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I would say that 1 + sqrt(7) could be uniformly chosen to the be the unique positive root of (x-1)^2-7, while there is no canonical choice for (x-1)^2+7. However, the problem should be in transforming the symbolic expression 1 + sqrt(-7) into an algebraic number, but once an element of QQbar is defined, i do not see any problem (an element of QQbar is embedded in the complex field). So for me, there should be an error, but it should appear when calling QQbar(1 + sqrt(-7)).
 Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.
 
                
                Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.