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  2. 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]

  3. CLMUL instruction set - Wikipedia

    en.wikipedia.org/wiki/CLMUL_instruction_set

    Mathematically, the instruction implements multiplication of polynomials over the finite field GF(2) where the bitstring … represents the polynomial + + + +. The CLMUL instruction also allows a more efficient implementation of the closely related multiplication of larger finite fields GF(2 k ) than the traditional instruction set.

  4. Polynomial evaluation - Wikipedia

    en.wikipedia.org/wiki/Polynomial_evaluation

    Horner's method evaluates a polynomial using repeated bracketing: + + + + + = + (+ (+ (+ + (+)))). This method reduces the number of multiplications and additions to just Horner's method is so common that a computer instruction "multiply–accumulate operation" has been added to many computer processors, which allow doing the addition and multiplication operations in one combined step.

  5. Carry-less product - Wikipedia

    en.wikipedia.org/wiki/Carry-less_product

    The elements of GF(2 n), i.e. a finite field whose order is a power of two, are usually represented as polynomials in GF(2)[X]. Multiplication of two such field elements consists of multiplication of the corresponding polynomials, followed by a reduction with respect to some irreducible polynomial which is taken from the construction of the ...

  6. Distributive property - Wikipedia

    en.wikipedia.org/wiki/Distributive_property

    Therefore, one would say that multiplication distributes over addition. This basic property of numbers is part of the definition of most algebraic structures that have two operations called addition and multiplication, such as complex numbers, polynomials, matrices, rings, and fields.

  7. Complex conjugate root theorem - Wikipedia

    en.wikipedia.org/wiki/Complex_conjugate_root_theorem

    Since every polynomial with complex coefficients can be factored into 1st-degree factors (that is one way of stating the fundamental theorem of algebra), it follows that every polynomial with real coefficients can be factored into factors of degree no higher than 2: just 1st-degree and quadratic factors.

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