I don't know how much verbiage to contribute to this notion of "returning infinity" being open to question. Just a few notes. When we say integrate from 0 to infinity, is "infinity" a value? Not really. We are asking about the computation of integration from 0 to Z where Z increases without limit in the positive real direction. Specifically, does it approach a finite value? Or alternatively, does it not have a specific limit (e.g. oscillates) or does it increase beyond any finite value? This last alternative is not the same as "returns a finite value named infinity" because you can do arithmetic with finite values that you can't do with infinity. If a user types in infinity, it is a shorthand for some kind of language involving limits. Even if the user doesn't acknowledge or realize that. Returning infinity is inevitably problematical, even if the system goes to the effort of simplifying infinity-infinity to something like "indefinite". Somewhat more supportive of continued computation is an interval [-oo,oo]. In this context oo can be identified as a special signifier for an interval that is unbounded at one or both ends. Not that it has the value infinity at an endpoint.
Sometimes doing math by computer ends up requiring subtleties. RJF On Monday, March 13, 2017 at 5:53:33 AM UTC-7, kcrisman wrote: > > As it happens, in this case the underlying problem is that we send such > unevaluated integrals to GSL when asked for a numerical approximation, > which can't handle this kind. Raising some kind of error or divergence > notification makes more sense than returning infinity in any case. > -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
