Hi! On Nov 6, 6:10 am, Nick Alexander <[EMAIL PROTECTED]> wrote: > >> Would you consider this weird if you read it in a paper, or > >> would you know how to interpret it? > > >> "Let $f = x^3 + x + 1$ and consider $f(10)$." > > > I'm not so sure I know what to do with that.
Neither am I. <pedantic> If I read $f(x) = x^3 + x + 1$ in a paper then I would interpret f as a polynomial function and hence expect $f(10)=10^3+10+1$. But in the way William stated it, I would interpret f as a polynomial, not a function. And then, being referee for Williams paper and being in pedantic mode, I might complain that he should use $ev(f,10)$ (evaluation) or something like that, since polynomials aren't functions. >From that point of view, I think that Sage should distinguish polynomials and polynomial functions. Of course, there should be an easy transition between the two things, say, if f is a polynomial in x and y, then f.as_function() should be a function in two variables. And there should be an evaluation function, say, f.eval(10,15), which does the same as f.as_function()(10,15) </pedantic> However, as a nice person and reader of Williams paper, I would probably correctly guess that $f = x^3 + x + 1$ denotes a polynomial *and* a polynomial function. Moreover, if we talk about *commutative* polynomials then the interpretation x^3(10) = x(x(x(10))) suggested by Robert simply can't be the one we want, since then x*y(10) = x(y(10)) \not= y(x(10)) = y*x(10). Hence, I think it is ok that multivariate commutative polynomials in Sage are callable, by being considered as polynomial functions. But for (freely) non-commutative polynomials I agree with Robert's objection. If f is a non-commutative polynomial in two variables, then I would want that f(a,b) is only defined for *callable* objects a and b, and would return a callable object, by interpreting x*y(a,b) = a(b(.)) and y*x(a,b) = b(a(.)) Cheers Simon --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---