From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2920 Path: news.gmane.org!not-for-mail From: jean benabou Newsgroups: gmane.science.mathematics.categories Subject: Fwd: Mathematica and CAS Date: Tue, 29 Nov 2005 17:51:04 +0100 Message-ID: <546F06B4-60F8-11DA-9B52-000393B90F2C@wanadoo.fr> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 (Apple Message framework v543) Content-Type: text/plain;charset=ISO-8859-1;format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241018984 6366 80.91.229.2 (29 Apr 2009 15:29:44 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:29:44 +0000 (UTC) To: Categories Original-X-From: rrosebru@mta.ca Wed Nov 30 15:04:51 2005 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 30 Nov 2005 15:04:51 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EhX9K-00027w-LN for categories-list@mta.ca; Wed, 30 Nov 2005 14:57:50 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 65 Original-Lines: 140 Xref: news.gmane.org gmane.science.mathematics.categories:2920 Archived-At: As I know nothing about Computer Algebra Systems, but was surprised by=20= examples given by Andrej Bauer on the Category list of limits that=20 Mathematica gets wrong, I forwarded his mail to a computer scientist=20 friend of mine, specialist of Mathematca, asking for her opinion. She wrote the following answer, where she disagrees with Bauer, and=20 asked me to forward it to the Category list as she would like to know=20 the reaction of some "experts" to her statements. To tell the truth, so=20= do I. Cordially to all, Jean Benabou D=E9but du message r=E9exp=E9di=E9 : > De: Jacqueline Zizi > Date: Ven 25 nov 2005 11:12:03 Europe/Paris > =C0: Jean B=E9nabou > Objet: Mathematica and CAS > > Thanks, Jean, for forwarding me some exchanges about Mathematica. > > Please find below my opinion. If you think that it might bring some=20 > light, please feel free to forward it to the discussion list =20 > "categories". > > > A) Andrej Bauer points out very interesting questions, but I think he=20= > is wrong: > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > > The interesting questions are: > 1) Symbolic systems and students fall in the same trap; > 2) People trust blindly computer results obtained via computers (not=20= > only using CAS); > 3) Utilization of scientific results by politic or technical people=20 > without checking the results could be very dangerous; > > But I have the impression that Andrej himself falls in the trap. And=20= > especially when he says that : > > " I guess I am trying to point out that current Computer Alegbra=20 > Systems are very tricky to use_correctly" > > Indeed CAS are very complex systems built over several thousands of=20 > functions, called primitive. CAS are NOT only tools and moreover they=20= > are NOT global closed tools. They live like a science. Improving all=20= > the time. Growing all the time. > > Each of the functions of a CAS has it's own rules of application. And=20= > exactly as in Mathematics you can't use a theorem if some of the=20 > hypothesis are not satisfied, you can't use properly a function in a=20= > CAS if you are not inside the limits of application of this primitive.=20= > The rules for application of the primitives are clearly given in=20 > Mathematica, in the "Help" menu. For example, I put a screen shot for=20= > the primitive "Limit" as EXAMPLE 1, at this address: > > http://homepage.mac.com/jacquelinezizi/CategoriesQA/ > > As you can see in this screen shot it is written : "Limit by default=20= > makes no explicit assumptions about symbolic functions" . That clearly=20= > means that you can't hope any discussion about the symbol "a" of the=20= > Andrej's limit. > > Nevertheless the solution of this limit can be easily done and=20 > discussed using Mathematica as you can see in the EXAMPLE 2, at the=20= > same address. > > But this does not mean at all that Mathematica is not able to deal=20 > with parameters, as we are going to see. > > > > B) Jacques Carette said: > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > "Engineers and physicists don't use CAS - they use Matlab. The errors=20= > you get there are both worse and better: worse because numerical=20 > algorithms are so much more prone to giving (silent) nonsense, and=20 > better because Matlab cannot phrase any problems which are parametric!=20= > " > > I agree with that. For example, in all numerical systems, the Integers=20= > are limited, depending on the machine you work on. That is not the=20 > case in CAS were Integers are as large as you want, like in=20 > Mathematics. This is important as it produces sometimes hidden=20 > mistakes in embedded computations, that lead to a wrong result. > > Now, I must say that I don't agree with what Jacques Carette says in=20= > the following paragraph about people developing CAS: > > "This is exactly the kind of parameter specialization problem where=20 > CAS designers have "chosen" to ignore and return a generic answer.=20 > This has been documented since at least 1991 in a nice paper in the=20 > Bulletin of the AMS" > > For example, Mathematica has been giving results, for quite a few=20 > years now, using "Assumptions" for some primitives. I give an example=20= > for the primitive " Integral" in EXAMPLE 3 at the same address. You=20= > can see, on this example, that Mathematica deals quite well with=20 > parameters, both for questions AND answers. Better than I can do... > > > Conclusion > =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D > Happily there are more and more people working hard and well in CAS=20 > theory! The problems that they cannot solve, just as in Mathematics,=20= > are infinite. But as Mathematics, Mathematica can already solve, to=20 > day, quite a lot... This has very little to do with specific numerical=20= > tools programmed for specific aims. > > > Jacqueline Zizi >