An application of a lattice basis reduction theorem resulted in the first efficient algorithm for doing this task and was invented by Lenstra, Lenstra, and Lovasz.
An application of a lattice basis reduction theorem resulted in the first efficient algorithm for doing this task and was invented by Lenstra, Lenstra, and Lovasz. Algorithms that do this task can be repurposed to compute discrete logs; one of those algorithms that works for Galois fields is the popular Cantor-Zassenhaus algorithm, which replaced the similar Berlekamp algorithm. This procedure can be done on "square-free" inputs, which have no repetitions. One method of doing this first divides the input by a common denominator before using the (*) Lagrange interpolation formula; that method is named for Kronecker. This procedure is predicated on the fundamental theorem of algebra, which states that expressions of degree n have n roots. For 10 points, name this procedure that takes an expression consisting of variables and coefficients and rewrites it as a product.
An application of a lattice basis reduction theorem resulted in the first efficient algorithm for doing this task and was invented by Lenstra, Lenstra, and Lovasz.
polynomial factorization [prompt on “factorization”; prompt on “root finding”; prompt on “decomposition”; do not accept “prime factorization”]