1 Rational functions and minimal factorizations of permutations Let f : C C be a rational function of degree n in one complex variable. A critical point of f is a point z C such...
We analyse and compare the complexity of several algorithms for computing modular polynomials. We show that an algorithm relying on floating point evaluation of modular functions...
Let O be an order of an algebraic number field. It was shown by Ge that given a factorization of an O-ideal a into a product of O-ideals it is possible to compute in polynomial tim...
Conceptual complexity is emerging as a new bottleneck as data-base developers, application developers, and database administrators struggle to design and comprehend large, complex...
We give new constructions of randomness extractors and lossless condensers that are optimal to within constant factors in both the seed length and the output length. For extractor...
Venkatesan Guruswami, Christopher Umans, Salil P. ...