On Thu, Nov 6, 2008 at 6:10 AM, Nick Alexander <[EMAIL PROTECTED]> wrote:
>
>
> 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 $x$?

What if I cite Sage instead? :-)

sage: x = SymmetricGroup(10).random_element(); x
(1,9,5,7,3,10,6,4,2)

sage: f = x^3; f
(1,7,6)(2,5,10)(3,4,9)

sage: f(10)
2

Franco

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