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 continuous functions is an Integral domain. 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.
