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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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to be factored, n = deg(f) is the degree of f, and for a polynomial ~ a ~ i with real coefficients a i. i An outline of the algorithm is as follows. First we find, for a suitable small prime number p, a padic irreducible factor h of f, to a certain precision. This is done with Berlekamp's algorithm
A theory of social comparison processes,”
 Human Relations,
, 1954
"... In this paper we shall present a further development of a previously published theory concerning opinion influence processes in social groups (7). This further development has enabled us to extend the theory to deal with other areas, in addition to opinion formation, in which social comparison is i ..."
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Cited by 1318 (0 self)
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In this paper we shall present a further development of a previously published theory concerning opinion influence processes in social groups (7). This further development has enabled us to extend the theory to deal with other areas, in addition to opinion formation, in which social comparison
FAKE DEGREES FOR REFLECTION ACTIONS ON ROOTS
"... A finite irreducible real reflection group of rank ℓ and Coxeter number h has root system of cardinality h·ℓ. It is shown that the fake degree for the permutation action on its roots is divisible by [h]q = 1+q +q2 + · · ·+q h−1, and that in simplylaced types it equals [h]q · Pℓ i=1 qd∗i where d ∗ ..."
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A finite irreducible real reflection group of rank ℓ and Coxeter number h has root system of cardinality h·ℓ. It is shown that the fake degree for the permutation action on its roots is divisible by [h]q = 1+q +q2 + · · ·+q h−1, and that in simplylaced types it equals [h]q · Pℓ i=1 qd∗i where d
A primitive derivation and logarithmic differential forms of Coxeter arrangements
, 2009
"... Let W be a finite irreducible real reflection group, which is a Coxeter group. We explicitly construct a basis for the module of differential 1forms with logarithmic poles along the Coxeter arrangement by using a primitive derivation. As a consequence, we extend the Hodge filtration, indexed by non ..."
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Cited by 8 (5 self)
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Let W be a finite irreducible real reflection group, which is a Coxeter group. We explicitly construct a basis for the module of differential 1forms with logarithmic poles along the Coxeter arrangement by using a primitive derivation. As a consequence, we extend the Hodge filtration, indexed
Complex reflection groups, Braid groups, Hecke algebras
, 1997
"... Presentations "a la Coxeter" are given for all (irreducible) finite complex reflection groups. They provide presentations for the corresponding generalized braid groups (for all but six cases), which allow us to generalize some of the known properties of finite Coxeter groups and their a ..."
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Cited by 174 (9 self)
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Presentations "a la Coxeter" are given for all (irreducible) finite complex reflection groups. They provide presentations for the corresponding generalized braid groups (for all but six cases), which allow us to generalize some of the known properties of finite Coxeter groups
Symplectic reflection algebras, CalogeroMoser space, and deformed HarishChandra homomorphism
 Invent. Math
"... To any finite group Γ ⊂ Sp(V) of automorphisms of a symplectic vector space V we associate a new multiparameter deformation, Hκ, of the algebra C[V]#Γ, smash product of Γ with the polynomial algebra on V. The parameter κ runs over points of CP r, where r = number of conjugacy classes of symplectic ..."
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Cited by 280 (39 self)
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To any finite group Γ ⊂ Sp(V) of automorphisms of a symplectic vector space V we associate a new multiparameter deformation, Hκ, of the algebra C[V]#Γ, smash product of Γ with the polynomial algebra on V. The parameter κ runs over points of CP r, where r = number of conjugacy classes of symplectic
Invariant Fields of Finite Irreducible Reflection Groups
 Math. Ann
, 1997
"... We prove the following result: If G is a finite irreducible reflection group defined over a base field k, then the invariant field of G is purely transcendental over k, even if jGj is divisible by the characteristic of k. It is well known that in the above situation the invariant ring is in general ..."
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Cited by 7 (4 self)
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We prove the following result: If G is a finite irreducible reflection group defined over a base field k, then the invariant field of G is purely transcendental over k, even if jGj is divisible by the characteristic of k. It is well known that in the above situation the invariant ring
Developments in the Measurement of Subjective WellBeing
 Psychological Science.
, 1993
"... F or good reasons, economists have had a longstanding preference for studying peoples' revealed preferences; that is, looking at individuals' actual choices and decisions rather than their stated intentions or subjective reports of likes and dislikes. Yet people often make choices that b ..."
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Cited by 284 (7 self)
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of others and depart from the standard model of the rational economic agent in other ways. If people display bounded rationality when it comes to maximizing utility, then their choices do not necessarily reflect their "true" preferences, and an exclusive reliance on choices to infer what people
Lattices in finite real reflection groups
 Trans. Amer. Math. Soc
"... This Article is brought to you for free and open access by the School of Mathematics at ..."
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Cited by 11 (0 self)
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This Article is brought to you for free and open access by the School of Mathematics at
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