Displaying similar documents to “A computer algorithm for finding new euclidean number fields”

Computing all monogeneous mixed dihedral quartic extensions of a quadratic field

István Gaál, Gábor Nyul (2001)

Journal de théorie des nombres de Bordeaux

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Let M be a given real quadratic field. We give a fast algorithm for determining all dihedral quartic fields K with mixed signature having power integral bases and containing M as a subfield. We also determine all generators of power integral bases in K . Our algorithm combines a recent result of Kable [9] with the algorithm of Gaál, Pethö and Pohst [6], [7]. To illustrate the method we performed computations for M = ℚ ( 2 ) , ℚ ( 3 ) , ℚ ( 5 ) .

Topics in computational algebraic number theory

Karim Belabas (2004)

Journal de Théorie des Nombres de Bordeaux

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We describe practical algorithms from computational algebraic number theory, with applications to class field theory. These include basic arithmetic, approximation and uniformizers, discrete logarithms and computation of class fields. All algorithms have been implemented in the system.

A generalization of the LLL-algorithm over euclidean rings or orders

Huguette Napias (1996)

Journal de théorie des nombres de Bordeaux

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Numerous important lattices ( D 4 , E 8 , the Coxeter-Todd lattice K 12 , the Barnes-Wall lattice Λ 16 , the Leech lattice Λ 24 , as well as the 2 -modular 32 -dimensional lattices found by Quebbemann and Bachoc) possess algebraic structures over various Euclidean rings, e.g. Eisenstein integers or Hurwitz quaternions. One obtains efficient algorithms by performing within this frame the usual reduction procedures, including the well known LLL-algorithm.

What is the inverse of repeated square and multiply algorithm?

H. Gopalkrishna Gadiyar, K. M. Sangeeta Maini, R. Padma, Mario Romsy (2009)

Colloquium Mathematicae

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It is well known that the repeated square and multiply algorithm is an efficient way of modular exponentiation. The obvious question to ask is if this algorithm has an inverse which would calculate the discrete logarithm and what is its time compexity. The technical hitch is in fixing the right sign of the square root and this is the heart of the discrete logarithm problem over finite fields of characteristic not equal to 2. In this paper a couple of probabilistic algorithms to compute...