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Perl, Python (only modern versions) choose the remainder with the same sign as the divisor d. [6] Scheme offer two functions, remainder and modulo – Ada and PL/I have mod and rem, while Fortran has mod and modulo; in each case, the former agrees in sign with the dividend, and the latter with the divisor.
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor. [1]
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
17 is divided into 3 groups of 5, with 2 as leftover. Here, the dividend is 17, the divisor is 3, the quotient is 5, and the remainder is 2 (which is strictly smaller than the divisor 3), or more symbolically, 17 = (3 × 5) + 2.
Three multiples can be subtracted (q 1 = 3), leaving a remainder of 21: 462 = 3 × 147 + 21. Then multiples of 21 are subtracted from 147 until the remainder is less than 21. Seven multiples can be subtracted (q 2 = 7), leaving no remainder: 147 = 7 × 21 + 0. Since the last remainder is zero, the algorithm ends with 21 as the greatest common ...
Python sets are very much like mathematical sets, and support operations like set intersection and union. Python also features a frozenset class for immutable sets, see Collection types. Dictionaries (class dict) are mutable mappings tying keys and corresponding values. Python has special syntax to create dictionaries ({key: value})
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 final algorithm takes the six most significant bits of the size of the array, adds one if any of the remaining bits are set, and uses that result as the minrun. This algorithm works for all arrays, including those smaller than 64; for arrays of size 63 or less, this sets minrun equal to the array size and Timsort reduces to an insertion sort.