Mingli Yuan mountain

Reference Snapshot: Tree and Spanning-Tree Foundations for Euler’s Formula in set.mm

Working snapshot of the Phase I graph-theory development toward a formal proof of Euler’s formula in set.mm.

It contains the complete mathbox implementation of finite tree and spanning-tree theory, together with an integration diff showing the required prerequisite promotions. These files are provided as reference material for the planned upstream PR series, not as a single patch intended for review or merge.

Gist

Package

\usepackage{tkz-euclide} % checked for version 3.02c

Point definitions

Keybase proof

I hereby claim:

I am mountain on github.
I am mingliyuan (https://keybase.io/mingliyuan) on keybase.
I have a public key whose fingerprint is ED86 CD82 A682 45D7 5CC5 2C3E 6EFF 88CB 304F 50A2

To claim this, I am signing this object:

Keybase proof

I hereby claim:

I am mountain on github.
I am mingliyuan (https://keybase.io/mingliyuan) on keybase.
I have a public key whose fingerprint is ED86 CD82 A682 45D7 5CC5 2C3E 6EFF 88CB 304F 50A2

To claim this, I am signing this object:

	import fitz # PyMuPDF
	import cv2
	import numpy as np
	import os
	from tqdm import tqdm


	class HighQualityMRCConverter:
	def __init__(self, input_path, output_path, quality=60, downsample=2, dpi=300):
	"""

	"""
	This is a demo script to debug prompts

	Example

	艾达：你好，我是艾达，竭诚为您服务？有什么可以帮到你的吗？
	麦克：我们可以一起玩个游戏吗？
	艾达：当然可以！你有什么喜欢的游戏？
	麦克：猜谜语？
	艾达：好的，那我们就开始吧！第一个谜语是：“我有四个脚，但不能走路，我会在水里游来游去，你知道我是什么吗？”

	import cv2
	import numpy as np


	# constructing an image with a frame in the center
	img = np.zeros([255, 255], dtype=np.int)
	img[64:192, 64] = np.ones([128], dtype=np.int) * 255
	img[64:192, 192] = np.ones([128], dtype=np.int) * 255
	img[64, 64:192] = np.ones([128], dtype=np.int) * 255
	img[192, 64:192] = np.ones([128], dtype=np.int) * 255

	DIRECTION=$1
	SOURCE=$2

	if test -f $HOME/.xiaoyi ; then
	. $HOME/.xiaoyi
	else
	echo "Please input ip of your node: "
	read NODEIP
	echo "NODEIP=$NODEIP" > $HOME/.xiaoyi
	fi

	# -- coding: utf-8 --

	'''
	This simple program is used to search for crossword sentences in selected Chinese poetries

	The selected Chinese poetries here is stored in a text file - tang_poetry_5char.txt.
	You can change to your version of candidates

	You should install networkx by pip

	# -- coding: utf-8 --

	import numpy as np
	import sys
	import keras

	from keras.layers import Input, Dense
	from keras.models import Model