On Nov 3, 2008, at 7:39 PM, Jason Grout wrote: > Bill Hart wrote: >> sage: R.<x>=RDF['t'] >> sage: s=1.0e1*t^3+1.0e-100*t^2+1.01234e-100*t+1.0e1 >> sage: u=1.0e1*t^3-1.0e1*t^2+1.0e1*t-1.0e1 >> sage: s*u >> 100.0*t^6 - 100.0*t^5 + 100.0*t^4 - 100.0*t^2 + 100.0*t - 100.0 >> >> What happened to the t^3 term? > > > Isn't it zero in RDF? > > sage: a0=RDF(1.0e1) > sage: a1=RDF(1.01234e-100) > sage: a2=RDF(1.0e-100) > sage: a3=RDF(1.0e1) > sage: b0=RDF(-1.0e1) > sage: b1=RDF(1.0e1) > sage: b2=RDF(-1.0e1) > sage: b3=RDF(1.0e1) > sage: # the coefficient of t^3 > sage: a0*b3 + a1*b2 + a2*b1 + a3*b0 > 0.0 > > Note that a0*b3+a3*b0 is zero (both are 100 in magnitude). However, > > sage: a2*b1 - a1*b2 > 2.01234e-99 > sage: a2*b1 - a1*b2 +1 -1 > 0.0 > > My guess is that adding 100 and subtracting 100 wipes out the > precision > and makes the resulting expression close enough to zero that it is > considered zero. > > Are you sure that RDF provides enough precision to carry out your > computation?
That's almost certainly what's happening. If you do sage: sage: (s.change_ring(RealField(400)) * u.change_ring(RealField (400)))[3] -1.233999999999992707276099007932117842977737442427998522647464651126978 20628822244138099718572056030722800920267941116652e-101 then it gets the correct answer. Even worse is sage: (t+1e100)^2 1.0*t^2 + 1e+200 because the wrong algorithm is being used. See http:// trac.sagemath.org/sage_trac/ticket/4055 - Robert --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
