Synonymer & Information om | Engelska ordet MODULO

Exempel på hur man kan använda MODULO i en mening

• 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.
• In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers.
• In informal contexts, mathematicians often use the word modulo (or simply mod) for similar purposes, as in "modulo isomorphism".
• For larger results, an old method, still in common use, consists of using several small moduli that are pairwise coprime, and applying the Chinese remainder theorem for recovering the result modulo the product of the moduli.
• In number theory, Euler's criterion is a formula for determining whether an integer is a quadratic residue modulo a prime.
• As with ordinary arithmetic, multiplication and addition are commutative and associative in modulo 2 arithmetic, and multiplication is distributive over addition.
• In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.
• Instead of checking for remainders of integers modulo prime numbers, we are checking for remainders of polynomials when divided by linears.
• The -th de Rham cohomology (group) is the vector space of closed -forms modulo the exact -forms; as noted in the previous section, the Poincaré lemma states that these vector spaces are trivial for a contractible region, for.
• so chains form a chain complex, whose homology groups (cycles modulo boundaries) are called simplicial homology groups.
• In practice, Wilson's theorem is useless as a primality test because computing (n − 1)! modulo n for large n is computationally complex, and much faster primality tests are known (indeed, even trial division is considerably more efficient).
• If each level of the factorization splits every polynomial into an O(1) (constant-bounded) number of smaller polynomials, each with an O(1) number of nonzero coefficients, then the modulo operations for that level take O(N) time; since there will be a logarithmic number of levels, the overall complexity is O (N log N).
• Hensel's lemma, also known as Hensel's lifting lemma, named after Kurt Hensel, is a result in modular arithmetic, stating that if a polynomial equation has a simple root modulo a prime number , then this root corresponds to a unique root of the same equation modulo any higher power of , which can be found by iteratively "lifting" the solution modulo successive powers of.
• from the group of (Weil) divisors modulo principal divisors to the group of isomorphism classes of line bundles.
• The multiplicative order of a number a modulo n is the order of a in the multiplicative group whose elements are the residues modulo n of the numbers coprime to n, and whose group operation is multiplication modulo n.
• Given a torus T (not necessarily maximal), the Weyl group of G with respect to T can be defined as the normalizer of T modulo the centralizer of T.
• Since the plane at infinity is a projective plane, it is homeomorphic to the surface of a "sphere modulo antipodes", i.
• This cyclical system is referred to as modular arithmetic and, in the usual case of chromatic twelve-tone scales, pitch-class numbering is "modulo 12" (customarily abbreviated "mod 12" in the music-theory literature)—that is, every twelfth member is identical.
• See the zlib source code for a more efficient implementation that requires a fetch and two additions per byte, with the modulo operations deferred with two remainders computed every several thousand bytes, a technique first discovered for Fletcher checksums in 1988.
• Simons clarifies something that is very difficult to determine by reading Leśniewski and his students, namely that Polish mereology is a first-order theory equivalent to what is now called classical extensional mereology (modulo choice of language).

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