On Feb 8, 7:53 pm, rjf <fate...@gmail.com> wrote: > Keepfloat is explicitly set to false in the solve program, and the > comments in the source code say so.
And there are other places this is mentioned as well. However, there is at least one (already existing, and not from a Sage user afaik) bug report of another place this is not documented. > Perhaps there should be a comment to the effect that indefinite > symbolic integration > is an algorithm that in its full generality requires the application > of exact rational arithmetic. > In particular the integration program (or more particularly if the > solve > program is called by integration) the system temporarily sets > keepfloat to false. Yes, this sounds like a good idea to make more explicit. As far as I understand it, using keepfloat:true is an attempt to keep things *more* exact, not less. From Ticket #2400: +++++++ sage: f = e^(-x^2) sage: f.integrate(x, 0, 0.1) 2066*sqrt(pi)/36741 sage: f.integrate(x, 0, 1/10) sqrt(pi)*erf(1/10)/2 Hmmmm. Does this mean erf(1/10) is a rational number? ++++++++ Current behavior is sage: f = e^(-x^2) sage: f.integrate(x,0,1/10) 1/2*sqrt(pi)*erf(1/10) sage: f.integrate(x,0,0.1) 0.0562314580091*sqrt(pi) sage: n(2066/36741) 0.0562314580441469 sage: numerical_integral(f,0,0.1) #GSL numerical integration (0.099667664290336341, 1.1065333570574191e-15) sage: f.nintegrate(x,0,0.1) #Maxima numerical integration (0.099667664290336355, 1.1065333570574201e-15, 21, 0) sage: f.integrate(x,0,0.1).n() #Maxima symbolic with keepfloat:true, then converted to RR 0.0996676642903363 sage: n(2066*sqrt(pi)/36741) #Maxima's own answer, converted to RR 0.0996676643523801 So I guess that explains the genesis of this, and why we should probably keep it in place for now. Maybe our integration should also have a note with exactly the kind of example from the original poster that points out there could be some error at high precision because of this? Also note that we still use the default for some matrix manipulations which otherwise would crash and burn, so it's not that keepfloat:true is considered a panacea, just a solution to a bug. - kcrisman -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
