Search results
Results From The WOW.Com Content Network
In mathematics, particularly in the area of arithmetic, a modular multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m. [1] In the standard notation of modular arithmetic this congruence is written as (),
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.
Existence: There exists an integer denoted a −1 such that aa −1 ≡ 1 (mod m) if and only if a is coprime with m. This integer a −1 is called a modular multiplicative inverse of a modulo m. If a ≡ b (mod m) and a −1 exists, then a −1 ≡ b −1 (mod m) (compatibility with multiplicative inverse, and, if a = b, uniqueness modulo m).
Perl's Math::BigInt module has a bmodpow() method to perform modular exponentiation; Raku has a built-in routine expmod. Go's big.Int type contains an Exp() (exponentiation) method whose third parameter, if non-nil, is the modulus; PHP's BC Math library has a bcpowmod() function to perform modular exponentiation
Some programming languages such as Lisp, Python, Perl, Haskell, Ruby and Raku use, or have an option to use, arbitrary-precision numbers for all integer arithmetic. Although this reduces performance, it eliminates the possibility of incorrect results (or exceptions) due to simple overflow.
Video: Keys pressed for calculating eight times six on a HP-32SII (employing RPN) from 1991. Reverse Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation or simply postfix notation, is a mathematical notation in which operators follow their operands, in contrast to prefix or Polish notation (PN), in which operators precede their operands.
It is trivial to change the padlock from open to closed without using the key, by pushing the shackle into the lock mechanism. Opening the padlock easily, however, requires the key to be used. Here the key t is the trapdoor and the padlock is the trapdoor function.
Using a residue numeral system for arithmetic operations is also called multi-modular arithmetic. Multi-modular arithmetic is widely used for computation with large integers, typically in linear algebra , because it provides faster computation than with the usual numeral systems, even when the time for converting between numeral systems is ...