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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.
Given the Euler's totient function φ(m), any set of φ(m) integers that are relatively prime to m and mutually incongruent under modulus m is called a reduced residue system modulo m. [5] The set {5, 15} from above, for example, is an instance of a reduced residue system modulo 4.
Bulk modulus, a measure of compression resistance; Elastic modulus, a measure of stiffness; Shear modulus, a measure of elastic stiffness; Young's modulus, a specific elastic modulus; Modulo operation (a % b, mod(a, b), etc.), in both math and programming languages; results in remainder of a division; Casting modulus used in Chvorinov's rule.
The term "modulus" is borrowed from mathematics (or more specifically, moduli space is borrowed from algebraic geometry), where it is used synonymously with "parameter". The word moduli ( Moduln in German) first appeared in 1857 in Bernhard Riemann 's celebrated paper "Theorie der Abel'schen Functionen".
Most commonly, the modulus is chosen as a prime number, making the choice of a coprime seed trivial (any 0 < X 0 < m will do). This produces the best-quality output, but introduces some implementation complexity, and the range of the output is unlikely to match the desired application; converting to the desired range requires an additional multiplication.
Z3 was developed in the Research in Software Engineering (RiSE) group at Microsoft Research Redmond and is targeted at solving problems that arise in software verification and program analysis.
Learn how to enable JavaScript in your browser to access additional AOL features and content.
The syntax of JavaScript is the set of rules that define a correctly structured JavaScript program. The examples below make use of the log function of the console object present in most browsers for standard text output .