Sorry my Mistake, but if you look into the text you quoted, I already corrected it: ... > ... The ring of analytic > functions is an Integral domain. ... Continous is of course not sufficient.
On Thursday, December 19, 2013 10:12:15 AM UTC+1, John Cremona wrote: > > On 19 December 2013 09:04, maldun <dom...@gmx.net <javascript:>> wrote: > > The fact, that SR is not a field is interesting, the Kronecker delta > example > > on the ticket shows it quite well. But the problem originates from the > fact, > > that the Kronecker delta is not a continuous function. The ring of > analytic > > functions is an Integral domain. > > No it is not. The product of max(0,x) and max(0,-x) is 0. > > John > > > > > Question: Should we define a subset of SR which is a field (at least in > > theory) to make some things cleaner? A quite practical approach > > would be the field of meromorphic functions, which covers the most daily > > problems in symbolic computation. (It would be also quite interesting in > > view of defining differential algebras) > > > > What I mean is that we should only allow expressions of meromorphic > > functions in the symbolic field, i.e. we would only allow variables, > > trigonometric functions and so on. > > SR should be then a superset where everything else should also be > allowed. > > > > On Wednesday, December 18, 2013 8:18:56 PM UTC+1, Nils Bruin wrote: > >> > >> On Wednesday, December 18, 2013 9:58:15 AM UTC-8, vdelecroix wrote: > >>> > >>> Users of polynomials should worry about the coefficient ring. What do > >>> someone should expect of > >>> > >>> sage: (6*x^2 - 12).factor() > >>> > >>> The answers are different in ZZ[x], QQ[x] and RR[x]. For a symbolic > >>> polynomial there is no way to make it coherent... > >> > >> It's worse: SR isn't even an exact ring (and it has zero divisors; > >> seehttp://trac.sagemath.org/ticket/11126#comment:2) , so a lot of > polynomial > >> arithmetic you'd normally expect to work, doesn't in general. > >> > >> So yes we can define polynomial rings with coefficients in SR: > >> > >> sage: SR['x'] > >> Univariate Polynomial Ring in x over Symbolic Ring > >> sage: (1+sin(2))*x-2.3 > >> (sin(2) + 1)*x - 2.30000000000000 > >> > >> but any nontrivial computation in it will be problematic (I take this > as > >> definition of nontrivial here). > >> > >>> > >>> And I guess a long term goal of Sage would be to make it disappear. > >> > >> > >> It IS good for some things: integration strategies and some symbolic > >> differential equation solving methods do benefit from the loose > approach > >> that SR takes with mathematical expressions. > >> I think a more attainable goal is to allow the user to avoid SR in as > many > >> cases as possible. > > > > -- > > You received this message because you are subscribed to the Google > Groups > > "sage-devel" group. > > To unsubscribe from this group and stop receiving emails from it, send > an > > email to sage-devel+...@googlegroups.com <javascript:>. > > To post to this group, send email to > > sage-...@googlegroups.com<javascript:>. > > > Visit this group at http://groups.google.com/group/sage-devel. > > For more options, visit https://groups.google.com/groups/opt_out. > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
