On Tue, May 5, 2009 at 11:16 PM, Henryk Trappmann <bo198...@googlemail.com> wrote: > > Ah now I see, you mean though it displays 1/384 it is internally still > the above sum, which is computed when evaluated with n.
True. In Sage right now the internal form of the expression (not the simplified form) is used by the "n" command. This will change when Sage switches from using maxima-based symbolics to Pynac. By the way, you can use the real interval field to get a floating point approximation to any symbolic expression to a given number of digits of precision. Every digit is definitely right except the one right before the question mark: sage: a = 1/(48*sqrt(1)) - 7/(96*1**(3/2)) + 3/(32*1**(5/2)) - 5/ (128*1**(7/2)) sage: RealIntervalField(100)(a) # increase 100 for more digits 0.002604166666666666666666666667? I think the n function (numerical_approx) for symbolics should be changed to using interval arithmetic. This will be a huge improvement. Notice, e.g., that interval arithmetic very nicely gives the right answer for the infamous sin(10^50): sage: a = sin(10^50) sage: a.n(53) -0.480500143493759 sage: a.n(100) 0.60974154556722786199645650055 sage: RealIntervalField(100)(a) 0.? sage: RealIntervalField(1000)(a) -0.7896724934293100827102895399174077539600834046214027191457808736221899969800609898633436757589688470442999273506152178357769064871103469499564331175635613221319397479785737324994506546860108913238488404198306006819757685879489185272089985858148036954222175628785469474395231359019098600625732453528693? sage: RealIntervalField(2000)(a) -0.78967249342931008271028953991740775396008340462140271914578087362218999698006098986334367575896884704429992735061521783577690648711034694995643311756356132213193974797857373249945065468601089132384884041983060068197576858794891852720899858581480369542221756287854694743952313590190986006257324535286926640214204183176856658976160340849634781130568053474154330242776565926107540133198976420887112928640131582614537425282391078909233424580311555104358881651194953182665408243214532152322603956371555619997139323527489307648072219268176687894373677502675114853503742816202001868587837402822439060931321957? I've made fixing this trac #5993: http://trac.sagemath.org/sage_trac/ticket/5993 And a big thanks to Carl Witty for implementing RealIntervalField, which makes the above possible. The above wasn't in Sage when I implemented numerical_approx, so it wasn't an option to use intervals back then. But now it is, and we should switch to it. William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
