Hi,

I was surprised to notice the following behavior: 

sage: r =     .123456789123456789
sage: r.parent()
Real Field with 57 bits of precision
sage: r =    0.123456789123456789
sage: r.parent()
Real Field with 60 bits of precision
sage: r =   00.123456789123456789
sage: r.parent()
Real Field with 57 bits of precision
sage: r =00000.123456789123456789
sage: r.parent()
Real Field with 57 bits of precision
sage: s =    ".123456789123456789"
sage: RealNumber(s).parent()
Real Field with 57 bits of precision
sage: s =   "0.123456789123456789"
sage: RealNumber(s).parent()
Real Field with 60 bits of precision
sage: s =  "00.123456789123456789"
sage: RealNumber(s).parent()
Real Field with 57 bits of precision


Is this intended behavior or should it provide the same result for all of 
the three kinds of input?

I don't quite understand how the precision for the parent of a RealNumber 
is determined. I guess the line  mpfr_init2(self.value, p.__prec)
in real_mpfr.pyx initializes mpfr and later mpfr_set_str(self.value, s, 
base, parent.rnd) is called. But where in the process is the precision of 
the parent "p" defined?

Cheers, 
 Moritz 

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