Algebraic number field
Relative integral basis for algebraic number fields
... RELATIVE INTEGRAL BASIS FOR ALGEBRAIC NUMBER FIELDS MOHMOOD HAGHIGHI Department of Computer Science Bradley University Peoria, Illinois 61625 U.S.Ao Received January 23, 1985 and in revi[r] ...
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Units in families of totally complex algebraic number fields
... of algebraic number fields F of degree less than or equal to 4, which have at least one real ...complex algebraic number fields, can be considered as a complement of ...
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Uniform distribution of Hasse invariants
... GREENFIELD, Uniform Distribution in Subgroups of the Brauer Group of an Algebraic Number Field, Pacific J.[r] ...
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Finding the ring of integers and its algorithms in algebraic number theory
... given algebraic number ...the number field sieve algorithm for factoring ...the number field that one may view as the "best guess" one has for the ring of ...
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Galois and Class Field Theory for Quantum Chemists
... We dare say there is a hidden symmetry, which originates from the automorphism of the number field. Traditionally we have analyzed the symmetry in molecules using the point group that acts upon the atomic ...
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On the coefficients of the polynomial in the number field sieve
... Remark 2: Usually the number of real roots is left as random. However, based on our analysis, we can adjust the value of the related coefficients in polynomial optimizing stage such that the polynomial have more ...
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Factorization of a 1061-bit number by the Special Number Field Sieve
... CPU-hours, required 14 gigabytes of memory, and produced a fifth degree polynomial with coefficients 4.03 gigabits in size. The algebraic square root, calculated using q-adic Newton iteration, required 13.5 ...
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Why Interpret Quantum Physics?
... a field theory should explain some of the parameters, such a particle masses and coupling constants, that are fed into the standard model by hand, based on experiments rather than ...effective field theory ...
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Algebraic Tori: A Computational Approach
... an algebraic torus is defined without using an ideal of a polynomial ...function field (resp. coordinate ring) of a general algebraic torus is defined as the field of invariants of a ...
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NOT require the Axiom of Choice; for each xA we have constructed an EXPLICIT left inverse to f. — On the other hand, if we had simply said that one should pick some
... Finally, we shall prove the result when 0 < y < x. By property (2) in the notes there is a rational number r such that y < r < x. Write r = p/q, where p and q are both positivei; replacing p and q by M ...
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An Upper Bound of the Bezout Number for Piecewise Algebraic Curves over a Rectangular Partition
... piecewise algebraic curve itself is difficult; on the other hand, the Bezout number BNm, r; n, t; Δ is also complicated; we know it not only relies on the degrees m, n and the smoothness orders r, t, but also ...
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Remarks on Local Symmetry Invariance in Perturbative Algebraic Quantum Field Theory
... Initially the paqft framework was developed for scalar fields, but recently there has been a lot of progress in constructing more complicated models. In particular, quantum electrodynamics (QED) was discussed in [23] and ...
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Algebraic Dependencies and PSPACE Algorithms in Approximative Complexity over Any Field
... To further motivate the concept of algebraic dependence, we list a few recent problems in computer science. The first problem is about constructing an explicit randomness extractor for sources which are polynomial ...
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On the continuous part of codimension two algebraic cycles on threefolds over a field
... is representable too. Representability of 0-cycles on a surface without non-trivial everywhere holomorphic 2-forms was conjectured by S.Bloch, and it was a part of the intuition leading to the whole Bloch-Beilinson ...
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On some power series with algebraic coefficients and Liouville numbers
... sums. In [], Nyblom employed a variation on the proof used to established Liouville’s theorem concerning the rational approximation of algebraic numbers, to deduce explicit growth conditions for a certain series ...
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Algebraic Analysis Approach for Multibody Problems II
... of algebraic trajectory (denoted by ALG) and the exact trajectory (denoted by DIM, direct integra- tion method) in the case of two-dimensional 442-body Coulomb collisions with an impact parameter b = ...the ...
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Solution of the Generalized Interval Linear Programming Problems: Pessimistic and Optimistic Approaches
... fuzzy number ˜ A can be represented with its α−cuts directly, see ...fuzzy number is an interval, all of the concepts given in the previous subsections are ...
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The Tower Number Field Sieve
... a small integer larger than 1. The state-of-art algorithm is the number field sieve (NFS) together with its many variants. When p has a special form (SNFS), as in many pairings constructions, NFS has a ...
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Algebraic Objects of MBFs and Recursive Computation of the Dedekind Number
... calculated by Church [2] in 1940, D(6) - by Ward [3] in 1946, D(7) - by Church [4] in 1965 and D(8) – by Wiedemann [5] in 1991. The inequivalent MBFs were conducted until the seventh rank in [6]. As it turned out, this ...
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A Cohomological Perspective on Algebraic Quantum Field Theory
... 1.1. Algebraic quantum field theory. The fundamental difference between quan- tum field theory and other models of quantum physics is locality. Consistency with relativity means that only some ...
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