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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 961 (11 self)
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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
Note on 2rational fields
"... Résumé. Nous déterminons le groupe de Galois de la pro2extension 2ramifiée maximale d’un corps de nombres 2rationnel. Abstract. We compute the Galois group of the maximal 2ramified and complexified pro2extension of any 2rational number field. Nota. This short Note is motivated by the pap ..."
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Résumé. Nous déterminons le groupe de Galois de la pro2extension 2ramifiée maximale d’un corps de nombres 2rationnel. Abstract. We compute the Galois group of the maximal 2ramified and complexified pro2extension of any 2rational number field. Nota. This short Note is motivated
Affective Computing
, 1995
"... Recent neurological studies indicate that the role of emotion in human cognition is essential; emotions are not a luxury. Instead, emotions play a critical role in rational decisionmaking, in perception, in human interaction, and in human intelligence. These facts, combined with abilities computers ..."
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Cited by 1909 (43 self)
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Recent neurological studies indicate that the role of emotion in human cognition is essential; emotions are not a luxury. Instead, emotions play a critical role in rational decisionmaking, in perception, in human interaction, and in human intelligence. These facts, combined with abilities
Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 523 (3 self)
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CalabiYau manifolds V, W of dimension n (not necessarily equal to 3) one has dim H p (V, Ω q) = dim H n−p (W, Ω q). Physicists conjectured that conformal field theories associated with mirror varieties are equivalent. Mathematically, MS is considered now as a relation between numbers of rational curves
GromovWitten classes, quantum cohomology, and enumerative geometry
 Commun. Math. Phys
, 1994
"... The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological ..."
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Cited by 474 (3 self)
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Field Theories are defined, and it is proved that tree level theories are determined by their correlation functions. Application to counting rational curves on del Pezzo surfaces and projective spaces are given. Let V be a projective algebraic manifold. Methods of quantum field theory recently led to a
On the quantum symmetry of rational field theories, Theor
 Math. Phys
, 1994
"... The aim of this talk is to describe a possible understanding of the quantum symmetry of twodimensional (D = 2) rational quantum field theories (or D = 1 chiral rational conformal field theories). We start by briefly sketching the operatoralgebraic approach to relativistic quantum field theory (for ..."
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Cited by 2 (1 self)
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The aim of this talk is to describe a possible understanding of the quantum symmetry of twodimensional (D = 2) rational quantum field theories (or D = 1 chiral rational conformal field theories). We start by briefly sketching the operatoralgebraic approach to relativistic quantum field theory
LinearDecoding of STBCs from Field Extensions of the Rational Field
 in Proc. IEEE Int. Symp. Inform. Theory,(ISIT 2002
, 2002
"... An n xl (l_> n) space time block code (STBC) C over a complex signal set S con sists of a finite number of n x I matrices with elements from $. For quasistatic, fiat fading channels a primary performance index of C is the minimum of the rank of the difference of any two codeword matrices, calle ..."
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with cycloromic field extensions of the rational field several families of codes over a wide range of signal sets can be constructed [18, 20]. As spe cial cases, our method gives optimal STBCs over symmetric mPSK signal sets (marbitrary) for a wide range of values of the number of antennas n. In this paper, we
The adaptive nature of human categorization
 Psychological Review
, 1991
"... A rational model of human categorization behavior is presented that assumes that categorization reflects the derivation of optimal estimates of the probability of unseen features of objects. A Bayesian analysis is performed of what optimal estimations would be if categories formed a disjoint partiti ..."
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Cited by 344 (2 self)
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nition. The term rational derives from similar "rationalman" analyses in economics. Rational analyses in other fields are sometimes called adaptationist analyses. Basically, they are efforts to explain the behavior in some domain on the assumption that the behavior is optimized with respect
Results 1  10
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5,367