It currently looks like there is nothing people really agree on. Which of the following find a qualified majority (it seems like 1,2,3 do have a majority, while 4 is unclear, and 5 is out, but needs an alternative).
1. importing UniversalCyclotomicField into the global name space 2. accessing the UCF as myUCF = UniversalCyclotomicField( genname="E"). Do people prefer name or names (as in CyclotomicField) over genname ? This would also mean that there is nothing to initialize at startup, and thus no startup time difference. 3. Having myUCF.gen(n) returning the "smallest" primitive n-th root of unity. What about UCF.gen(n,k) to get E(n)^k for the same cost as getting E(n), this is currently as well provided by the function "E". 4. Making the UCF unique for a given name. I actually don't (yet) see the point of not making it unique. One can embed the CyclotomicField in various ways and staying consistent, though it does not behave well currently, see sage: CyclotomicField(5,embedding = CC(exp( 2 * pi * I / 5 ))) Cyclotomic Field of order 5 and degree 4 sage: CF5 = CyclotomicField(5,embedding = CC(exp( 2 * pi * I / 5 ))) sage: CF10 = CyclotomicField(5,embedding = CC(exp( 2 * pi * I / 5 ))) KeyboardInterrupt sage: CF5 = CyclotomicField(5,embedding = CC(exp( 4 * pi * I / 5 ))) sage: CF10 = CyclotomicField(10) sage: CF10( CF5.gen()) zeta10^2 sage: CC(CF10( CF5.gen())) 0.309016994374947 + 0.951056516295154*I sage: CC( CF5.gen()) -0.809016994374947 + 0.587785252292473*I But different embeddings do not seem to be possible for the UCF if I am not mistaken. 5. importing the function "E" into the global name space as the main point of entry for the UCF. Since multiple people strongly voted against this (if counted right, there are 3 pros, 5 cons, and 4 unclear): is there any alternative beside zeta[n] ? One other thing in this context: the function "E" can as well be used as in E(n,k) to get E(n)^k for the same cost as getting E(n), so any solution should as well provide this usage. Or do people prefer to not have any extra function to work with the UCF? -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To post to this group, send email to sage-devel@googlegroups.com. To unsubscribe from this group, send email to sage-devel+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel?hl=en.
