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  2. Factorization - Wikipedia

    en.wikipedia.org/wiki/Factorization

    In elementary algebra, factoring a polynomial reduces the problem of finding its roots to finding the roots of the factors. Polynomials with coefficients in the integers or in a field possess the unique factorization property , a version of the fundamental theorem of arithmetic with prime numbers replaced by irreducible polynomials .

  3. Cantor–Zassenhaus algorithm - Wikipedia

    en.wikipedia.org/wiki/Cantor–Zassenhaus_algorithm

    The Cantor–Zassenhaus algorithm takes as input a square-free polynomial (i.e. one with no repeated factors) of degree n with coefficients in a finite field whose irreducible polynomial factors are all of equal degree (algorithms exist for efficiently factoring arbitrary polynomials into a product of polynomials satisfying these conditions, for instance, () / ((), ′ ()) is a squarefree ...

  4. Factorization of polynomials - Wikipedia

    en.wikipedia.org/wiki/Factorization_of_polynomials

    Modern algorithms and computers can quickly factor univariate polynomials of degree more than 1000 having coefficients with thousands of digits. [3] For this purpose, even for factoring over the rational numbers and number fields, a fundamental step is a factorization of a polynomial over a finite field.

  5. FOIL method - Wikipedia

    en.wikipedia.org/wiki/FOIL_method

    In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials [1] —hence the method may be referred to as the FOIL method.The word FOIL is an acronym for the four terms of the product:

  6. Factorization of polynomials over finite fields - Wikipedia

    en.wikipedia.org/wiki/Factorization_of...

    In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors.This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm.

  7. QR decomposition - Wikipedia

    en.wikipedia.org/wiki/QR_decomposition

    More generally, we can factor a complex m×n matrix A, with m ≥ n, as the product of an m×m unitary matrix Q and an m×n upper triangular matrix R.As the bottom (m−n) rows of an m×n upper triangular matrix consist entirely of zeroes, it is often useful to partition R, or both R and Q: