Abstract. We present an algorithm for computing the set of torsion points satisfying a given system of multivariate polynomial equations. Its complexity is quasilinear in the logarithm of the degree and in the height of the input equations but exponential in their number of variables and nonzero terms.
Describing an emerging field of research, one that is fundamentally interdisciplinary and heuristic in its phenomenological approach, can be overwhelming. In one sense, everything has yet to be done, but to state even this would be to negate precursory forays into the study of contemporary circus as practiced in Quebec and disseminated throughout the world from an unexpected new circus capital. In this short essay, I give a first-hand account of the creation of the Montreal Working Group for Circus Research, its rapid growth and integration into Montreal’s vibrant cosmopolitan circus scene. The Working Group and its ongoing collaboration with National Circus School of Montreal have served as a nexus for developing research strategies and a vocabulary for the new field of contemporary circus studies in North America.
Abstract. We show that, for a system of univariate polynomials given in sparse encoding, we can compute a single polynomial defining the same zero set, in time quasi-linear in the logarithm of the degree. In particular, it is possible to determine whether such a system of polynomials does have a zero in time quasi-linear in the logarithm of the degree. The underlying algorithm relies on a result of Bombieri and Zannier on multiplicatively dependent points in subvarieties of an algebraic torus.We also present the following conditional partial extension to the higher dimensional setting. Assume that the effective Zilber conjecture holds. Then, for a system of multivariate polynomials given in sparse encoding, we can compute a finite collection of complete intersections outside hypersurfaces that defines the same zero set, in time quasi-linear in the logarithm of the degree.
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