On Wednesday, June 16, 2010, Tom Coates <t.coa...@imperial.ac.uk> wrote: > > > On 16 June, 07:48, rjf <fate...@gmail.com> wrote: > >> By your reasoning, and for other domains we would have the following >> behavior: >> >> 1-2 --> error. 1 and 2 are both positive integers. In order to >> provide the answer -1, one must >> expand the domain to include negative integers. >> >> 1 / 2 --> error.. (integers vs. rationals). Indeed there are >> some systems (Axiom) that warn about such things. >> >> sqrt(-1) --> error. after all, some Sage users may not have >> encountered imaginary numbers. > > This is not correct, because by "domain" I meant "the set on which the > function is defined", i.e. the set of permissible *inputs* to the > function. With this definition of domain, none of the operations you > discuss should raise an error: there is no reason in general why the > *output* from a function should lie in the domain of that function. > > That said, if the consensus is that factorial(x) should be > analytically continued, to allow x to be an explicit non-integral > number (as is the case in Maple and Mathematica), then I am happy with > this. But then we should change the documentation of factorial() to > make this clear. > > At the moment there does not seem to be a clear consensus either way. > If you have an opinion on this, please vote! Let x be an explicit > numerical value such that x is not a non-negative integer (e.g. x=2/3, > x=1.5, or x=i). The options are: > > A) factorial(x) should raise an error; > > B) factorial(x) should return gamma(x+1). >
I vote for B, because: * backwards compatibility - we don't break existing code; voting for A means potentially breaking tons of code out there and pissing off users * gamma(x+1) is "socially" the canonical extension of factorial to C * there are technical conditions one can impose under which gamma(x+1) really is the canonical extension of factorial - see wikipedia William > Best, > > Tom > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org > -- William Stein Professor of Mathematics University of Washington http://wstein.org -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
