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Like distinct-degree factorization algorithm, Rabin's algorithm [5] is based on the Lemma stated above. Distinct-degree factorization algorithm tests every d not greater than half the degree of the input polynomial. Rabin's algorithm takes advantage that the factors are not needed for considering fewer d. Otherwise, it is similar to distinct ...
Miller–Rabin primality test. The Miller–Rabin primality test or Rabin–Miller primality test is a probabilistic primality test: an algorithm which determines whether a given number is likely to be prime, similar to the Fermat primality test and the Solovay–Strassen primality test. It is of historical significance in the search for a ...
The Miller–Rabin primality test and Solovay–Strassen primality test are more sophisticated variants, which detect all composites (once again, this means: for every composite number n, at least 3/4 (Miller–Rabin) or 1/2 (Solovay–Strassen) of numbers a are witnesses of compositeness of n). These are also compositeness tests.
Irreducibility (mathematics) In mathematics, the concept of irreducibility is used in several ways. A polynomial over a field may be an irreducible polynomial if it cannot be factored over that field. In abstract algebra, irreducible can be an abbreviation for irreducible element of an integral domain; for example an irreducible polynomial.
But if the test shows that there is no rational root, then the polynomial may be irreducible, in which case casus irreducibilis applies, cos(θ ⁄ 5) and sin(θ ⁄ 5) are not constructible, the angle θ ⁄ 5 is not constructible, and the angle θ is not classically pentasectible. An example of this is when one attempts to construct a 25-gon ...
Irreducible element. In algebra, an irreducible element of an integral domain is a non-zero element that is not invertible (that is, is not a unit), and is not the product of two non-invertible elements. The irreducible elements are the terminal elements of a factorization process; that is, they are the factors that cannot be further factorized.
When the low 13 bits of the fingerprint are zero LBFS calls those 48 bytes a breakpoint and ends the current block and begins a new one. Since the output of Rabin fingerprints are pseudo-random the probability of any given 48 bytes being a breakpoint is (1 in 8192). This has the effect of shift-resistant variable size blocks.
In algebra, Weyl's theorem on complete reducibility is a fundamental result in the theory of Lie algebra representations (specifically in the representation theory of semisimple Lie algebras). Let be a semisimple Lie algebra over a field of characteristic zero. The theorem states that every finite-dimensional module over is semisimple as a ...