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In mathematics, a polynomial decomposition expresses a polynomial f as the functional composition of polynomials g and h, where g and h have degree greater than 1; it is an algebraic functional decomposition. Algorithms are known for decomposing univariate polynomials in polynomial time.
A decomposition with local endomorphism rings [5] (cf. #Azumaya's theorem): a direct sum of modules whose endomorphism rings are local rings (a ring is local if for each element x, either x or 1 − x is a unit). Serial decomposition: a direct sum of uniserial modules (a module is uniserial if the lattice of submodules is a finite chain [6]).
In mathematics, the Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many primary ideals (which are related to, but not quite the same as, powers of prime ideals).
For example, the p i may be the factors of the square-free factorization of g. When K is the field of rational numbers , as it is typically the case in computer algebra , this allows to replace factorization by greatest common divisor computation for computing a partial fraction decomposition.
This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector spaces and through matrices. Linear equations
Decomposition method is a generic term for solutions of various problems and design of algorithms in which the basic idea is to decompose the problem into subproblems. The term may specifically refer to: Decomposition method (constraint satisfaction) in constraint satisfaction
Senate Democrats held a closed-door election Tuesday morning to name who would fill their top leadership posts for the next two years, most notably filling the No. 3 position held by a retiring ...
The RQ decomposition transforms a matrix A into the product of an upper triangular matrix R (also known as right-triangular) and an orthogonal matrix Q. The only difference from QR decomposition is the order of these matrices. QR decomposition is Gram–Schmidt orthogonalization of columns of A, started from the first column.