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  2. List of NP-complete problems - Wikipedia

    en.wikipedia.org/wiki/List_of_NP-complete_problems

    Route inspection problem (also called Chinese postman problem) for mixed graphs (having both directed and undirected edges). The program is solvable in polynomial time if the graph has all undirected or all directed edges. Variants include the rural postman problem. [3]: ND25, ND27 Clique cover problem [2] [3]: GT17

  3. NP-completeness - Wikipedia

    en.wikipedia.org/wiki/NP-completeness

    A polynomial-time problem can be very difficult to solve in practice if the polynomial's degree or constants are large enough. In addition, information-theoretic security provides cryptographic methods that cannot be broken even with unlimited computing power. "A large-scale quantum computer would be able to efficiently solve NP-complete problems."

  4. Horner's method - Wikipedia

    en.wikipedia.org/wiki/Horner's_method

    In mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation.Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by Horner himself, and can be traced back many hundreds of years to Chinese and Persian mathematicians. [1]

  5. System of polynomial equations - Wikipedia

    en.wikipedia.org/wiki/System_of_polynomial_equations

    To work with a polynomial system whose coefficients belong to a number field, it suffices to consider this generator as a new variable and to add the equation of the generator to the equations of the system. Thus solving a polynomial system over a number field is reduced to solving another system over the rational numbers.

  6. Category:Polynomial-time problems - Wikipedia

    en.wikipedia.org/wiki/Category:Polynomial-time...

    This category is for combinatorial optimization problems solvable in polynomial time. Pages in category "Polynomial-time problems" The following 18 pages are in this category, out of 18 total.

  7. Polynomial long division - Wikipedia

    en.wikipedia.org/wiki/Polynomial_long_division

    If one root r of a polynomial P(x) of degree n is known then polynomial long division can be used to factor P(x) into the form (x − r)Q(x) where Q(x) is a polynomial of degree n − 1. Q ( x ) is simply the quotient obtained from the division process; since r is known to be a root of P ( x ), it is known that the remainder must be zero.