -51,10 +55,16 @@ with open("$SCRIPT_DIR/.vscode/settings.json", "w") as f:
|
||||
f.write("\n")
|
||||
EOF
|
||||
|
||||
"$python_path" -m venv "$SCRIPT_DIR/.venv"
|
||||
make -C "$SCRIPT_DIR/plantri"
|
||||
|
||||
"$sage_python_path" -m venv "$SCRIPT_DIR/.venv"
|
||||
"$VENV_PYTHON" -m pip install -r "$SCRIPT_DIR/requirements.txt"
|
||||
}
|
||||
|
||||
run_sage() {
|
||||
PATH="$PATH:$SCRIPT_DIR/plantri" sage "$@"
|
||||
}
|
||||
|
||||
lint() {
|
||||
"$VENV_PYTHON" -m pyright lib/ --pythonpath "$SAGE_PYTHON_PATH"
|
||||
"$VENV_PYTHON" -m pylint lib/ \
|
||||
@@ -62,6 +72,63 @@ lint() {
|
||||
--disable=fixme
|
||||
}
|
||||
|
||||
completion() {
|
||||
local shell="${1:-zsh}"
|
||||
case "$shell" in
|
||||
zsh)
|
||||
cat <<'EOF'
|
||||
_run_sh() {
|
||||
local curcontext="$curcontext" state line
|
||||
typeset -A opt_args
|
||||
|
||||
_arguments -C \
|
||||
'1: :->subcmd' \
|
||||
'*: :->args'
|
||||
|
||||
case $state in
|
||||
subcmd)
|
||||
local subcmds=(
|
||||
'init_paper:Initialize a new paper directory from the AMS template'
|
||||
'setup:Configure Python/Sage environment and install dependencies'
|
||||
'sage:Run sage with plantri available on PATH'
|
||||
'lint:Run pyright and pylint on lib/'
|
||||
'completion:Output shell completion code'
|
||||
)
|
||||
_describe 'subcommand' subcmds
|
||||
;;
|
||||
args)
|
||||
case $words[2] in
|
||||
init_paper)
|
||||
_message 'paper title (spaces become underscores)'
|
||||
;;
|
||||
setup)
|
||||
case $((CURRENT - 2)) in
|
||||
1) _files ;;
|
||||
2) _files -/ ;;
|
||||
3) _message 'system name (e.g. macbook, workstation)' ;;
|
||||
esac
|
||||
;;
|
||||
sage)
|
||||
_files
|
||||
;;
|
||||
completion)
|
||||
_values 'shell' 'zsh'
|
||||
;;
|
||||
esac
|
||||
;;
|
||||
esac
|
||||
}
|
||||
|
||||
compdef _run_sh run.sh
|
||||
EOF
|
||||
;;
|
||||
*)
|
||||
echo "Unsupported shell: $shell. Supported: zsh" >&2
|
||||
exit 1
|
||||
;;
|
||||
esac
|
||||
}
|
||||
|
||||
case "${1:-}" in
|
||||
init_paper)
|
||||
shift
|
||||
@@ -71,11 +138,19 @@ setup)
|
||||
shift
|
||||
setup "$@"
|
||||
;;
|
||||
sage)
|
||||
shift
|
||||
run_sage "$@"
|
||||
;;
|
||||
lint)
|
||||
lint
|
||||
;;
|
||||
completion)
|
||||
shift
|
||||
completion "$@"
|
||||
;;
|
||||
*)
|
||||
echo "Usage: $0 {init_paper|setup|lint} [args]" >&2
|
||||
echo "Usage: $0 {init_paper|setup|sage|lint|completion} [args]" >&2
|
||||
exit 1
|
||||
;;
|
||||
esac
|
||||
|
||||
Reference in New Issue
Block a user