(Sq16)^7 in F3 breaks web interface

[Brian-Catcow-B]

Selecting Prime: 3 and entering

Sq16*Sq16*Sq16*Sq16*Sq16*Sq16*Sq16

causes it to hang on generate, despite Sq16 having nilpotence height 4.

Funny enough if you start with (Sq16)^4 then add factors, generating each time then it doesn't hang.

[JoeyBF]

Do you mean that it hangs forever or that it just takes a long time? If it hangs forever, I'm not able to reproduce that bug. If it takes a while, that's a consequence of how the algorithm works.

If you want to compute a product that is known to live in degree d, the algorithm will compute a vector space basis of every degree of the Steenrod algebra between 0 and d, then perform the computation to figure out the vector that corresponds to the output. For (Sq16)^7 at p=3, we're looking at computing the first 448 degrees. This is manageable, but on my computer it takes about 1.6 GB of RAM and around 1 minute to finish.

It is possible to compute certain products more quickly by using relations and Groebner bases. In that way, it would be instant to figure out that (Sq16)^4 * x is 0 for all x. Right now the code doesn't use relations apart from the computation of the products themselves.