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Algebraic Factorization and GCD Computation
"... This chapter describes several algorithms for factorization and GCD computation of polynomials over algebraic extension fields. These algorithms are common in using the characteristic set method introduced in the previous chapters. Some performance comparisons between these algorithms are reported. ..."
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This chapter describes several algorithms for factorization and GCD computation of polynomials over algebraic extension fields. These algorithms are common in using the characteristic set method introduced in the previous chapters. Some performance comparisons between these algorithms are reported
Fast parallel matrix and GCD computations
 IN PROC. OF THE 23RD ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS’82
, 1982
"... Parallel algorithms to compute the determinant and characteristic polynomial of matrices and the gcd of polynomials are presented. The rank of matrices and solutions of arbitrary systems of linear equations are computed by parallel Las Vegas algorithms. All algorithms work over arbitrary fields. The ..."
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Cited by 47 (1 self)
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Parallel algorithms to compute the determinant and characteristic polynomial of matrices and the gcd of polynomials are presented. The rank of matrices and solutions of arbitrary systems of linear equations are computed by parallel Las Vegas algorithms. All algorithms work over arbitrary fields
A modular reduction for GCD computation
, 2002
"... Most of integer GCD algorithms use one or several basic transformations which reduce at each step the size of the inputs integers u and v.These transformations called reductions are studied in a general framework.Our investigations lead to many applications such as a new integer division and a new r ..."
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Cited by 4 (0 self)
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Most of integer GCD algorithms use one or several basic transformations which reduce at each step the size of the inputs integers u and v.These transformations called reductions are studied in a general framework.Our investigations lead to many applications such as a new integer division and a new
GCD Computations Modulo Regular Chains
, 2010
"... The computation of triangular decompositions involves two fundamental operations: polynomial GCDs modulo regular chains and regularity test modulo saturated ideals. We propose new algorithms for these core operations based on modular methods and fast polynomial arithmetic. We rely on new results con ..."
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The computation of triangular decompositions involves two fundamental operations: polynomial GCDs modulo regular chains and regularity test modulo saturated ideals. We propose new algorithms for these core operations based on modular methods and fast polynomial arithmetic. We rely on new results
Polynomial gcd computations over towers of algebraic extensions
 IN PROC. AAECC11
, 1995
"... ..."
ON SCHÖNHAGE’S ALGORITHM AND SUBQUADRATIC INTEGER GCD COMPUTATION
"... Abstract. We describe a new subquadratic lefttoright gcd algorithm, inspired by Schönhage’s algorithm for reduction of binary quadratic forms, and compare it to the first subquadratic gcd algorithm discovered by Knuth and Schönhage, and to the binary recursive gcd algorithm of Stehlé and Zimmerman ..."
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Abstract. We describe a new subquadratic lefttoright gcd algorithm, inspired by Schönhage’s algorithm for reduction of binary quadratic forms, and compare it to the first subquadratic gcd algorithm discovered by Knuth and Schönhage, and to the binary recursive gcd algorithm of Stehlé
AutoConfigurable Array for GCD Computation (Extended Abstract)
, 1997
"... A novel onedirectional passthrough array for the computation of integer greatest common divisor is designed and implemented on Atmel FPGA. The design is based on the plusminus GCD algorithm and works in LSB pipelined manner. In contrast with previous designs, the length of the new array is indepe ..."
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A novel onedirectional passthrough array for the computation of integer greatest common divisor is designed and implemented on Atmel FPGA. The design is based on the plusminus GCD algorithm and works in LSB pipelined manner. In contrast with previous designs, the length of the new array
A New Algorithm and Refined Bounds for Extended Gcd Computation
, 1996
"... . Extended gcd computation is interesting itself. It also plays a fundamental role in other calculations. We present a new algorithm for solving the extended gcd problem. This algorithm has a particularly simple description and is practical. It also provides refined bounds on the size of the multipl ..."
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Cited by 5 (2 self)
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. Extended gcd computation is interesting itself. It also plays a fundamental role in other calculations. We present a new algorithm for solving the extended gcd problem. This algorithm has a particularly simple description and is practical. It also provides refined bounds on the size
Algorithms for Polynomial GCD Computation over Algebraic Function Fields
 Proceedings of ISSAC ’04, ACM Press
, 2004
"... Let L be an algebraic function field in k ≥ 0 parameters t1,...,tk. Let f1,f2 be nonzero polynomials in L[x]. We give two algorithms for computing their gcd. The first,a modular GCD algorithm,is an extension of the modular GCD algorithm of Brown for Z[x1,...,xn] andEncarnacion for Q(α)[x] to functi ..."
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Cited by 10 (7 self)
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Let L be an algebraic function field in k ≥ 0 parameters t1,...,tk. Let f1,f2 be nonzero polynomials in L[x]. We give two algorithms for computing their gcd. The first,a modular GCD algorithm,is an extension of the modular GCD algorithm of Brown for Z[x1,...,xn] andEncarnacion for Q
Results 1  10
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