|Title||A New Algorithm for the Geometric Decomposition of a Variety|
|Author(s)|| Mohamed Elkadi, Bernard Mourrain|
|Type||Article in Conference Proceedings|
|Abstract||In this article, we present a new method for computing the decomposition of a variety into irreducible components. It is based on a property of Bezoutian matrices, which allows us to compute a multiple of the Chow form of the isolated points of the variety and to deduce a rational representation of these points. This tools is used recursively to compute the irreducible components from the lowest to the highest dimension. The asymptotic complexity is of the same order than the best complexity bound known for this problem. Our approach provides a substantial simplification of the previous methods and yields bounds on the height of the polynomials involved|
in these representations. An implementation in maple of this algorithm is described at the end. In this paper, we present a new method for computing the decomposition of a variety into irreducible
components. It is based on matrix formulations, and more specifically on Bezoutian matrices.
|Conferencename||International Symposium on Symbolic and Algebraic Computation|