Here is a nice example https://groups.google.com/d/msg/sympy/YpV5tyLvWe4/WWRYOTMNIhIJ. It shows great precision loss when evaluating Legendre polynomials naively. Unlike Wilkinson's polynomial, Legendre polynomials are a bit more "real-life", and someone solving real problems could definitely run into this issue if they aren't careful.
Aaron Meurer On Fri, Oct 31, 2014 at 6:15 AM, Christophe Bal <[email protected]> wrote: > Thanks for the answers. > > I do not think I'm wrong when pointing to numerical issues, instead of only > the formal ones. A lot of people do not know the floating points : if you do > not know than 1.0/3 is not the same thing that 1/3, you can go in big > troubles. I will not say that SageMath is guilty but that when numerical > calculations are done, you have to be careful, and SageMath gives RIF than > can be useful instead of RField. > > I will look at Wilinson's polynomial and rootfinding, but I'm also > interested in a link to bugs, and in results which are more fundamental to > the way the software works (like floating point precision loss). > > Christophe BAL > > > > 2014-10-31 0:04 GMT+01:00 Richard Fateman <[email protected]>: >> >> >> >> On Wednesday, October 29, 2014 3:38:47 AM UTC-7, Christophe Bal wrote: >>> >>> Hello. >>> >>> I'm writing a french book about SageMathCloud and I'm looking for known >>> wrong results given by Sage or Sympy due to floats calculations, or due to >>> the formal method used. Do you know such things ? My idea is to show to new >>> user that a CAS or a numerical tool is not Math God. >> >> >> Numerical calculation via SageMathCloud is certainly the wrong place to >> look. As Gupta points out, numerical error happens rather independent of >> that. >> >> How would you react if I said... >> >> I'm writing an English book about French mille-feuille pastries and would >> like to know about food poisoning. My idea is to show that you can die from >> desserts. >> >> In reality, I think you should have some very simple examples that >> distinguish between exact computation and (unstable) numerical calculation. >> The classic one is Wilkinson's polynomial and rootfinding. >> >> >> >>> >>> >>> I've already posted this question on the Sage list without a lot of >>> success. >>> >>> Christophe BAL >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sympy" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> To post to this group, send email to [email protected]. >> Visit this group at http://groups.google.com/group/sympy. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sympy/c7190e1f-9677-4008-a949-30185b8b30e4%40googlegroups.com. >> >> For more options, visit https://groups.google.com/d/optout. > > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAAb4jGkw1KWYTDWcHT7keGqmWY3cMu-2%3D0hfuX_MbZpm%2B0C9AA%40mail.gmail.com. > > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6J24tuwZujZYzo3AnszQBh6-dN0jJ3PE%3D7Le9q2U-e1XA%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
