On Monday, January 6, 2014 6:50:05 PM UTC-10, Robert Bradshaw wrote:
>
> By that logic, rather than preparsing 1/2 we should force the user to 
> write ZZ(1) / ZZ(2).


+1  It is important that the Sage REPL be easy to use with "mathematical" 
notation as far as possible. You should be able to input high precision 
floats in a natural way.

But there is also a fundamental difference to the real literals here, "1/2" 
becomes a honest element of the rational ring whereas real literals just 
masquerade as elements of RR (using it as their parent) while not actually 
being 53-bit floats. In particular, this makes RR(1e-20) again a real 
literal (since the parent is the same), which is quite unexpected.

Would it be possible to move real literals to their own parent? Arithmetic 
operations with other parents should always cast the literal to the other 
parent first, and arithmetic operations within the real literals would end 
up in RR. 


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