The lazy fields are not just wrappers around self._value:

sage: a = RLF(0.1)
sage: RealIntervalField(150)(a)
0.1000000000000000000000000000000000000000000000?
sage: RealIntervalField(150)(a._value)
0.10000000000000000555111512312578270211815834046?



On Monday, May 8, 2017 at 8:50:48 PM UTC+2, Thierry (sage-googlesucks@xxx) 
wrote:
>
> Hi, 
>
> RealLazyField() and ComplexLazyField() claim to be exact, but currently 
> they are not: 
>
> sage: RLF.is_exact() 
> True 
> sage: a = RLF(0.1) ; a 
> 0.10000000000000001? 
> sage: a._value 
> 0.100000000000000 
> sage: a._value.parent() 
> Real Field with 53 bits of precision 
>
> Also, the doc explicitely states: 
>
>     This class represents the set of real numbers to unspecified 
>     precision. For the most part it simply wraps exact e lements and 
>     defers evaluation until a specified precision is requested. 
>
> I opened https://trac.sagemath.org/ticket/22960 but i am not sure whether 
> RLF should stop claiming it is exact or whether we should forbid things 
> like RLF(0.1), what do you think (the first is easier to implement) ? 
>
> Ciao, 
> Thierry 
>
>

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