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Modern algorithms and computers can quickly factor univariate polynomials of degree more than 1000 having coefficients with thousands of digits. [3] For this purpose, even for factoring over the rational numbers and number fields, a fundamental step is a factorization of a polynomial over a finite field.
The polynomial x 2 + cx + d, where a + b = c and ab = d, can be factorized into (x + a)(x + b).. In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches of mathematics.Due to the applicability of the concept in other topics of mathematics and sciences like computer science there has been a resurgence of interest in finite fields and this is partly due to important applications in coding theory and cryptography.
with a corresponding factor graph shown on the right. Observe that the factor graph has a cycle. If we merge (,) (,) into a single factor, the resulting factor graph will be a tree. This is an important distinction, as message passing algorithms are usually exact for trees, but only approximate for graphs with cycles.
Applicable to: square, hermitian, positive definite matrix Decomposition: =, where is upper triangular with real positive diagonal entries Comment: if the matrix is Hermitian and positive semi-definite, then it has a decomposition of the form = if the diagonal entries of are allowed to be zero
American YouTube personality MrBeast is the most-subscribed channel on YouTube, with 371 million subscribers as of March 2025.. A subscriber to a channel on the American video-sharing platform YouTube is a user who has chosen to receive the channel's content by clicking on that channel's "Subscribe" button, and each user's subscription feed consists of videos published by channels to which the ...
Explained is an American documentary television series on the streaming service Netflix. The show is produced by Vox Media [2] and is based on Vox's previous YouTube video series which followed a similar format. [3] The show's episodes averaged between 16 and 24 minutes, with each focusing on a different topic. [4]
The channel originally began with Dadbeh presenting theories regarding the mysteries that were set up by Star Wars: The Force Awakens.From there, the channel has grown and evolved over the years, with recurring motifs and series such as Star Wars Explained, a narration of many of the Star Wars comics, animated (and often humorous) fan fiction, and many others.