On Fri, Oct 3, 2014 at 7:34 AM, kcrisman <kcris...@gmail.com> wrote: >> I ran exactly into this some time ago while sanity-checking some >> high-precision MPFR computations with the results of Wolfram Alpha (which >> also wraps real literals into its own, I presume exact, representation). >> > > Default precision for reals is 53 bits, if I recall correctly, so the extra > zeros are "assumed".
It's not the *default* precision, but the minimum precision. There is no default. The number of bits of precision is determined by the number of digits you enter. However, it would be dumb if 1.5 had way too few bits of precision, so precision is determined by number digits entered with a minimum of 53 bits. sage: 1.2908240834908209348208340283482394820384028340823048203480238.prec() 206 sage: 1.5.prec() 53 That we print all the trailing zeros is to be more explicit about the precision. Compare: sage: 1.5 1.50000000000000 sage: float(1.5) 1.5 In Python all floats have the same precision, so you get no extra information by seeing trailing zeros. In sage you do: sage: RealField(300)(1.5) 1.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 sage: 1.5 1.50000000000000 And no discussion about precision is complete without mentioning RealIntervalField: sage: RealIntervalField(300)(1.5) 1.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000? -- William > >> >> On 3 October 2014 11:42, Volker Braun <vbrau...@gmail.com> wrote: >>> >>> Real literals are wrapped in their own type on the Sage command line, >>> they are not hardware-floats (like in plain Python): >>> >>> sage: 0.001 >>> 0.00100000000000000 >>> sage: type(_) >>> <type 'sage.rings.real_mpfr.RealLiteral'> >> >> >> I am curious, why the extra zeroes in that representation in the second >> line? > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/d/optout. -- William Stein Professor of Mathematics University of Washington http://wstein.org wst...@uw.edu -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
