gagern

from collections import deque
from itertools import chain

# Counting the number of ways how a 4×N rectangle can be filled with terominoes,
# counting symmetric versions of the same tiling only once.
#
# https://math.stackexchange.com/a/4976754/35416
# Martin von Gagern

# We store tiles and unfinished rows as the bits of a single number:

gagern

https://math.stackexchange.com/a/4493218/35416

For each of the 52 incidences (columns), this table
shows the line coordinates, point coordinates, and
352 different suite assignments. The first 8 of
these have a 13-fold symmetry, the others don't.

0000000000000000111111111111111111112222222222222222
0000111111112222000000001111111122220000111111112222
1111000011111111000011110000111111111111000011111111

gagern

https://math.stackexchange.com/q/4141558/35416

0 = (-d + R)*a^2
  + (-2*L)*a
  + (-d + R)

or

0 = (-c + L)*a^2
  + (-c - L)

gagern

https://math.stackexchange.com/a/4134048/35416

0 = (4*h^2 - 8*h*R + 4*R^2)*N^4
  + (-4*b^2*h - 4*e^2*h + 4*f^2*h - 12*h^3 + 4*b^2*R + 4*e^2*R - 4*f^2*R + 36*h^2*R - 40*h*R^2 + 16*R^3)*N^3
  + (b^4 + 2*b^2*e^2 + e^4 + 2*b^2*f^2 - 2*e^2*f^2 + f^4 + 16*b*e*f*h + 10*b^2*h^2 + 14*e^2*h^2 - 10*f^2*h^2 + 13*h^4 - 16*b*e*f*R - 20*b^2*h*R - 28*e^2*h*R + 20*f^2*h*R - 52*h^3*R + 8*b^2*R^2 + 16*e^2*R^2 - 12*f^2*R^2 + 88*h^2*R^2 - 72*h*R^3 + 24*R^4)*N^2
  + (-8*b*e^3*f - 2*b^4*h - 6*e^4*h - 4*b^2*f^2*h - 2*f^4*h - 24*b*e*f*h^2 - 8*b^2*h^3 - 12*e^2*h^3 + 8*f^2*h^3 - 6*h^5 + 2*b^4*R + 6*e^4*R + 4*b^2*f^2*R + 2*f^4*R + 48*b*e*f*h*R + 24*b^2*h^2*R + 36*e^2*h^2*R - 24*f^2*h^2*R + 30*h^4*R - 24*b*e*f*R^2 - 20*b^2*h*R^2 - 44*e^2*h*R^2 + 28*f^2*h*R^2 - 68*h^3*R^2 + 4*b^2*R^3 + 20*e^2*R^3 - 12*f^2*R^3 + 84*h^2*R^3 - 56*h*R^4 + 16*R^5)*N
  + (b^4*e^2 - 2*b^2*e^4 + e^6 + 2*b^2*e^2*f^2 + 2*e^4*f^2 + e^2*f^4 + 8*b*e^3*f*h + b^4*h^2 + 3*e^4*h^2 + 2*b^2*f^2*h^2 + f^4*h^2 + 8*b*e*f*h^3 + 2*b^2*h^4 + 3*e^2*h^4 - 2*f^2*h^4 + h^6 - 8*b*e^3

gagern

gagern

<p>Original problem:</p>

<ol>
<li><p>First item.</p></li>
<li><pre><code>Some code.
More code.
</code></pre>

<p>There is code here.</p></li>
</ol>

gagern

#!/usr/bin/python3

# https://github.com/shainer/spinning-switches citing a problem from
# “So you think you've got problems?” by Alex Bellos.
# This is optimizing for minimum number of operations in the worst case.

def allrot(x):
  return [((x << i) | (x >> (4 - i))) & 0b1111 for i in range(4)]

def normal(x):

gagern

 dpkg-buildpackage -us -uc -ui -i -b
dpkg-buildpackage: info: source package sagemath
dpkg-buildpackage: info: source version 8.8-1~mvg1
dpkg-buildpackage: info: source distribution unstable
dpkg-buildpackage: info: source changed by Martin von Gagern <Martin.vGagern@gmx.net>
 dpkg-source -i --before-build .
dpkg-buildpackage: info: host architecture amd64
dpkg-source: info: using options from sagemath/debian/source/options: --tar-ignore=debian/ccache --extend-diff-ignore=^(sage/m4/sage_spkg_configures.m4)
 debian/rules clean
dh clean --with=python2,sphinxdoc

gagern

// Numeric experiment for https://math.stackexchange.com/q/2434673/35416

#include <cmath>
#include <random>
#include <iostream>
#include <iomanip>

// Barycentric coordinates
struct vec {
  double c[3];

gagern

/*
 * Copyright 2013 Martin von Gagern
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software