This is now #12968 <http://trac.sagemath.org/sage_trac/ticket/12968>. (I 
couldn't find a ticket for it, but the problem was documented in the source 
code (see other answers to that posting). Does someone know that there is a 
ticket for it already?)

Am Sonntag, 13. Mai 2012 18:50:11 UTC+2 schrieb Lorenzo:
>
> Hi everyone, first time sage user here. 
>
> I am puzzled by the behavior of round(): 
>
> sage: t=sqrt(4320373582484102551677386613153502) 
> sage: floor(t) 
> 65729548777426599 
> sage: round(t) #everything as expected, floor ≤ round ≤ ceil 
> 65729548777426600 
> sage: ceil(t) 
> 65729548777426600 
> sage: u = sqrt(43203735824841025516773866131535024) #add one digit 
> sage: floor(u) 
> 207855083711803944 
> sage: round(u) # ?? smaller than floor(u)! No warning message... 
> 207855083711803936 
> sage: r = round(u) 
> sage: ceil(u) 
> 207855083711803945 
> sage: type(r) # seems to have still the same precision...? (i.e., it 
> wasn’t converted to some "float type" – I admit of course that I don't know 
> how the sage type system works) 
> <type 'sage.rings.integer.Integer'> 
> sage: version() 
> 'Sage Version 4.8, Release Date: 2012-01-20' 
>
> uname -a 
> Darwin iMac.local 10.8.0 Darwin Kernel Version 10.8.0: Tue Jun  7 16:33:36 
> PDT 2011; root:xnu-1504.15.3~1/RELEASE_I386 i386 
>
> Can someone explain this behavior? If this isn’t a bug, it is a very 
> unintuitive "feature" for sage-neophytes, to say the least. 
>
> Thank you very much! 
>

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