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  2. Partial fraction decomposition - Wikipedia

    en.wikipedia.org/wiki/Partial_fraction_decomposition

    When K is the field of real numbers, some of the p i may be quadratic, so, in the partial fraction decomposition, quotients of linear polynomials by powers of quadratic polynomials may also occur. In the preceding theorem, one may replace "distinct irreducible polynomials" by " pairwise coprime polynomials that are coprime with their derivative".

  3. Integer factorization - Wikipedia

    en.wikipedia.org/wiki/Integer_factorization

    To factorize a small integer n using mental or pen-and-paper arithmetic, the simplest method is trial division: checking if the number is divisible by prime numbers 2, 3, 5, and so on, up to the square root of n. For larger numbers, especially when using a computer, various more sophisticated factorization algorithms are more efficient.

  4. Lie group decomposition - Wikipedia

    en.wikipedia.org/wiki/Lie_group_decomposition

    The Jordan–Chevalley decomposition of an element in algebraic group as a product of semisimple and unipotent elements; The Bruhat decomposition = of a semisimple algebraic group into double cosets of a Borel subgroup can be regarded as a generalization of the principle of Gauss–Jordan elimination, which generically writes a matrix as the product of an upper triangular matrix with a lower ...

  5. Quotient group - Wikipedia

    en.wikipedia.org/wiki/Quotient_group

    When dividing 12 by 3 one obtains the result 4 because one can regroup 12 objects into 4 subcollections of 3 objects. The quotient group is the same idea, although one ends up with a group for a final answer instead of a number because groups have more structure than an arbitrary collection of objects: in the quotient ⁠ G / N {\displaystyle G ...

  6. Arithmetic - Wikipedia

    en.wikipedia.org/wiki/Arithmetic

    Arithmetic systems can be distinguished based on the type of numbers they operate on. Integer arithmetic is about calculations with positive and negative integers. Rational number arithmetic involves operations on fractions of integers. Real number arithmetic is about calculations with real numbers, which include both rational and irrational ...

  7. Highly composite number - Wikipedia

    en.wikipedia.org/wiki/Highly_composite_number

    Note: Numbers in bold are themselves highly composite numbers. Only the twentieth highly composite number 7560 (= 3 × 2520) is absent. 10080 is a so-called 7-smooth number (sequence A002473 in the OEIS ) .

  8. Stocks in these 4 sectors are best positioned to rally into ...

    www.aol.com/stocks-4-sectors-best-positioned...

    UBS recommends tech, financials, industrials and utilities stocks going into 2025, citing continued AI growth and pro-business policies under Trump.

  9. Polynomial decomposition - Wikipedia

    en.wikipedia.org/wiki/Polynomial_decomposition

    Algorithms are known for decomposing univariate polynomials in polynomial time. Polynomials which are decomposable in this way are composite polynomials ; those which are not are indecomposable polynomials or sometimes prime polynomials [ 1 ] (not to be confused with irreducible polynomials , which cannot be factored into products of polynomials ).