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  2. Partition function (number theory) - Wikipedia

    en.wikipedia.org/wiki/Partition_function_(number...

    This expands the product into a sum of monomials of the form for some sequence of coefficients , only finitely many of which can be non-zero. The exponent of the term is n = ∑ i a i {\textstyle n=\sum ia_{i}} , and this sum can be interpreted as a representation of n {\displaystyle n} as a partition into a i {\displaystyle a_{i}} copies of ...

  3. Gröbner basis - Wikipedia

    en.wikipedia.org/wiki/Gröbner_basis

    Once a monomial ordering is fixed, the terms of a polynomial (product of a monomial with its nonzero coefficient) are naturally ordered by decreasing monomials (for this order). This makes the representation of a polynomial as a sorted list of pairs coefficient–exponent vector a canonical representation of the polynomials (that is, two ...

  4. Computational complexity of mathematical operations - Wikipedia

    en.wikipedia.org/wiki/Computational_complexity...

    Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.

  5. Monomial order - Wikipedia

    en.wikipedia.org/wiki/Monomial_order

    When a monomial order has been chosen, the leading monomial is the largest u in S, the leading coefficient is the corresponding c u, and the leading term is the corresponding c u u. Head monomial/coefficient/term is sometimes used as a synonym of "leading". Some authors use "monomial" instead of "term" and "power product" instead of "monomial".

  6. Polynomial long division - Wikipedia

    en.wikipedia.org/wiki/Polynomial_long_division

    This pen-and-paper method uses the same algorithm as polynomial long division, but mental calculation is used to determine remainders. This requires less writing, and can therefore be a faster method once mastered. The division is at first written in a similar way as long multiplication with the dividend at the top, and the divisor below it.

  7. Buchberger's algorithm - Wikipedia

    en.wikipedia.org/wiki/Buchberger's_algorithm

    In the theory of multivariate polynomials, Buchberger's algorithm is a method for transforming a given set of polynomials into a Gröbner basis, which is another set of polynomials that have the same common zeros and are more convenient for extracting information on these common zeros.

  8. Ruffini's rule - Wikipedia

    en.wikipedia.org/wiki/Ruffini's_rule

    In mathematics, Ruffini's rule is a method for computation of the Euclidean division of a polynomial by a binomial of the form x – r. It was described by Paolo Ruffini in 1809. [ 1 ] The rule is a special case of synthetic division in which the divisor is a linear factor.

  9. Monomial - Wikipedia

    en.wikipedia.org/wiki/Monomial

    In mathematics, a monomial is, roughly speaking, a polynomial which has only one term.Two definitions of a monomial may be encountered: A monomial, also called a power product or primitive monomial, [1] is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly with repetitions. [2]