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  2. Modulo - Wikipedia

    en.wikipedia.org/wiki/Modulo

    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. [1]

  3. Euclidean division - Wikipedia

    en.wikipedia.org/wiki/Euclidean_division

    In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental property is that the quotient and the remainder ...

  4. Division algorithm - Wikipedia

    en.wikipedia.org/wiki/Division_algorithm

    Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.

  5. Computation of cyclic redundancy checks - Wikipedia

    en.wikipedia.org/wiki/Computation_of_cyclic...

    Every step, the appropriate multiple of the polynomial is subtracted to make the zero group one bit longer, and the unchanged group becomes one bit shorter, until only the final remainder is left. In the msbit-first example, the remainder polynomial is x 7 + x 5 + x {\displaystyle x^{7}+x^{5}+x} .

  6. String operations - Wikipedia

    en.wikipedia.org/wiki/String_operations

    A string substitution or simply a substitution is a mapping f that maps characters in Σ to languages (possibly in a different alphabet). Thus, for example, given a character a ∈ Σ, one has f(a)=L a where L a ⊆ Δ * is some language whose alphabet is Δ. This mapping may be extended to strings as f(ε)=ε

  7. Python syntax and semantics - Wikipedia

    en.wikipedia.org/wiki/Python_syntax_and_semantics

    For example, one could define a dictionary having a string "toast" mapped to the integer 42 or vice versa. The keys in a dictionary must be of an immutable Python type, such as an integer or a string, because under the hood they are implemented via a hash function. This makes for much faster lookup times, but requires keys not change.

  8. Remainder - Wikipedia

    en.wikipedia.org/wiki/Remainder

    In this case, s is called the least absolute remainder. [3] As with the quotient and remainder, k and s are uniquely determined, except in the case where d = 2n and s = ± n. For this exception, we have: a = k⋅d + n = (k + 1)d − n. A unique remainder can be obtained in this case by some convention—such as always taking the positive value ...

  9. Satisfiability modulo theories - Wikipedia

    en.wikipedia.org/wiki/Satisfiability_modulo_theories

    In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable.It generalizes the Boolean satisfiability problem (SAT) to more complex formulas involving real numbers, integers, and/or various data structures such as lists, arrays, bit vectors, and strings.