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pip (also known by Python 3's alias pip3) is a package-management system written in Python and is used to install and manage software packages. [4] The Python Software Foundation recommends using pip for installing Python applications and its dependencies during deployment. [ 5 ]
The Python Package Index, abbreviated as PyPI (/ ˌ p aɪ p i ˈ aɪ /) and also known as the Cheese Shop (a reference to the Monty Python's Flying Circus sketch "Cheese Shop"), [2]: 8 [3]: 742 is the official third-party software repository for Python. [4] It is analogous to the CPAN repository for Perl [5]: 36 and to the CRAN repository for R.
To avoid installing the large SciPy package just to get an array object, this new package was separated and called NumPy. Support for Python 3 was added in 2011 with NumPy version 1.5.0. [15] In 2011, PyPy started development on an implementation of the NumPy API for PyPy. [16] As of 2023, it is not yet fully compatible with NumPy. [17]
Since 7 October 2024, Python 3.13 is the latest stable release, and it and, for few more months, 3.12 are the only releases with active support including for bug fixes (as opposed to just for security) and Python 3.9, [55] is the oldest supported version of Python (albeit in the 'security support' phase), due to Python 3.8 reaching end-of-life.
The congruence relation, modulo m, partitions the set of integers into m congruence classes. Operations of addition and multiplication can be defined on these m objects in the following way: To either add or multiply two congruence classes, first pick a representative (in any way) from each class, then perform the usual operation for integers on the two representatives and finally take the ...
These executables can run on a system without Python installed. [3] It is the most common tool for doing so. py2exe was used to distribute the official BitTorrent client (before the version 6.0) and is still used to distribute SpamBayes as well as other projects. Since May 2014, version 0.9.2.0 of py2exe is available for Python 3. [1]
For any integer n, n ≡ 1 (mod 2) if and only if 3n + 1 / 2 ≡ 2 (mod 3). Equivalently, 2n − 1 / 3 ≡ 1 (mod 2) if and only if n ≡ 2 (mod 3). Conjecturally, this inverse relation forms a tree except for a 1–2 loop (the inverse of the 1–2 loop of the function f(n) revised as indicated above).
A right R-module M R is defined similarly in terms of an operation · : M × R → M. Authors who do not require rings to be unital omit condition 4 in the definition above; they would call the structures defined above "unital left R-modules". In this article, consistent with the glossary of ring theory, all rings and modules are assumed to be ...