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Everything about Factorization of polynomials
Computational method
In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain. Polynomial factorization is one of the fundamental components of computer algebra systems. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Factorization of polynomialsA 5-minute orientation
- Skim a recent paper: Spectral theory for bounded banded matrices with positive bidiagonal factorization and mixed multiple orthogonal polynomialsInfluential work since 2022
- Pick up a classic book: Factorization of matrix and operator functionsThe most-reprinted book on the subject
- Read the landmark paper: Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum ComputerCited 6,084 times
- Go sideways: Irreducible polynomialA closely related topic
- Go sideways: Primitive part and contentA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
Factoring polynomials with rational coefficients
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
Factorization of polynomials over finite fields
Spectral factorization of Laurent polynomials
On Factorization of Trigonometric Polynomials
Factorization indices for matrix polynomials
Factorization of multivariate positive Laurent polynomials
🆕 Influential since 2022
Spectral theory for bounded banded matrices with positive bidiagonal factorization and mixed multiple orthogonal polynomials
A multi-Bennett 8R mechanism obtained from factorization of bivariate motion polynomials
An explicit Wiener–Hopf factorization algorithm for matrix polynomials and its exact realizations within ExactMPF package
Factorization of Singular Matrix Polynomials and Matrices with Circular Higher Rank Numerical Ranges
Certain Properties and Characterizations of Multivariable Hermite-Based Appell Polynomials via Factorization Method
📚 Books worth reading
Factorization of matrix and operator functionsH. Bart · 2008
Optimization of Objective FunctionsNinul Anatoly Sergeevich · 2009- 📕Integral Domains Inside Noetherian Power Series RingsWilliam J. Heinzer, Christel Rotthaus · 2021
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Irreducible polynomial In mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials.…
- Primitive part and content In algebra, the content of a nonzero polynomial with integer coefficients (or, more generally, with coefficients in a unique factorization domain) is the…
- Factorization In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object…
- Polynomial ring In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more…
- Polynomial greatest common divisor In algebra, the greatest common divisor (frequently abbreviated GCD or gcd) of two polynomials is a polynomial, of the highest possible degree, which is…
- Factorization of polynomials over finite fields In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition…
- Monic polynomial In algebra, a monic polynomial is a non-zero univariate polynomial (that is, a polynomial in a single variable) in which the leading coefficient (the coefficien…
- Square-free polynomial In mathematics, a square-free polynomial is a univariate polynomial (over a field or an integral domain) that has no multiple root in an algebraically…