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165
The Euclide algorithm in dimension n
, 1996
"... We present in this paper an algorithm which is a natural extension in dimension n of the Euclide algorithm computing the greatest common divisor of two integers. Let H be a subgroup of Z^n, given by a set of generators... ..."
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Cited by 10 (0 self)
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We present in this paper an algorithm which is a natural extension in dimension n of the Euclide algorithm computing the greatest common divisor of two integers. Let H be a subgroup of Z^n, given by a set of generators...
The Euclid algorithm is “totally ” gaussian
"... We consider Euclid’s gcd algorithm for two integers (p, q) with 1 ≤ p ≤ q ≤ N, with the uniform distribution on input pairs. We study the distribution of the total cost of execution of the algorithm for an additive cost function d on the set of possible digits, asymptotically for N → ∞. For any addi ..."
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We consider Euclid’s gcd algorithm for two integers (p, q) with 1 ≤ p ≤ q ≤ N, with the uniform distribution on input pairs. We study the distribution of the total cost of execution of the algorithm for an additive cost function d on the set of possible digits, asymptotically for N → ∞. For any
The Mixed Binary Euclid Algorithm
"... We present a new GCD algorithm for two integers that combines both the Euclidean and the binary gcd approaches. We give its worst case time analysis and prove that its bittime complexity is still O(n 2) for two nbit integers. However, our preliminar experiments show that it is very fast for small ..."
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We present a new GCD algorithm for two integers that combines both the Euclidean and the binary gcd approaches. We give its worst case time analysis and prove that its bittime complexity is still O(n 2) for two nbit integers. However, our preliminar experiments show that it is very fast
Analysis of fast versions of the Euclid Algorithm
 Proceedings of ANALCO’07, Janvier 2007
"... There exist fast variants of the gcd algorithm which are all based on principles due to Knuth and Schönhage. On inputs of size n, these algorithms use a Divide and Conquer approach, perform FFT multiplications and stop the recursion at a depth slightly smaller than lg n. A rough estimate of the wors ..."
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–complexity on random inputs of size n is Θ(n(log n) 2 log log n), with a precise remainder term. We view such a fast algorithm as a sequence of what we call interrupted algorithms, and we obtain three results about the (plain) Euclid Algorithm which may be of independent interest. We precisely describe the evolution
Abstract Analysis of fast versions of the Euclid Algorithm
"... There exist fast variants of the gcd algorithm which are all based on principles due to Knuth and Schönhage. On inputs of size n, these algorithms use a Divide and Conquer approach, perform FFT multiplications and stop the recursion at a depth slightly smaller than lg n. A rough estimate of the wors ..."
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–complexity on random inputs of size n is Θ(n(log n) 2 log log n), with a precise remainder term. We view such a fast algorithm as a sequence of what we call interrupted algorithms, and we obtain three results about the (plain) Euclid Algorithm which may be of independent interest. We precisely describe the evolution
University of Białystok Recursive Euclide Algorithm 1
"... Summary. The earlier SCM computer did not contain recursive function, so Trybulec and Nakamura proved the correctness of the Euclid’s algorithm only by way of an iterative program. However, the recursive method is a very important programming method, furthermore, for some algorithms, for example Qui ..."
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Summary. The earlier SCM computer did not contain recursive function, so Trybulec and Nakamura proved the correctness of the Euclid’s algorithm only by way of an iterative program. However, the recursive method is a very important programming method, furthermore, for some algorithms, for example
Sharp estimates for the main parameters of the Euclid Algorithm
 Proceedings of LATIN’06, LNCS 3887
"... Abstract. We provide sharp estimates for the probabilistic behaviour of the main parameters of the Euclid algorithm, and we study in particular the distribution of the bitcomplexity which involves two main parameters: digit–costs and length of continuants. We perform a “dynamical analysis ” which h ..."
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Cited by 5 (5 self)
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Abstract. We provide sharp estimates for the probabilistic behaviour of the main parameters of the Euclid algorithm, and we study in particular the distribution of the bitcomplexity which involves two main parameters: digit–costs and length of continuants. We perform a “dynamical analysis ” which
Sharp Estimates for the Main Parameters of the Euclid Algorithm
"... Abstract. We provide sharp estimates for the probabilistic behaviour of the main parameters of the Euclid algorithm, and we study in particular the distribution of the bitcomplexity which involves two main parameters: digit–costs and length of continuants. We perform a “dynamical analysis ” which ..."
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Abstract. We provide sharp estimates for the probabilistic behaviour of the main parameters of the Euclid algorithm, and we study in particular the distribution of the bitcomplexity which involves two main parameters: digit–costs and length of continuants. We perform a “dynamical analysis
Gaussian laws for the main parameters of the Euclid algorithms
 Algorithmica
, 2008
"... Abstract. We provide sharp estimates for the probabilistic behaviour of the main parameters of the Euclid Algorithms, both on polynomials and on integer numbers. We study in particular the distribution of the bitcomplexity which involves two main parameters: digit–costs and length of remainders. We ..."
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Cited by 4 (2 self)
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Abstract. We provide sharp estimates for the probabilistic behaviour of the main parameters of the Euclid Algorithms, both on polynomials and on integer numbers. We study in particular the distribution of the bitcomplexity which involves two main parameters: digit–costs and length of remainders
FINE COSTS FOR THE EUCLID ALGORITHM ON POLYNOMIALS AND FAREY MAPS
"... Abstract. This paper studies digitcost functions for the Euclid algorithm on polynomials with coefficients in a finite field, in terms of the number of operations performed on the finite field Fq. The usual bitcomplexity is defined with respect to the degree of the quotients; we focus here on a no ..."
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Cited by 1 (1 self)
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Abstract. This paper studies digitcost functions for the Euclid algorithm on polynomials with coefficients in a finite field, in terms of the number of operations performed on the finite field Fq. The usual bitcomplexity is defined with respect to the degree of the quotients; we focus here on a
Results 1  10
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165