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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]
The numbers whose trajectory under iteration of sum of squares of digits map includes 1. A007770: Factorial primes: 2, 3, 5, 7, 23, 719, 5039, 39916801, ... A prime number that is one less or one more than a factorial (all factorials > 1 are even). A088054: Wolstenholme primes: 16843, 2124679
Multiplying a matrix M by either or on either the left or the right will permute either the rows or columns of M by either π or π −1.The details are a bit tricky. To begin with, when we permute the entries of a vector (, …,) by some permutation π, we move the entry of the input vector into the () slot of the output vector.
The two exceptions are the three pandas held at Taipei Zoo, which are given from the Chinese Mainland, and one panda held in Mexico. Giant pandas are on the IUCN Red List so part of the reason these contracts exist between China and international zoos is to try to help the species reproduce before they are brought back to their native land. For ...