Hi all ! I wanted to know whether Sagemath had any support for cyclic algebras. From the manual, I strongly suspect the answer is "no", but you never know.
Let me be more concrete. For a prime p, let K be QQ with the p-th roots of unity adjoined. For a, b in K, there is a cyclic algebra (a,b) over K (technically, this depends on a choice of primitive root in K); for p=2, this is the quaternion algebra (a, b) over QQ. I would like to be able to answer questions such as: is (a,b) trivial? For p=2, Sage does this, essentially with hilbert_conductor(a,b). Also, (a,b) is trivial if and only if b is a norm from K[a^(1/p)]. Finding explicitly an element from this field whose norm is b would be awesome. When p=2 and so K=QQ, it's a matter of finding x, y in QQ such that x^2 - ay^2 = b, and trying random values for x and y (essentially...) works fine. Over more complicated fields, PARI has functions accessible through sage to find points on conics. If any of the above can be facilitated by Sage for p odd, it would be great. Thanks! Pierre -- 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 post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
