Proceedings 41st Annual Symposium on Foundationsâ€¦

12 November 2000

TLDR

A probabilistic algorithm is presented to find the determinant of a nonsingular, integer matrix by computing the Smith form of the integer matrix an extremely useful canonical form in itself.Expand

An algorithm to evaluate a polynomial $g\in\KK[x]$ at $T$ which requires only $\softO(\MM(n))$ operations in $\KK$ when $\deg g\leq n^2$ is given.Expand

By interpolating the black box evaluated at random primitive roots of unity, this work gives efficient and numerically robust solutions to the problem of sparse interpolation of an approximate multivariate black-box polynomial in floating-point arithmetic.Expand

Efficient algorithms are presented for factoring polynomials in the skew-polynomial ringFx;?, a non-commutative generalization of the usual ring of polynomialsFx, whereFis a finite field and ?:F?Fisâ€¦ Expand

This work improves on the best-known algorithm for interpolation over large finite fields by presenting a Las Vegas randomized algorithm that uses fewer black box evaluations and provides the first provably stable algorithm for this problem, at the cost of modestly more evaluations.Expand

The design of this generic library LinBox is described, its current range of capabilities are sketched, its guiding design principle of re-usability is given, and several examples of its use are given.Expand

A new probabilistic algorithm to compute the Smith normal form of a sparse integer matrix and an asymptotically fast algorithm for dense matrices that return the correct answer with a controllable, exponentially small probability of error.Expand

This new Monte Carlo algorithm is a hybrid of the diversified and recursive interpolation algorithms, the two previous fastest known probabilistic methods for this problem, and improves on the bit complexity of previous methods by a "soft-Oh" factor of T, log D, or log q.Expand

A new probabilistic algorithm for interpolating a "sparse" polynomial f given by a straight-line program is given, which is asymptotically more efficient in terms of the total cost of the probes required than previous methods.Expand