Search results
Results From The WOW.Com Content Network
Like raw strings, there can be any number of equals signs between the square brackets, provided both the opening and closing tags have a matching number of equals signs; this allows nesting as long as nested block comments/raw strings use a different number of equals signs than their enclosing comment: --[[comment --[=[ nested comment ...
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.
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. Common Lisp and Haskell also have mod and rem, but mod uses the sign of the divisor and rem uses the sign of the dividend.
If a ≡ b (mod m), then it is generally false that k a ≡ k b (mod m). However, the following is true: If c ≡ d (mod φ(m)), where φ is Euler's totient function, then a c ≡ a d (mod m) —provided that a is coprime with m. For cancellation of common terms, we have the following rules: If a + k ≡ b + k (mod m), where k is any integer ...
Modulo is a mathematical jargon that was introduced into mathematics in the book Disquisitiones Arithmeticae by Carl Friedrich Gauss in 1801. [3] Given the integers a, b and n, the expression "a ≡ b (mod n)", pronounced "a is congruent to b modulo n", means that a − b is an integer multiple of n, or equivalently, a and b both share the same remainder when divided by n.
The congruence relation, modulo m, partitions the set of integers into m congruence classes. Operations of addition and multiplication can be defined on these m objects in the following way: To either add or multiply two congruence classes, first pick a representative (in any way) from each class, then perform the usual operation for integers on the two representatives and finally take the ...
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
The constants R mod N and R 3 mod N can be generated as REDC(R 2 mod N) and as REDC((R 2 mod N)(R 2 mod N)). The fundamental operation is to compute REDC of a product. When standalone REDC is needed, it can be computed as REDC of a product with 1 mod N. The only place where a direct reduction modulo N is necessary is in the precomputation of R ...