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  2. Extended Euclidean algorithm - Wikipedia

    en.wikipedia.org/wiki/Extended_Euclidean_algorithm

    For example, if the polynomial used to define the finite field GF(2 8) is p = x 8 + x 4 + x 3 + x + 1, and a = x 6 + x 4 + x + 1 is the element whose inverse is desired, then performing the algorithm results in the computation described in the following table. Let us recall that in fields of order 2 n, one has −z = z and z + z = 0 for every ...

  3. Divide-and-conquer algorithm - Wikipedia

    en.wikipedia.org/wiki/Divide-and-conquer_algorithm

    Divide-and-conquer approach to sort the list (38, 27, 43, 3, 9, 82, 10) in increasing order. Upper half: splitting into sublists; mid: a one-element list is trivially sorted; lower half: composing sorted sublists. The divide-and-conquer paradigm is often used to find an optimal solution of a problem. Its basic idea is to decompose a given ...

  4. Separable extension - Wikipedia

    en.wikipedia.org/wiki/Separable_extension

    An arbitrary polynomial f with coefficients in some field F is said to have distinct roots or to be square-free if it has deg f roots in some extension field.For instance, the polynomial g(X) = X 2 − 1 has precisely deg g = 2 roots in the complex plane; namely 1 and −1, and hence does have distinct roots.

  5. GF (2) - Wikipedia

    en.wikipedia.org/wiki/GF(2)

    every element x of GF(2) satisfies x 2 = x (i.e. is idempotent with respect to multiplication); this is an instance of Fermat's little theorem. GF(2) is the only field with this property (Proof: if x 2 = x, then either x = 0 or x ≠ 0. In the latter case, x must have a multiplicative inverse, in which case dividing both sides by x gives x = 1 ...

  6. Purely inseparable extension - Wikipedia

    en.wikipedia.org/wiki/Purely_inseparable_extension

    An algebraic extension is a purely inseparable extension if and only if for every , the minimal polynomial of over F is not a separable polynomial. [1] If F is any field, the trivial extension is purely inseparable; for the field F to possess a non-trivial purely inseparable extension, it must be imperfect as outlined in the above section.

  7. Chegg - Wikipedia

    en.wikipedia.org/wiki/Chegg

    Chegg, Inc., is an American education technology company based in Santa Clara, California. It provides homework help, digital and physical textbook rentals, textbooks, online tutoring, and other student services. [2] The company was launched in 2006, and began trading publicly on the New York Stock Exchange in November 2013.

  8. Realty Income (O) Q4 2024 Earnings Call Transcript - AOL

    www.aol.com/realty-income-o-q4-2024-230015215.html

    Image source: The Motley Fool. Realty Income (NYSE: O) Q4 2024 Earnings Call Feb 25, 2025, 2:00 p.m. ET. Contents: Prepared Remarks. Questions and Answers. Call ...

  9. Simple extension - Wikipedia

    en.wikipedia.org/wiki/Simple_extension

    A field extension L/K is called a simple extension if there exists an element θ in L with L = K ( θ ) . {\displaystyle L=K(\theta ).} This means that every element of L can be expressed as a rational fraction in θ , with coefficients in K ; that is, it is produced from θ and elements of K by the field operations +, −, •, / .