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/624280b6-2fe4-42ca-98f4-3f2ab1518839n%40googlegroups.com.
