I might add that even transcendental functions can be dealt with by similar tricks; e.g. if you need sin(z) you can set introduce u,v satisfying u^2+v^2=1 and set u=sin(z).
On Thursday, January 5, 2017 at 4:30:16 PM UTC, John Cremona wrote: > > On 5 January 2017 at 15:59, Eric Gourgoulhon <egourg...@gmail.com > <javascript:>> wrote: > > > > > > Le jeudi 5 janvier 2017 16:32:55 UTC+1, Dima Pasechnik a écrit : > >> > >> > >> we can work modulo the ideal generated by w^2+z and w'^2+z', sure, why > >> not? > > > > > > What I meant is that, suppose you start with the ring modulo the ideal > > generated by w^2+z and at some point in the work flow, you decide to > > introduce a new square root, then you have to change the base ring to > that > > modulo the ideal generated by (w^2+z, w'^2+z'). Maybe this is feasible, > but > > it looks quite heavy at first glance: changing the base ring each time > you > > introduce an object that is not polynomial... > > It may seem heavy-handed but the final outcome is likely to be better > this way. I did a complicated computation involving a whole lot of > different number fields, mostly cyclotomic fields, and I kept on > restarting with a larger and larger such field with the others defined > as subfields of it (I think I ended up using the 1092'th roots of > unity). This worked out much better in the end than trying to > construct towers from the bottom up. > > Your situation seems to be like this with function fields instead of > number fields. Instead of starting with Q and adjoining roots of > polynomials you are starting with Q(x) and extending that > algebraically. Unfortunately Sage's support in this situation is not > so good. > > Perhaps in your example, rather than starting with rational functions > in z and then trying to adjoin w=sqrt(-z), start with rational > functions in w and define z=-w^2. > > John > > > > > -- > > You received this message because you are subscribed to the Google > Groups > > "sage-devel" group. > > To unsubscribe from this group and stop receiving emails from it, send > an > > email to sage-devel+...@googlegroups.com <javascript:>. > > To post to this group, send email to sage-...@googlegroups.com > <javascript:>. > > Visit this group at https://groups.google.com/group/sage-devel. > > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
