search

thetensor-space / Auto-Sandbox

Algorithms for automorphism groups
3 stars 1 forks source link

der-densor stabilizer #9

Closed joshmaglione closed 5 years ago

joshmaglione commented 5 years ago

There must be a better way to do what I wrote in src/builds/der-densor.m. In lines 223 through 228, I do the following.

  1. Construct the vector stabilizer, using Magma's Stabilizer.
  2. Build a homomorphism from my original matrix group to a different matrix group given by the action on the densor subspace.
  3. Use @@ on the computed stabilizer to get the stabilizer in my original matrix group.

@galois60 is there a better way to do what I need in Magma?

galois60 commented 5 years ago

That seems pretty sensible to me. Which is to say, that's more or less how I would do it.

Eamonn raised an interesting aspect of this sort of computation, though, that's worth bearing in mind (although it probably won't have much impact here). When you compute a stabilizer, you often end up with many more generators that you need. Then, lifting them––as you are doing here––can become expensive. One can apply ReduceGenerators to your stabilizer before you lift it. I just wrote such an intrinsic and put it in Auto-Sandbox "Util.m" file.

By the way, when you write @galois60, are you trying to apply me to something?

joshmaglione commented 5 years ago

Hah! Yes, I'm applying you to the post in hopes you turn my ideas into something sensible.

OK that is good to know. I will change the code to reduce the generators soon, or anyone can do it if they want to. Thanks!