Sylvester's Algorithm
The Sylvester's algorithm allows to compute the symmetric rank of a symmetric
tensor $T\in S^dV$ if $V$ is a two dimensional vector space. In the first
part of the talk I will present the versions of this that gives in a finite
number of steps the symmetric rank of the tensor without giving an explicit
decomposition of it. In the second part of the talk I will show how the same
geometric idea can be applied to write effective algorithms also for some
higher dimensional cases. What is presented in this talk comes from a work
in progress with A. Gimigliano and M. Idà .