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An LLL-reduction algorithm with quasi-linear time complexity: extended abstract
This work establishes a new framework for analyzing unimodular transformation matrices which reduce shifts of reduced bases, this includes bit-size control and new perturbation tools and illustrates the power of this framework by generating a family of reduction algorithms.
The notion of generating subfields is introduced, a set of up to n subfields whose intersections give the rest, and an efficient algorithm which uses linear algebra in k or lattice reduction along with factorization is provided.
Practical Divide-and-Conquer Algorithms for Polynomial Arithmetic
An algorithm originally described by Brent and Kung for composition of power series is revisited, showing that it can be applied practically to composition of polynomials in Z[x] given in the standard monomial basis, and a complexity analysis is offered.
Gradual Sub-lattice Reduction and a New Complexity for Factoring Polynomials
A lattice algorithm specifically designed for some classical applications of lattice reduction, for lattice bases with a generalized knapsack-type structure, where the target vectors have bounded depth, which is an improvement over the quadratic complexity floating-point LLL algorithms.
Practical polynomial factoring in polynomial time
This work presents an algorithm which gives a practical improvement (less Hensel lifting) for these more common polynomials and illustrates that this complexity gap can be closed by providing an implementation which is comparable to the best current implementations and for which competitive complexity results can be proved.
Factoring univariate polynomials over the rationals
An algorithm for factoring a polynomial, f, in one variable with rational coefficients, is presented, a variant of the Belabas [Belabas] version of the van Hoeij [van HoeIJ] factoring algorithm, which contains a practical speed-up over BelabAS' but also allows us to prove a new complexity result for Factoring polynomials.
Can GAN-Generated Network Traffic be used to Train Traffic Anomaly Classifiers?
This paper presents the ‘GAN vs Real (GvR) score’, a task-based metric which quantifies how well a traffic GAN generator informs a classifier compared to the original data.
An LLL-reduction algorithm with quasi-linear time complexity
A new framework for analyzing unimodular transformation matrices which reduce shifts of reduced bases, this includes bit-size control and new perturbation tools is established, which is illustrated by generating a family of reduction algorithms.
Fast computation of Smith forms of sparse matrices over local rings
An algorithm which is time- and memory-efficient when the number of nontrivial invariant factors is small is given, and a method for dimension reduction while preserving the invariant Factors is described.
Factoring univariate polynomials over the rationals (abstract only)
- A. Novocin
- Computer ScienceACM Commun. Comput. Algebra
- 25 July 2008
This poster presents an algorithm for factoring polynomials over the rationals which follows the approach of the van Hoeij algorithm and should outperform prior algorithms in many common classes of polynOMials (including irreducibles).