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  2. Multiplicity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Multiplicity_(mathematics)

    This means that 1 is a root of multiplicity 2, and −4 is a simple root (of multiplicity 1). The multiplicity of a root is the number of occurrences of this root in the complete factorization of the polynomial, by means of the fundamental theorem of algebra.

  3. Hilbert–Samuel function - Wikipedia

    en.wikipedia.org/wiki/Hilbert–Samuel_function

    This integer is called the multiplicity of the ideal . When I = m {\displaystyle I=m} is the maximal ideal of A {\displaystyle A} , one also says e {\displaystyle e} is the multiplicity of the local ring A {\displaystyle A} .

  4. Polynomial - Wikipedia

    en.wikipedia.org/wiki/Polynomial

    In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms.

  5. Root-finding algorithm - Wikipedia

    en.wikipedia.org/wiki/Root-finding_algorithm

    Graeffe's method – Algorithm for finding polynomial roots; Lill's method – Graphical method for the real roots of a polynomial; MPSolve – Software for approximating the roots of a polynomial with arbitrarily high precision; Multiplicity (mathematics) – Number of times an object must be counted for making true a general formula

  6. Polynomial expansion - Wikipedia

    en.wikipedia.org/wiki/Polynomial_expansion

    In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by the equivalent sum of products, continuing until the expression becomes a ...

  7. Ukrainian mayor laid to rest after death in Russian captivity

    www.aol.com/news/ukrainian-mayor-laid-rest-death...

    As Russian troops approached Dniprorudne in their February 2022 invasion of Ukraine, the city's long-term mayor Yevhen Matvieiev could have fled to safety. Instead, he stayed behind to coordinate ...

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