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672
Simulating Physics with Computers
 SIAM Journal on Computing
, 1982
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 601 (1 self)
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A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration
Quantum measurements and the Abelian stabilizer problem
"... We present a polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm. Thus we extend famous Shor’s results [7]. Our method is based on a procedure for measuring an eigenvalue of a unitary operator. Another application of this procedure ..."
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Cited by 194 (0 self)
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We present a polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm. Thus we extend famous Shor’s results [7]. Our method is based on a procedure for measuring an eigenvalue of a unitary operator. Another application
The projective Noether Maple package: computing the dimension of a projective variety. Manuscript available at ftp://medicis.polytechnique.fr/pub/publications/lecerf
"... Recent theoretical advances in elimination theory use straightline programs as a datastructure to represent multivariate polynomials. We present here the Projective Noether Package which is a Maple implementation of one of these new algorithms, yielding as a byproduct a computation of the dimension ..."
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Cited by 9 (2 self)
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Recent theoretical advances in elimination theory use straightline programs as a datastructure to represent multivariate polynomials. We present here the Projective Noether Package which is a Maple implementation of one of these new algorithms, yielding as a byproduct a computation
A Gröbner free alternative for polynomial system solving
 Journal of Complexity
, 2001
"... Given a system of polynomial equations and inequations with coefficients in the field of rational numbers, we show how to compute a geometric resolution of the set of common roots of the system over the field of complex numbers. A geometric resolution consists of a primitive element of the algebraic ..."
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Cited by 107 (19 self)
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Given a system of polynomial equations and inequations with coefficients in the field of rational numbers, we show how to compute a geometric resolution of the set of common roots of the system over the field of complex numbers. A geometric resolution consists of a primitive element
On triangular decompositions of algebraic varieties
 Presented at the MEGA2000 Conference
, 1999
"... We propose an efficient algorithm for computing triangular decompositions of algebraic varieties. It is based on an incremental process and produces components in order of decreasing dimension. The combination of these two major features is obtained by means of lazy evaluation techniques and a lifti ..."
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Cited by 81 (35 self)
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We propose an efficient algorithm for computing triangular decompositions of algebraic varieties. It is based on an incremental process and produces components in order of decreasing dimension. The combination of these two major features is obtained by means of lazy evaluation techniques and a
Quantum Programming
 In Mathematics of Program Construction
, 1999
"... In this paper a programming language is presented for the expression of quantum algorithms. It contains the features required to program a `universal' quantum computer (including initialisation and observation), has a formal semantics and body of laws, and provides a renement calculus supportin ..."
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Cited by 81 (3 self)
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In this paper a programming language is presented for the expression of quantum algorithms. It contains the features required to program a `universal' quantum computer (including initialisation and observation), has a formal semantics and body of laws, and provides a renement calculus
The Projective Noether Package  User's Manual
, 1998
"... Let V be a projective variety given by a list of homogeneous polynomials. We are interested in computing its dimension r. So far the most efficient implemented algorithms rely on Gröbner basis computations. The present paper reports on an implementation done by M. Giusti , G. Lecerf , Joel Marchand ..."
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Cited by 1 (0 self)
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Let V be a projective variety given by a list of homogeneous polynomials. We are interested in computing its dimension r. So far the most efficient implemented algorithms rely on Gröbner basis computations. The present paper reports on an implementation done by M. Giusti , G. Lecerf , Joel Marchand
Counting Points on Hyperelliptic Curves over Finite Fields
"... . We describe some algorithms for computing the cardinality of hyperelliptic curves and their Jacobians over finite fields. They include several methods for obtaining the result modulo small primes and prime powers, in particular an algorithm `a la Schoof for genus 2 using Cantor 's divisio ..."
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Cited by 66 (8 self)
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. We describe some algorithms for computing the cardinality of hyperelliptic curves and their Jacobians over finite fields. They include several methods for obtaining the result modulo small primes and prime powers, in particular an algorithm `a la Schoof for genus 2 using Cantor &apos
A RECOMBINATION ALGORITHM FOR THE DECOMPOSITION OF MULTIVARIATE RATIONAL FUNCTIONS
, 2010
"... In this paper we show how we can compute in a deterministic way the decomposition of a multivariate rational function with a recombination strategy. The key point of our recombination strategy is the used of Darboux polynomials. We study the complexity of this strategy and we show that this method i ..."
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Cited by 4 (1 self)
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improves the previous ones. In appendix, we explain how the strategy proposed recently by J. Berthomieu and G. Lecerf for the sparse factorization can be used in the decomposition setting. Then we deduce a decomposition algorithm in the sparse bivariate case and we give its complexity.
Results 1  10
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672