PM2Ring

""" BBerg32

    Primality test for 32 bit integers using a single SPRP test.
    The SPRP base comes from a hash table.

    Hash and bases by Bradley Berg
    See https://techneon.com/download/is.prime.32.base.data
"""

bases = [

PM2Ring

(0, 1) : 50
(1, 0) : 50
(0, 2) : 258
(1, 1) : 600
(2, 0) : 258
(0, 3) : 186
(1, 2) : 1086
(2, 1) : 1086
(3, 0) : 186
(0, 4) : 5

PM2Ring

""" Maxwell–Boltzmann distribution
    See https://en.m.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution
    Written by PM 2Ring 2021.06.20
"""
# Gas constant g⋅m^2⋅s^−2⋅K^−1⋅mol^−1
R = 8314.46261815324

@interact
def _(T=('temp (°C)', 20), mass=('mass (g/mol)', 29),
  auto_update=False):

PM2Ring

""" Lorenz attractor 

    From https://en.wikipedia.org/wiki/Lorenz_system
    Modified for Sagemath by PM 2Ring 2023.01.04
"""

import numpy as np
from scipy.integrate import odeint

# Build Bezier curves

PM2Ring

""" Borwein + Borwein quadratic pi
    Algorithm 2.1 from "Pi and the AGM" (Wiley, 1987)

    Written by PM 2Ring 2023.1.2
"""
from math import floor, log, pi
from decimal import Decimal as D, getcontext

def borwein_pi(loops):
    x = D(2).sqrt()

PM2Ring

""" pi from 10 * asin((phi-1)/2)

    Uses Carlson's accelerated version of
    Borchardt's modified AGM algorithm
    Written by PM 2Ring 2022.05.11
"""

from itertools import count
from decimal import Decimal as D, getcontext

PM2Ring

Standard Solar Model (BP2004)
https://www.sns.ias.edu/~jnb/SNdata/Export/BP2004/bp2004stdmodel.dat
astro-ph/0402114

Columns in the Standard Model table (below) represent:

1)  Mass fraction in units of the solar mass
2)  Radius of the zone in units of one solar radius
3)  Temperature in units of deg (K)
4)  Density in units of g/cm^3

PM2Ring

""" Deterministic Miller-Rabin primality test

    See https://en.m.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test
    and https://miller-rabin.appspot.com/

    Written by PM 2Ring 2015.04.29
    Updated 2022.04.20
"""

small_primes = [

PM2Ring

#!/usr/bin/env python3

''' Find all divisors in a range by sieving

    Written by PM 2Ring 2017.05.03

    Prime GP version
'''

from itertools import product

PM2Ring

""" Julian day number to date conversion
    Proleptic Gregorian and Julian, with Astronomical years
    i.e., 1 AD = year 1, 1 BC = year 0, 2 BC = year -1, etc

    Derived from RG Tantzen (1963), ACM.
    Algorithm 199: conversions between calendar date and Julian day number.

    https://en.wikipedia.org/wiki/Julian_day
    Julian day number 0 assigned to the day starting at noon on
    January 1, 4713 BC, proleptic Julian calendar