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For example, mod(2*J,n) will multiply every element in J by 2, and then reduce each element modulo n. MATLAB does include standard for and while loops, but (as in other similar applications such as APL and R), using the vectorized notation is encouraged and is often faster to execute.
MOD: AMPL model file AMPL: MOD: Modula language source MOD: Modula-2 source code file Clarion Modula-2 MOD Tracker file format created for Ultimate Soundtracker for the Amiga: MOD (file format) MOD MOD is recording format for use in digital tapeless camcorders. MOD and TOD: MODULES: Module GTK+: MOE same as Modelica Model .mo. MOL: MDL Molfile ...
Time-keeping on this clock uses arithmetic modulo 12. Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus.
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.
The multiplicative order of a number a modulo n is the order of a in the multiplicative group whose elements are the residues modulo n of the numbers coprime to n, and whose group operation is multiplication modulo n. This is the group of units of the ring Z n; it has φ(n) elements, φ being Euler's totient function, and is denoted as U(n) or ...
c = b e mod m = d −e mod m, where e < 0 and b ⋅ d ≡ 1 (mod m). Modular exponentiation is efficient to compute, even for very large integers. On the other hand, computing the modular discrete logarithm – that is, finding the exponent e when given b , c , and m – is believed to be difficult.
So a nonzero number is a residue mod 8, 16, etc., if and only if it is of the form 4 k (8n + 1). A number a relatively prime to an odd prime p is a residue modulo any power of p if and only if it is a residue modulo p. [8] If the modulus is p n, then p k a is a residue modulo p n if k ≥ n is a nonresidue modulo p n if k < n is odd
MATLAB was created in the 1970s by Cleve Moler, who was chairman of the computer science department at the University of New Mexico at the time. It was a free tool for academics. Jack Little, who would eventually set up the company, came across the tool while he was a graduate student in electrical engineering at Stanford University.