Context
Any symmetric tensor F of rank $d$ and dimension 2 ($F \in S^d\mathbb{C^2}$ for our purpose) can be associated with a homogeneous polynomial $P(F)\in k[x_0,x_1]_d$ in 2 variables of degree $d$. I would like to find a decomposition of F into a sum of a minimal number of $r$ rank-one symmetric tensors, that is
$$ F=\sum_{i=1}^r \lambda_i F_i^{\otimes d}, ~~\lambda_i \in \mathbb{C} $$
where $F_i\in S^1\mathbb{C^2}$ is a symmetric tensor of rank one and $r$ is the symmetric rank of F. It is easier to look for a decomposition of the associated homogeneous polynomial into a sum of $r$ degree $d$ homogeneous monomials, that is
$$ P(F)=\sum_{i=1}^r \alpha_i P_i, ~~ \alpha_i \in \mathbb{C} $$ where $P_i$ is a monomial of degree $d$. Such a decomposition always exists and is called a Waring decomposition of an homogeneous polynomial, which is not always unique.
Question
I've already seen some algorithms for this kind of decomposition (Sylvester's theorem based algorithm, J.Brachat's algorithm, ...) but I'm looking for an already implemented algorithm which is currently working (online or on a software such as Mathematica, etc). Note that I'm working with low $d$ (that is $3 \leq d \leq 6$). Non-uniqueness is not a deal, I would like to find just one of those Waring decompositions.