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Factoring polynomials with rational coefficients
 MATH. ANN
, 1982
"... In this paper we present a polynomialtime algorithm to solve the following problem: given a nonzero polynomial fe Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive polynomia ..."
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Cited by 955 (11 self)
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for factoring polynomials over small finite fields, combined with Hensel's lemma. Next we look for the irreducible factor h o of f in
Prime Ideals And Decompositions Of Modules
, 1999
"... this article, we discuss this question and more generally consider how the prime ideals behave in various general rings with certain properties. We also describe the prime ideal structure for certain specific rings. Although we have more to say when the ring is Noetherian, we include statements for ..."
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Cited by 1 (1 self)
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this article, we discuss this question and more generally consider how the prime ideals behave in various general rings with certain properties. We also describe the prime ideal structure for certain specific rings. Although we have more to say when the ring is Noetherian, we include statements
PRIMARY DECOMPOSITION OF ZERODIMENSIONAL IDEALS OVER FINITE FIELDS
, 2006
"... A new algorithm is presented for computing primary decomposition of zerodimensional ideals over finite fields. Like Berlekamp’s algorithm for univariate polynomials, the new method is based on the invariant subspace of the Frobenius map acting on the quotient algebra. The dimension of the invaria ..."
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Cited by 2 (0 self)
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A new algorithm is presented for computing primary decomposition of zerodimensional ideals over finite fields. Like Berlekamp’s algorithm for univariate polynomials, the new method is based on the invariant subspace of the Frobenius map acting on the quotient algebra. The dimension
Requirements for Internet Hosts  Application and Support
 STD 3, RFC 1123, IETF
, 1989
"... This RFC is an official specification for the Internet community. It incorporates by reference, amends, corrects, and supplements the primary protocol standards documents relating to hosts. Distribution of this document is unlimited. Summary This RFC is one of a pair that defines and discusses the r ..."
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Cited by 319 (1 self)
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This RFC is an official specification for the Internet community. It incorporates by reference, amends, corrects, and supplements the primary protocol standards documents relating to hosts. Distribution of this document is unlimited. Summary This RFC is one of a pair that defines and discusses the requirements for Internet host software. This RFC covers the application and support protocols; its companion RFC1122 covers the communication protocol layers: link layer, IP layer, and transport layer.
Prime Decomposition of Ideals in Polynomial Rings
"... Given a natural number n, one of the most fundamental problems in algebra is representing n as a product of primes. Likewise, given an ideal I in a polynomial ring k[x1,..., xn], one of the most fundamental operations that can be performed on I is to ..."
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Given a natural number n, one of the most fundamental problems in algebra is representing n as a product of primes. Likewise, given an ideal I in a polynomial ring k[x1,..., xn], one of the most fundamental operations that can be performed on I is to
Prime Ideals Of Finite Height In Polynomial Rings
"... . We investigate the structure of prime ideals of finite height in polynomial extension rings of a commutative unitary ring R. We consider the question of finite generation of such prime ideals. The valuative dimension of prime ideals of R plays an important role in our considerations. If X is an in ..."
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. We investigate the structure of prime ideals of finite height in polynomial extension rings of a commutative unitary ring R. We consider the question of finite generation of such prime ideals. The valuative dimension of prime ideals of R plays an important role in our considerations. If X
Network Centric Warfare: Developing and Leveraging Information Superiority
 Command and Control Research Program (CCRP), US DoD
, 2000
"... the mission of improving DoD’s understanding of the national security implications of the Information Age. Focusing upon improving both the state of the art and the state of the practice of command and control, the CCRP helps DoD take full advantage of the opportunities afforded by emerging technolo ..."
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Cited by 308 (5 self)
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the mission of improving DoD’s understanding of the national security implications of the Information Age. Focusing upon improving both the state of the art and the state of the practice of command and control, the CCRP helps DoD take full advantage of the opportunities afforded by emerging technologies. The CCRP pursues a broad program of research and analysis in information superiority, information operations, command and control theory, and associated operational concepts that enable us to leverage shared awareness to improve the effectiveness and efficiency of assigned missions. An important aspect of the CCRP program is its ability to serve as a bridge between the operational, technical, analytical, and educational communities. The CCRP provides leadership for the command and control research community by: n n
Factorization of Multivariate Polynomials over Finite Fields
, 1999
"... xv Zusammenfassung xvii 1 Introduction 1 1.1 Mathematical preliminaries . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Finite Fields . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Unique Factorization Domains . . . . . . . . . . . . . . . . . 3 1.1.3 Irreducibility . . . . . . . ..."
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Cited by 7 (1 self)
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xv Zusammenfassung xvii 1 Introduction 1 1.1 Mathematical preliminaries . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Finite Fields . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Unique Factorization Domains . . . . . . . . . . . . . . . . . 3 1.1.3 Irreducibility
New Algorithms for Finding Irreducible Polynomials over Finite Fields
 Mathematics of Computation
, 1990
"... . We present a new algorithm for finding an irreducible polynomial of specified degree over a finite field. Our algorithm is deterministic, and it runs in polynomial time for fields of small characteristic. We in fact prove the stronger result that the problem of finding irreducible polynomials of s ..."
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Cited by 83 (5 self)
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. We present a new algorithm for finding an irreducible polynomial of specified degree over a finite field. Our algorithm is deterministic, and it runs in polynomial time for fields of small characteristic. We in fact prove the stronger result that the problem of finding irreducible polynomials
SubfieldCompatible Polynomials over Finite Fields
"... Abstract. Polynomial functions over finite fields are important in computer science and electrical engineering in that they present a mathematical representation of arithmetic circuits. This paper establishes necessary and sufficient conditions for polynomial functions with coefficients in a finite ..."
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Abstract. Polynomial functions over finite fields are important in computer science and electrical engineering in that they present a mathematical representation of arithmetic circuits. This paper establishes necessary and sufficient conditions for polynomial functions with coefficients in a finite
Results 1  10
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