Can you go into more detail on this? On Monday, December 16, 2024 at 9:29:13 AM UTC-8 Nils Bruin wrote:
> On Saturday, 14 December 2024 at 09:28:37 UTC-8 skchandh...@gmail.com > wrote: > > I want to compute a single place of degree 8 so I can use it as described > in the OP. > > > If you want to evaluate a function at a place, you'll just get a value in > the residue field. In the case of a degree 8 place, that will be a degree 8 > extension of GF(2^16), so indeed in GF(2^128). The value you get will be > exactly the value that you get by evaluating the corresponding degree 1 > point over GF(2^128). So from what you describe, it would seem you don't > need to bother with degree 8 places over GF(2^16) but you can just work > with degree 1 points over GF(2^128). The advantage of that is that a lot of > the computational complexity gets pushed into the field arithmetic (which > is highly optimized), instead of the maximal order machinery of function > fields. > > It shouldn't be hard to get your hands on a point over GF(2^128). They are > as abundant as points over lower degree fields. If you really want to make > sure it's really a degree 8 place over GF(2^16) you probably want to check > that its Frobenius orbit has the right length for that. > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/sage-support/362d977f-5627-4f16-ae61-8851e0a14f6bn%40googlegroups.com.
