pjt33’s gists

pjt33 / MO456035.py

Created October 13, 2023 18:04

For which set A, Alice has a winning strategy?

	#!/usr/bin/pypy3

	from functools import lru_cache

	# Limit memory usage to 8GB
	import resource
	resource.setrlimit(resource.RLIMIT_AS, (8 * 1024*3, 8 1024**3))


	"""

pjt33 / orbifold.py

Created March 30, 2023 14:37

MO442252: enumeration of Deligne-Mostow lattices

	#!/usr/bin/pypy3

	"""
	Ethan Dlugie asked [1] "How do we know there are no more Deligne-Mostow/Thurston lattices?"
	than the 94 enumerated by Thurston [3]. This program combines case analysis with exhaustive search
	to show that the list is in fact complete.

	There is a subtle difference between Thurston's claim (Theorem 0.2) and Mostow's ΣINT condition [2]:
	Mostow only allows one set of equal angles to give half-integer reciprocals (condition (c) below),
	whereas Thurston allows multiple sets. This code uses Thurston's condition, as more straightforward,

pjt33 / MO442038.log

Created March 3, 2023 22:34

MO 442038

pjt33 / MO438701.sage

Created January 17, 2023 22:18

CAS-assisted proof of Tito Pieza's conjecture re Emma Lehmer's quintic

	R.<n> = PolynomialRing(QQ)

	def p(x):
	return x^5 + n^2x^4 - (2n^3 + 6n^2 + 10n + 10)x^3 + (n^4 + 5n^3 + 11n^2 + 15n + 5)x^2 + (n^3 + 4n^2 + 10n + 10)x + 1

	def s(x):
	return (n + 2 + nx - xx) / (1 + 2x + nx)

	R2.<xtmp> = PolynomialRing(FractionField(R))
	R3.<x1> = R2.quotient(p(xtmp))

pjt33 / MO419698.py

Created April 6, 2022 21:35

MO419698

	"""
	Identify and count (by size) the subsets with odd beta_n using MacMahon's inclusion-exclusion formula for beta_n
	as presented in theorem 2.3 of https://arxiv.org/pdf/1710.11033.pdf
	"""

	def bit_subsets_of(bitmask):
	# Nice bit hack from Thomas Beuman
	current = bitmask
	yield current
	while current:

pjt33 / A074881.py

Last active February 22, 2022 19:09

B-file for A074881

	from collections import Counter
	from math import gcd


	def phi(n):
	# Not exactly over-optimised...
	rv = 1
	for p in range(2, n + 1):
	if n == 1:
	break

pjt33 / MO405736.py

Last active October 20, 2021 22:37

Counting Dynkin systems

	def extend_closure(omega, included, extension, excluded):
	# We start with a closure which we want to extend
	closure = set(included)

	# Use a queue
	q = set([extension])
	while q:
	x = next(iter(q))
	q.remove(x)
	closure.add(x)

pjt33 / MO405101.sage

Created October 6, 2021 19:07

MO405101: lines through (c^m, c^n)

	from collections import defaultdict
	from itertools import combinations
	from sage.rings.polynomial.real_roots import real_roots

	R.<alpha, x, y> = PolynomialRing(QQ, order='lex')
	S.<z> = PolynomialRing(QQ)

	def P(n, p, q):
	return ((1 - x^p) + alpha * (x^n - x^q)) // (1 - x^gcd(p, abs(n-q)))

pjt33 / MO404760.py

Last active October 4, 2021 12:37

Interpolating integer polynomials with small coefficients

	#!/usr/bin/pypy3

	from heapq import heappush, heappop

	def mod_inv(a: int, m: int) -> int:
	lastremainder, remainder = a % m, m
	x, lastx, y, lasty = 0, 1, 1, 0
	while remainder:
	lastremainder, (quotient, remainder) = remainder, divmod(lastremainder, remainder)
	x, lastx = lastx - quotient*x, x

pjt33 / Permutations.txt

Created September 7, 2021 11:19

MO403263