On polynomial factorization
نویسندگان
چکیده
منابع مشابه
On the Complexity of Noncommutative Polynomial Factorization
In this paper we study the complexity of factorization of polynomials in the free noncommutative ring F〈x1, x2, . . . , xn〉 of polynomials over the field F and noncommuting variables x1, x2, . . . , xn. Our main results are the following: • Although F〈x1, . . . , xn〉 is not a unique factorization ring, we note that variabledisjoint factorization in F〈x1, . . . , xn〉 has the uniqueness property....
متن کاملFactorization in Polynomial Rings
We begin with some basic definitions. Definition 1.1. Let f, g ∈ F [x]. We say that f divides g, written f ∣∣g, if there exists an h ∈ F [x] such that g = fh, i.e. g is a multiple of f . Thus, for example, every f ∈ F [x] divides the zero polynomial 0, but g is divisible by 0 ⇐⇒ g = 0. By definition, f is a unit ⇐⇒ f ∣∣1. Recall also that the group of units (F [x])∗ of the ring F [x] is F ∗, th...
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Joachim von zur Gathen has proposed a challenge for factoring univariate poly-nomials over nite elds to evaluate the practicability of current factorization algorithms (\A Factorization Challenge", SIGSAM Bulletin 26(2):22-24, 1992). More recently, Victor Shoup has proposed an alternate family of polynomials with a similar goal in mind. Our eeort is to take these challenges on using the general...
متن کاملPolynomial factorization over F2
We describe algorithms for polynomial factorization over the binary field F2, and their implementation. They allow polynomials of degree up to 250 000 to be factored in about one day of CPU time, distributing the work on two processors.
متن کاملPolynomial Factorization 1987-1991
Algorithms invented in the past 25 years make it possible on a computer to efficiently factor a polynomial in one, several, or many variables with coefficients from a certain field, such as a finite field or the rational, real, or complex numbers. I have surveyed work up to 1986 in the papers (Kaltofen 1982 and 1990a). This article discusses important developments of the past five years; I also...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1985
ISSN: 0035-7596
DOI: 10.1216/rmj-1985-15-2-657