On Feb 9, 7:19 am, kcrisman <kcris...@gmail.com> wrote:
> ... snip... > > 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? No, it means that you have not noticed the value set for ratepsilon, which governs the tolerance for conversion of floats to rationals. It is by default set to 2.0e-8, presumably for "single float" systems. It should probably be set to something more like 10e-16 for double float systems. Once 0.1 is converted to a nearby rational, everything should be done in rational arithmetic if possible. Conflating symbolic algebraic anti-differentiation and approximating the area under a curve by application of (whatever... the "fundamental theorem of integral calculus"?) is potentially hazardous, especially if you start with numbers like 0.1, which could be exactly 1/10, but could also be some nearby binary number. It would, of course, be highly unlikely for erf(1/10 ) or erf(0.1e0) or erf(0.1d0) to be rational. RJF -- 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
