I disagree. I think this is really not a good example because it is just too long.
The point is: taking a long symbolic formula produced by a CAS and then putting numbers in it can provide an answer that may be inaccurate. Sometimes there are OTHER formulas that are mathematically equivalent that produce much more accurate answers. You will only confuse people if they think this has to do with Legendre polynomials, especially since there are fine ways to evaluate Legendre polynomials accurately. And someone using Legendre polynomials professionally probably would not encounter this difficulty because he/she would not use this formula. It is a mistake to highlight "bugs" if by that you mean errors in the system programs. Those can always be fixed, and then your book will be wrong. If you mean design errors (sometimes called "features") then then may persist. I am sure there are many such things in Sage. Perhaps RIF and RF are one. You do not need to write 1.0/3 to have a problem. 0.1 is already a problem if that is a floating-point number. Just compute 0.1 -1/10 exactly. On Friday, October 31, 2014 10:11:50 AM UTC-7, Christophe Bal wrote: > > I definitely like this example ! > > Christophe BAL > > 2014-10-31 17:33 GMT+01:00 Aaron Meurer <[email protected] <javascript:>>: > >> 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] >> <javascript:>> 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] >> <javascript:>>: >> >> >> >> >> >> >> >> 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] <javascript:>. >> >> To post to this group, send email to [email protected] >> <javascript:>. >> >> 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] <javascript:>. >> > To post to this group, send email to [email protected] >> <javascript:>. >> > 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] <javascript:>. >> To post to this group, send email to [email protected] <javascript:> >> . >> 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. >> > > -- You received this message because you are subscribed to the Google Groups "sympy" group. 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