Robert Bradshaw wrote: > I've actually been working on a patch for coercion that will allow > number fields to come with specified embeddings, in which case we > will let I be in QQ[sqrt(-1)] (or even perhaps ZZ[sqrt(-1)]), but > with a specified embedding into CC (and by extension SR) so that > stuff like I + sqrt(2) works as expected, but (1-I)/(1+I) simplifies > automatically (and fast).
How will this work with cwitty's AA and QQbar classes? If I understand things correctly, this is the sort of things that his classes handle pretty nicely. Also, note that Carl's QQbar class can provide an answer to the original question: sage: i=QQbar(I) sage: 1/(1+i) -1/2*I + 1/2 sage: (1-i)/(1+i) -1*I sage: sqrt(2)*i 1.414213562373095?*I This last number is actually sqrt(2), it just prints it out as a floating point approximation. Behind the scenes, Sage knows that it is sqrt(2): sage: a=sqrt(2)*i sage: a 1.414213562373095?*I sage: a.minpoly() x^2 + 2 This says that the number is a root of x^2+2 (i.e., in this case, sqrt(2)*I). Maybe QQbar could be enhanced to print out square roots exactly if it knows that it has a square root (without doing any extra calculations). It may not always recognize that it has an exact square root after a long calculation, but it would probably work fine for most cases. Thanks, Jason --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
