dmishin’s gists

dmishin / rosier_q

Created March 27, 2025 23:40

Implementation of "Rosier Q function", supports all rationals with odd denominator

	from fractions import Fraction
	from typing import List, Union, Tuple
	def _orbit(x:Fraction)->Tuple[List[int], List[int]]:
	"""Returns Collatz orbit of x, as a tuple of two lists: initial path and cycle. Assumes the cycle is always reached."""
	if x == 0: return [],[0]
	if x.denominator%2 == 0: raise ValueError("2-adically fractional values are not allowed")
	visited = {x}
	orbit = [x]
	while True:
	if x.numerator % 2 == 0:

dmishin / rational_in_range.py

Created March 26, 2025 23:51

Calculate the simplest rational number between log_2(3) and log_2(3)-1/2^{70}

	import mpmath
	from typing import Tuple
	def simplest_rational_in_range(a:mpmath.mpf, b:mpmath.mpf)->Tuple[int,int]:
	#take integer part of both numbers
	d1 = int(mpmath.floor(a))
	d2 = int(mpmath.floor(b))
	if d1 != d2:
	assert d1 < d2
	return d1+1, 1
	#take fractional part of both numbers

dmishin / naive_collatz_checker.py

Created May 19, 2024 19:57

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dmishin / l1_gravity_planet.py

Created April 2, 2024 00:11

Planet shape in L1 gravity, 2D case

	import numpy as np

	N = 300 #size of the grid
	M = 20000 #number of pixels

	potential = np.zeros((N, N), dtype=np.float64)
	masses = np.zeros((N, N), dtype=np.bool8)
	def potential_of_mass_at(i, j):
	"""Returns L1 potential of a mass at (i, j) with mass m
	potential is calcualted as:

dmishin / tsp_conjecture_counterexample.py

Created November 11, 2023 23:51

Use linear programming to find counterexample for a conjecture regarding the Traveling Salesman Problem

	from scipy.optimize import linprog
	import numpy as np
	import itertools

	#Searching for the counterexample for the following conjecture:
	# in the shortest hamiltonian path, there is at least one
	# node, connected to its 12 nearest neighbors
	# https://www.reddit.com/r/math/comments/17rxc28/travelling_salesman_algorithm/

	# Use linear programming to find a counterexample

dmishin / grotsen_iterates.py

Created June 28, 2023 21:05

Calculating and plotting smooth fractional iterates of 1-sqrt(1-x^2)

	"""Calculate smooth iterates of the function

	f:[0,1]->[0,1]
	f(x) = 1-sqrt(1-x^2)

	https://mathoverflow.net/questions/449748/what-are-the-iterates-of-x-mapsto-1-sqrt1-x2
	https://twitter.com/gro_tsen/status/1674132770203881477

dmishin / thue_morse_hilbert_fft.py

Created October 27, 2022 11:43

Visualize Fourier transform of the Thue-Morse sequence arranged along the Hilbert curve

	import numpy as np
	from matplotlib import pyplot as plt
	import scipy

	def ht(n:int)->np.array:
	"""Generates Thue-Morse sequence, arranged along the Hilbert curve of order N. Result is (2n, 2n) matrix"""
	if n < 0: raise ValueError("Bad order")
	if n == 0:
	return np.array([[1]], dtype=np.int8)
	else:

dmishin / addon_grow_table_crash.js

Created April 15, 2021 18:08

	$("#run").click(() => tryCatch(run));

	async function run() {
	Excel.run(async function (context) {

	var sctivesheet = context.workbook.worksheets.getActiveWorksheet();
	var table = sctivesheet.tables.add(sctivesheet.getRangeByIndexes(0, 0, 1, 2), true);
	var data = [[1, "A"], [2, "B"], [3, "C"]];
	table.rows.add(0, data);

dmishin / check_invfib_sum.py

Created April 22, 2020 09:35

Numerically checking surprising identities regarding the sums involving Fibonacci numbers

	#%metadata%
	#url: https://twitter.com/diegorattaggi/status/1252654580720119810/photo/1
	from sympy import *

	mfib = Matrix([[0,1],[1,1]])
	fib0 = Matrix([0,1])
	luc0 = Matrix([2,1])
	eye = Matrix([[1,0],[0,1]])

	def fibo(n):

dmishin / schreiber.py

Created November 18, 2019 11:22

Detect optimal step for minimal order Schreiber test signal

	import numpy as np
	import scipy as sp
	import scipy.linalg
	from math import floor, pi

	#Detect optimal step for minimal order Schreiber test signal

	#Set to False to disable printing
	_verbose = True

Dmitry dmishin