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Mathematics of cyclic redundancy checks. The cyclic redundancy check (CRC) is a check of the remainder after division in the ring of polynomials over GF (2) (the finite field of integers modulo 2). That is, the set of polynomials where each coefficient is either zero or one, and arithmetic operations wrap around.
Rule of mixtures. Relation between properties and composition of a compound. The upper and lower bounds on the elastic modulus of a composite material, as predicted by the rule of mixtures. The actual elastic modulus lies between the curves. In materials science, a general rule of mixtures is a weighted mean used to predict various properties ...
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.
In number theory, the Legendre symbol is a multiplicative function with values 1, −1, 0 that is a quadratic character modulo of an odd prime number p: its value at a (nonzero) quadratic residue mod p is 1 and at a non-quadratic residue (non-residue) is −1. Its value at zero is 0. The Legendre symbol was introduced by Adrien-Marie Legendre ...
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. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...
Modular exponentiation can be performed with a negative exponent e by finding the modular multiplicative inverse d of b modulo m using the extended Euclidean algorithm. That is: c = be 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.
A residue numeral system (RNS) is a numeral system representing integers by their values modulo several pairwise coprime integers called the moduli. This representation is allowed by the Chinese remainder theorem, which asserts that, if M is the product of the moduli, there is, in an interval of length M, exactly one integer having any given set of modular values.
The Weibull modulus is a dimensionless parameter of the Weibull distribution. It represents the width of a probability density function (PDF) in which a higher modulus is a characteristic of a narrower distribution of values. Use case examples include biological and brittle material failure analysis, where modulus is used to describe the ...