Overall, I think the proposed change makes sense in the long run, and Peter presents a good case. But there are some dangers.
Foremost, Clemens argues that a change will potentially brake user code: while this is true, I think it should be overruled for the long benefits, if another behaviour is mathematically preferable. Note also that the proposed change *only* differs from current behaviour when *both* n and k are negative (and |n| <= |k|); I think that the most common out-of-ordinary-bounds call on binomial coefficients has k negative while n positive (*). As Nils Bruin points out on #17123, agreement with Maxima is also a concern. But Nils Bruin's own test demonstrates that Sage currently *doesn't* agree to Maxima. Maxima seems to use a strange mix between Knuth's definition and the one proposed in #17123: it seems to match #17123 except on binomial(n, n) for negative n, where it is zero while #17123 dictates 1. binomial(n, n), n<0 is a case explicitly discussed in Concrete Mathematics, so that might be why Maxima does this? Volker Braun argued to add an optional argument `extension` to allow choosing which behaviour to use. This covers all bases but leaves the question as to which default to choose. I vote for having #17123 as the default *in the long run*. If so, what to do in the short run to mitigate user problems. We could 1) Return the value of #17123 but print a deprecation warning on input with conflicting behaviour. The warning tells the user to explicitly set the optional argument if he wants to disable the warning. Warning is removed in ~1 year. 2) Return the current value, but print a deprecation warning on input with conflicting behaviour. After one year, change the behaviour with no more deprecation warnings. Best, Johan (*): Admittedly, that might be a total bogus impression. Peter Luschny writes: > > Sage seems to use the definition from Concrete Mathematics by Graham, >> Knuth and Patashnik: >> That gives e.g. >> sage: binomial(-4, 5) >> -56 > > Right. GKP call it "upper negation". If you look at my demo-function > you will see that this condition is preserved in the suggested extension > (case 3). The proposal returns a superset of the current values. > >> Concrete Mathematics is seen as something >> of a bible in large parts of computer science, and it's unfortunate to >> disagree with a basic definition in there. > > It /extends/ this definition. As long as k>=0 nothing will change > compared to the GKP definition. Upper negation will be untouched. > > Peter -- -- 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 https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
