bernoulli		 index
/home/tomek/Desktop/py/bernoulli/bernoulli.py

Summary:
    Intended for calculating partial sums of powers of natural numbers.
    Can also print n+1 Bernoulli numbers,
     do python math, cache crucial numbers.
    Warning: Not fitting for server. Has many vunerabilities.
    Can launch arbitrary code.
 
Help, usage:
    You can take advantage of command line interface
     to see some available commands.
    Use "python Bernoulli.py help" terminal command for that purpose.
 
    You can also enter interactive mode by launching Bernoulli.py
     without any parameters.
 
Caching:
    App saves calculated values that are most vital for calculations.
    These are generally needed to quickly construct
     a sequence of Bernoulli numbers.
 
    This optimization makes futher uses of bernoulli app faster.
    Overhead for reading/writing these numbers from/to cache file
    dependes on quantity stored numbers
    (it's ~0.5s for 3001 Bernoulli & 3001 generator numbers).

 
Modules
       
atexit
fractions
os
pickle
re
sys

 
Functions
       
ensure_nth_bn(n: int)
Ensures that nth Bernoulli number is directly accessible in RAM.
Concreatly in `bernoulli_nums` collection.
 
This function u Akiyama–Tanigawa algorithm
exec_command(cmd: str)
Function `exec_command` can be used to emulate command line mode.
Usage: 'exec_command(your_command)'
Eg. use: 'exec_command("nth_Bernoulli_num 8")'
Ommit interpreter name & file name you're inside them!
explain_commands(*commands: str)
It explains commands from CLI.
fa_fact(n: int, fall_num: int)
Returns falling factorial,
where `n` is base and `fall_num` is amount of decreasing factors,
which make up falling factorial
get_cli_func(func_name: str)
Gets CLI function by its name or name shorthand.
nth_Bernoulli_num(n: int) -> int
Returns `n`th Bernoulli number.
print_up_to_n_Bernoulli_num(n: int)
Prints list of all Bernoulli numbers up to `n`th term
without creating new sequence inside Python kernel.
It naturally has smaller overhead than printing
result of `up_to_n_Bernoulli_num(n)` .
save_key_nums()
Saves numbers that are most vital for calculations.
These are generally numbers that are needed
 to quickly reconstruct sequence of Bernoulli numbers.
This optimization makes futher calculations faster.
Overhead for reading/writing these numbers from/to cache file
hasn't been measured.
sum_of_pows(n: int, p: int) -> int
Returns sum of `p` powers of all natural numbers from range [0,`n`].
 
This function uses optimized Faulhaber's formula.
up_to_n_Bernoulli_num(n: int) -> list[fractions.Fraction]
Returns list of all Bernoulli numbers up to `n`th term.

 
Data
        ACTIVE_CFNAME = 'ActiveBernoulli.pycache'
CACHE_FNAME = 'Bernoulli.pycache'
CLI = {'help': <function explain_commands>, 'nth_Bernoulli_num': <function <lambda>>, 'sum_of_pows': <function <lambda>>, 'up_to_n_Bernoulli_num': <function <lambda>>}
CLI_shorthands = {'h': 'help', 'nth': 'nth_Bernoulli_num', 'psum': 'sum_of_pows', 'up_to': 'up_to_n_Bernoulli_num'}
MAX_NO_NUMS_SAVED_TO_CACHE_FILE = 3000
bernoulli_nums = [Fraction(1, 1), Fraction(1, 2), Fraction(1, 6), Fraction(0, 1), Fraction(-1, 30), Fraction(0, 1), Fraction(1, 42), Fraction(0, 1), Fraction(-1, 30), Fraction(0, 1), Fraction(5, 66), Fraction(0, 1), Fraction(-691, 2730), Fraction(0, 1), Fraction(7, 6), Fraction(0, 1), Fraction(-3617, 510), Fraction(0, 1), Fraction(43867, 798), Fraction(0, 1), ...]
bernoulli_nums_read_from_cache = 3001
fi = <_io.BufferedReader name='Bernoulli.pycache'>
generator_nums = [Fraction(-28919392162925009628147618267854828678...43417141322454179981, 12072109463901626300591430), Fraction(289193921629250096281476182678548286786...43417141322454179981, 12072109463901626300591430), Fraction(-28909498656239440817132902266130953561...42948191954615203, 24136170854827318183649132380), Fraction(240902974703323072350074180714794148154...047997999635144924, 6034042713706829545912283095), Fraction(-15706785477727606373313358586735811532...5176978896050, 157383522484529752314211715053647), Fraction(125626711935336963187417254920581429377...7005833254955, 629534089938119009256846860214588), Fraction(-61860632867156655391591165272550541148...63464751458391, 18606918914427162835177739710776), Fraction(320142944028610659753320487209140615727...21263200795892, 67450081064798465277519306451563), Fraction(-21177330654661567986589889557655011964...3375391, 357295295359363650741508916992764327410), Fraction(469937051619038511607177992674275654902...75458095, 71459059071872730148301783398552865482), Fraction(-94348138629144884118571424764082017089...1, 143751317779967301444181829536663148547726396), Fraction(712852865880697737750146541043868326549...63, 11979276481663941787015152461388595712310533), Fraction(-11170448402525564512134399000657189200...774958239416726467448947512630223325145058085660), Fraction(244402324284826588666321863415543426801...221416639833350419271127860751492378612873738760), Fraction(-23144710245345478159447687749486972122...896188885311113389236150381433532317148383165168), Fraction(209691180216455519695246566095186015550...570113397197049881463370643770210126346462203237), Fraction(-46898559563627223444503090233042627402...643016614905537175226201298616681820692080528030), Fraction(303330602887989453096020316266518533259...404779623878393019469577922068520202299120058670), Fraction(-68771984184923501551629267139661434359...510370711039766117075646973125280286847164361460), Fraction(205025750937149931018303466360660355305...434631588478655173184970095470361649371195078395), ...]
glob = {'ACTIVE_CFNAME': 'ActiveBernoulli.pycache', 'CACHE_FNAME': 'Bernoulli.pycache', 'CLI': {'help': <function explain_commands>, 'nth_Bernoulli_num': <function <lambda>>, 'sum_of_pows': <function <lambda>>, 'up_to_n_Bernoulli_num': <function <lambda>>}, 'CLI_shorthands': {'h': 'help', 'nth': 'nth_Bernoulli_num', 'psum': 'sum_of_pows', 'up_to': 'up_to_n_Bernoulli_num'}, 'MAX_NO_NUMS_SAVED_TO_CACHE_FILE': 3000, '__builtins__': {'ArithmeticError': <class 'ArithmeticError'>, 'AssertionError': <class 'AssertionError'>, 'AttributeError': <class 'AttributeError'>, 'BaseException': <class 'BaseException'>, 'BaseExceptionGroup': <class 'BaseExceptionGroup'>, 'BlockingIOError': <class 'BlockingIOError'>, 'BrokenPipeError': <class 'BrokenPipeError'>, 'BufferError': <class 'BufferError'>, 'BytesWarning': <class 'BytesWarning'>, 'ChildProcessError': <class 'ChildProcessError'>, ...}, '__cached__': '/home/tomek/Desktop/py/bernoulli/__pycache__/bernoulli.cpython-312.pyc', '__doc__': '\nSummary:\n Intended for calculating partial s...5s for 3001 Bernoulli & 3001 generator numbers).\n', '__file__': '/home/tomek/Desktop/py/bernoulli/bernoulli.py', '__loader__': <_frozen_importlib_external.SourceFileLoader object>, ...}
help = Type help() for interactive help, or help(object) for help about object.
public_functions = ['exit aka quit', 'print_up_to_n_Bernoulli_num aka print_up', 'exec_command aka ec', 'save_key_nums aka save']