Skip to main content
Donate to the Python Software Foundation or Purchase a PyCharm License to Benefit the PSF! Donate Now

Convert integers to and from the factoradic number system

Project description

The factorial number system (also known as factoradic) is a way of representing an integer as the sum of multiples of factorials. All integers have a unique representation in the factoradic number system. For example, the number 1337 can be represented as:

1*6! + 5*5! + 0*4! + 2*3! + 2*2! + 1*1! + 0*0!

with coefficients 1 5 0 2 2 1 0. This is the unique factoradic representation of decimal 1337.

Factoradic numbers have uses in combinatorics, particularly in the numbering of permutations. This factoradic library is useful for converting to and from factoradic number representations both in Python and from the command-line.

Status

https://travis-ci.org/rob-smallshire/factoradic.svg?branch=master https://coveralls.io/repos/github/rob-smallshire/factoradic/badge.svg?branch=master

Installation

The factoradic package is available on the Python Package Index (PyPI):

https://badge.fury.io/py/factoradic.svg

The package supports Python 3 only. To install:

$ pip install factoradic

Python Interface

For full help:

>>> import factoradic
>>> help(factoradic)

In the meantime, here are some highlights.

To convert from an integer to factoradic use to_factoradic():

>>> factoradic.to_factoradic(1337)
[0, 1, 2, 2, 0, 5, 1]

The result is the list of coefficients where the factorial of each zero-based index gives a place value, and the item at that index is the coefficient by with the place value is to be multiplied. The elements are from least-significant to most-significant. Since the coefficient at any index must be less that or equal to the index, the coefficient at index 0 is always 0.

To convert from factoradic use from_factoradic():

>>> factoradic.from_factoradic([0, 1, 2, 2, 0, 5, 1])
1337

Command-Line Interface

There’s also a handy command-line interface. Run factoradic --help to see a list of commands:

$ factoradic --help
Factoradic.

Convert to and from the factorial number system.

Usage:
  factoradic from-integer <integer> [--expression]
  factoradic to-integer <coefficient-0> [<coefficient-1> [<coefficient-n>...]]

Options:
  -e --expression  Show as a mathematical expression.

To convert from an integer to factoradic, use the from-integer subcommand:

$ factoradic from-integer 1729
0 1 0 0 2 2 2

The coefficients are reported from least-significant to most-significant. The see the results as a math expression, specify the --expression flag:

$ factoradic from-integer 1729 --expression
2*6! + 2*5! + 2*4! + 0*3! + 0*2! + 1*1! + 0*0!

To convert from factoradic representation use the to-integer subcommand, specifying the coefficients from least-significant to most-significant:

$ factoradic to-integer 0 1 0 0 2 2 2
1729

Project details


Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Filename, size & hash SHA256 hash help File type Python version Upload date
factoradic-1.0.3-py3-none-any.whl (7.4 kB) Copy SHA256 hash SHA256 Wheel py3
factoradic-1.0.3.tar.gz (5.9 kB) Copy SHA256 hash SHA256 Source None

Supported by

Elastic Elastic Search Pingdom Pingdom Monitoring Google Google BigQuery Sentry Sentry Error logging AWS AWS Cloud computing DataDog DataDog Monitoring Fastly Fastly CDN SignalFx SignalFx Supporter DigiCert DigiCert EV certificate StatusPage StatusPage Status page