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-- Chocolate Bar Theorem 🍫, as illustrated in https://www.instagram.com/p/CzGr1yfAHFB/
-- Credits: https://leanprover.zulipchat.com/#narrow/stream/113489-new-members/topic/Formulating.20the.20chocolate.20bar.20theorem
-- Run on https://live.lean-lang.org/

import Mathlib.Data.Nat.Basic


inductive ChocoTablet : Nat -> Nat -> Type where
  | square : ChocoTablet 1 1
  | hJoin {a b b' : Nat} : ChocoTablet a b -> ChocoTablet a b' -> ChocoTablet a (b + b')

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from automathon import DFA
from collections import defaultdict
from itertools import zip_longest
from math import floor
from random import randint

# See https://www21.in.tum.de/teaching/sar/SS20/9.pdf

def ineq_to_dfa(A: list[int], b: int) -> DFA:
    n = len(A)

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from typing import Iterator


HereditaryRepresentation = list[tuple[int, "HereditaryRepresentation"]]

def to_base(n: int, base: int, prefix: bool = False) -> list[int]:
    """
    Computes the representation of n in the specified base.
    """
    if n == 0:

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// See lipsum.dev

import React, { useEffect, useRef, useState } from "react";

const L = 8;

function baseFunc(u, v) {
    return (x, y) =>
        Math.cos(((2 * x + 1) * u * Math.PI) / 16) *
        Math.cos(((2 * y + 1) * v * Math.PI) / 16);

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# See https://mitpress.mit.edu/9780262046305/introduction-to-algorithms/, chapter 30
# /!\ Do not use it in production /!\

from math import e, pi

import numpy as np
from numpy.testing import assert_array_equal


def fft(L, sign=-1):

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# Part of https://lipsum.dev/2021-06-1-miller-rabin-openssl/
# /!\ Warning /!\ — Not safe for real cryptographic usage

from collections import Counter
from random import randrange
import statistics

# Fermat

def fermat_test(n, max_witness=100):

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// RotatingCube React component, used in https://lipsum.dev/2020-09-1-rotations/
import * as BABYLON from 'babylonjs'
import * as GUI from 'babylonjs-gui'
import React, { useEffect, useRef, useState } from 'react'

const canvasWidth = 500;
const canvasHeight = 300;

function initScene(canvas, rotationCb) {
    const engine = new BABYLON.Engine(canvas);

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# See https://lipsum.dev/2020-05-1-pourquoi-les-polynomes/

from numbers import Number

class Polynomial:
    def __init__(self, *coefficients):
        self.degree = -1
        self.coefficients = tuple(coefficients)
        for i, coef in enumerate(self.coefficients):
            if coef != 0:

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from num2words import num2words


def money_amount_words(amount, units='euros', cents='centimes', lang='fr'):
    """
    Returns an iterator over the words describing the given amount

    Args:
        amount: decimal.Decimal, the amount of money
        units: str, the currency units