A new algorithm for the geometric decomposition of a variety

In this article, we present a new met.hod for computing the deconiposition of a variety into irreducible componc:nts. It. is bawd on a property of Bczoutia.n mat.ricc:s; which allows us to c:omput,e a multiple of t.lio Chow form of t.he isolat,cil points of the varict.y and to deduce a rational representation of thcsc points. This t,ools is used recursively to compute t,he irreduc.iblc components from the lowest to the highest. dimension. The asymptotic complexity is of the same order t.han the best complesity bound known for this problem. Our approach provides a subst,nntial simplification of the previous methods and yields bounds on the height of polynomials involved in these representations. =\n iml.‘lelllrnt.ation in MAPLE of t.his algorithm is described at, thr end.

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