This question is about the classical Adams spectral sequence. Squaring operations are defined on its $E\_2$ term. I'd like to know how to compute some of the non-trivial operations, such as $Sq^2 ( c\_0 ) = h\_0 e\_0$. I feel like this ought to be doable in the May spectral sequence, but I don't know the details.


I'm aware of some work of Milgram on the subject, but there are some problems with his approach because of indeterminacies of Massey products.


Thanks!



Computing squaring operations in the Adams spectral sequence
I think for $k>0$ currently no-one knows an efficient **algorithmic** way to compute the $Sq^k$, e.g., from a minimal resolution. (The $Sq^0$ is easy since it is induced by the "Frobenius" map on $A\_\ast$ and one just needs to compute a chain map). 


For the May spectral sequence you might want to check out *Nakamura, Osamu.* On the squaring operations in the May
spectral sequence. *Mem. Fac. Sci. Kyushu Univ. Ser. A 26
(1972), no. 2, 293–308* (Google can find this online).


