tkmharris

def hurwitz_radon(n):
    '''Takes a positve integer n; returns the Hurwitz-Radon number p(n).
    p(n) defined as follows:
    Let n = (2^v)m with m odd and write v = 4a + b, 0<= b < 4.
    Then p(n) = 8a + 2^b.'''
    if not isinstance(n, int):
        raise TypeError("hurwitz_radon only defined for positive integers")
    if n <= 0:
        raise ValueError("hurwitz_radon only defined for positive integers")
    # helper to get largest power of 2 divinding n

tkmharris

## Mordell's equation

'''
Get integer solutions of the Mordell equation
y^2 = x^3 - d
for certain special values of d.
See mordell.txt for details.
'''

def mordell_test(d, x,y):

tkmharris

{--
We provide a function 'nextPrimeBias' that when called as
  nextPrimeBias a b n r
returns the probability that, among the first r primes, a prime that is equivalent to a mod n is followed by a prime that is equivalent to b mod n.

We see that these probabilities are not evenly distributed among equivalence classes, as described in https://arxiv.org/abs/1603.03720 :
nextPrimeBias 7 1 10 100000 = 0.25736558
nextPrimeBias 7 3 10 100000 = 0.27695382
nextPrimeBias 7 7 10 100000 = 0.144993
nextPrimeBias 7 9 10 100000 = 0.3206876

tkmharris

tkmharris

"""
Quick implementation of the two trees for partitions discussed here:
https://11011110.github.io/blog/2005/08/07/two-trees-on.html
"""

from treelib import Node, Tree

# partition class

class InvalidPartitionError(Exception):

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# coding: utf8

import random

class OutOfTimeError(Exception):
    """Raised when game passes maximum number of turns"""
    pass

class Player:

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{-- Implementation of the Akiyama-Tanigawa algorithm
	for computing Bernoulli numbers. --}

{-- Implement the algorithm by:
	1. Begin with list of reciprocals of positive integers.
	2. Write function to get next row and iteratie it to get list of lists.
	3. Take the head of each list in the list to get Bernoulli nums.
	Everything evaluates lazily, so we can do this nicely with infinite lists. 

	See tkmh.space/flotsam/haskell-akiyama-tanigawa for more.--}

tkmharris

"""
Function to calculate terms of OEIS sequence A345209.
"""

from sympy import primefactors

def a345209(n):
    """
    Calculate OEIS entry A345209(n)
    (Number of Petrie polygons on regular triangular map corresponding to the principal congruence subgroup Γ(n) of the mmodular group)

tkmharris

"""
Function to calculate terms of OEIS sequence A345225.
"""

def a345225(n):
	"""
    Calculate OEIS entry A345225(n)
    (Orders of 2-primary subgroups of K_n(Z), the algebraic K-theory of the integers.)
    
    n: int, >=0

tkmharris

"""
Function to calculate terms of the order of the image of the J-homomorphism.
"""
from sympy import bernoulli

def a345262(n):
	"""
    Calculate the terms of OEIS entry A345262.
    (Order of the image of the J-homomorphism in the stable homotopy group π_n^S).