On 19 December 2013 09:04, maldun <dom...@gmx.net> 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+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. -- 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.
