IANAM (I am not a mathematician), but from what I see, all the problem comes from the fact that mathematical notation itself (in paper) may be ambiguous. Imagine for example that you see in a paper $f(a+b)$. From common notation one would guess that f is a function and that I'm replacing it's variable with (a+b). However, if one sees $x(a+b)$ the most common interpretation would be the same as $x*(a+b)$. So, what's the difference? Just a name change. As robert put it, x^3(10) could be x(x(x(10))) if that meant x*(x*x*(10))), but in paper we usually don't write the multiplication operators, using implicit multiplication like William himself explained:
sage: implicit_multiplication(True) sage: var('x') x sage: 3x^3 + 5x - 2 3*x^3 + 5*x - 2 though writing xx wouldn't give the desired result. Then, it becomes important that a computer doesn't have the same parsing system as we humans do (and any attempt to replicate that would, well, you can imagine). The thing is that we are building a computer system to deal with those problems, and in that we must make design decisions based on what's easier/common/fast/etc. In my opinion, it would be better to have all functions be declared like $ f(x) = x^3 + x + 1 $ or just use python's def for functions and "*" for multiplication to make all cases clear. After all, quoting import this: "There should be one-- and preferably only one --obvious way to do it." Ronan Paixão Em Qua, 2008-11-05 às 21:10 -0800, Nick Alexander escreveu: > > On 5-Nov-08, at 8:55 PM, Robert Dodier wrote: > > > > > William Stein 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. > > I find this bizarre. I am absolutely certain that I want to view $f$ > as a polynomial in one variable and evaluate it at 10. > > I can think of lots of alternate ideas (evaluate everything to > bottom!) but I believe none of them are common. Can you cite a paper > that uses the notion of $x^3$ denoting the three-fold composition of a > function $x$ and considering $f = x^3$ and $f(10)$ intending the three- > fold composition of $x$? > > Nick > > > --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---