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In mathematics, Arnold's cat map is a chaotic map from the torus into itself, named after Vladimir Arnold, who demonstrated its effects in the 1960s using...

desired reducer. A typical default is to hash the key and use the hash value modulo the number of reducers. It is important to pick a partition function that...

modulo 2 with at most t nonzero coefficients, then R(x) is not a multiple of P(x) modulo 2. If follows that the corresponding hash function will map keys...

In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable...

In mathematics, the term modulo ("with respect to a modulus of", the Latin ablative of modulus which itself means "a small measure") is often used to assert...

the modulo operator with real arguments. The map depends on only the one constant α. Due to roundoff error, successive applications of the modulo operator...

curve (dual of holomorphic 1-forms modulo periods) is isomorphic to its Jacobian variety (divisors of degree 0 modulo equivalence). For higher-dimensional...

are taken modulo 2 π {\displaystyle 2\pi } . The properties of chaos of the standard map were established by Boris Chirikov in 1969. This map describes...

cycles. The n-th (co)homology group Hn (Hn) is the group of (co)cycles modulo (co)boundaries in degree n, that is, H n = ker ⁡ d n / im  d n + 1 ( H n...

curvature is a moment map for the action of the gauge group on connections. In particular the moduli space of flat connections modulo gauge equivalence μ...

the reduction modulo m {\displaystyle m} of the determinant of such a matrix is equal to the determinant of the matrix reduced modulo m {\displaystyle...

and θ i {\displaystyle \theta _{i}} should be interpreted modulo 1 {\displaystyle 1} . This map displays very diverse behavior depending on the parameters...

this identifies the group of versors with the group of rotations of R3, modulo the fact that the versors q and −q determine the same rotation. As noted...

send the boundary of X to the boundary of Y. One can also define degree modulo 2 (deg2(f)) the same way as before but taking the fundamental class in Z2...

modulo a prime number p, then this root can be lifted to a unique root modulo any higher power of p. More generally, if a polynomial factors modulo p...

is credited to Arnold Dumey, who discussed the idea of using remainder modulo a prime as a hash function.: 15  The word "hashing" was first published...

reducing modulo 2 is also 2Z, so the sequence is exact at the second Z. the image of reducing modulo 2 is Z/2Z, and the kernel of the zero map is also...

{Z} } where n = 1 , 2 , 3 , … {\displaystyle n=1,2,3,\dots } with the modulo maps Z / n Z → Z / m Z {\displaystyle \mathbb {Z} /n\mathbb {Z} \to \mathbb...

1, or 2, where addition in the x-coordinate is modulo 2 and addition in the y-coordinate is modulo 3. These structures are isomorphic under addition...

map that sends every integer to its parity (that is, 0 if the number is even, 1 if the number is odd) would be a homomorphism to the integers modulo 2...