Doh! Mma = mathematica. I need to learn how to read!! Thanks for checking that.
Bill. On 5 Nov, 00:45, Bill Hart <[EMAIL PROTECTED]> wrote: > On 5 Nov, 00:26, Jason Grout <[EMAIL PROTECTED]> wrote: > > > > > Bill Hart wrote: > > > > On 4 Nov, 03:39, Jason Grout <[EMAIL PROTECTED]> 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? > > > > No. RDF has the possibility to have exponents down to -1023. > > > I just *knew* I was getting into it over my head and that you knew the > > precision issues at stake. Sorry for giving you the naive answer; I > > should have realized that of all people, you would know exactly the > > capabilities of machine precision arithmetic! > > Well, I wouldn't suppose that I know *anything* about floating point > computations. Not really my area. I learned during my conversation > about these algorithms how to use RDF['x'] to do multivariate > polynomial multiplication over the integers using Kronecker > Segmentation, which I did not know about before. > > The "correct" answer to the example I concocted can certainly be > expressed in RDF['x'], but it is nontrivial to design an efficient > algorithm to return that correct answer, on account of there only > being 53 bits of mantissa to work with. The order of operations is > relevant. > > > > > So I take it your question was really: > > > Shouldn't Sage realize that the naive computation of the coefficient of > > t^3 is seen as zero, while it is very possible to do the computation in > > such a way that you (correctly) don't get zero? Shouldn't Sage be smart > > about the precision issues here? > > > To which I answer: Yes, sure, of course! > > Well, I agree with you, though I suspect opinion will be divided on > this one. > > > > > It would make for a very interesting demo to show other systems > > incorrectly returning 0 for the coefficient, while Sage is just a bit > > smarter about the arithmetic issues and doesn't return 0. > > I absolutely agree. > > > > > Mma returns the term as "0. t^3" > > That's interesting. Which version of Magma? > > I am using the one on sage.math (v 2.13-5) and I get: > > > R<t>:=PolynomialRing(RealField(53 : Bits := true)); > > s:=1.0e1*t^3+1.0e-100*t^2+1.01234e-100*t+1.0e1; > > u:=1.0e1*t^3-1.0e1*t^2+1.0e1*t-1.0e1; > > s*u; > > 100.000000000000*t^6 - 100.000000000000*t^5 + 100.000000000000*t^4 - > 100.000000000000*t^2 + 100.000000000000*t - 100.000000000000 > > It would be interesting to see if the Magma people considered this to > be a bug. > > Bill. --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
