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Re: How to use a returned pure function from say, Maximize
*To*: mathgroup at smc.vnet.net
*Subject*: [mg89264] Re: How to use a returned pure function from say, Maximize
*From*: dh <dh at metrohm.ch>
*Date*: Mon, 2 Jun 2008 04:31:18 -0400 (EDT)
*References*: <g1v178$24j$1@smc.vnet.net>
Hi Christoph,
we do not have any functions here, we have Root objects (look it up in
the manual), that is, definite algebraic numbers. You may get a machine
Number by using N[..], but you know this already.
The first number in your output is the maximum, the second gives the
correponding x value.
hope this helps, Daniel
christophsk at gmail.com wrote:
> When I as Mathematica to maximize (over x) the expression
>
> \frac{1}{2} \left(x \left(-2 \sqrt{1-x^2}+\sqrt{3-4 x (x+1)}+2\right)+
> \sqrt{1-x^2}\right)
>
> I am returned this (after simplifying) - you can try it yourself,
>
> {1/2 Root[
> 47972 - 156976 #1 + 144464 #1^2 + 616 #1^3 - 55340 #1^4 +
> 18312 #1^5 + 1316 #1^6 - 964 #1^7 - 47 #1^8 + 64 #1^9 +
> 16 #1^10 &, 5], {x ->
> Root[-351 + 1440 #1 + 2520 #1^2 - 12672 #1^3 - 8192 #1^4 +
> 38528 #1^5 + 18176 #1^6 - 44032 #1^7 - 19968 #1^8 +
> 16384 #1^9 + 8192 #1^10 &, 5]}}
>
> Bear in mind, this is just an example, but it illustrates the point.
> It is Ron Graham's Biggest Little Hexagon in case you want to look
> it up.
>
> I can obviously recover the numerical value. But if I actually wanted
> to use this function, ie, substitute other expressions, manipulate it in some
> way, how do I do this?
>
> More to the point, I've always been a bit confused how to make use of
> such a returned pure function.
>
> Any help appreciated.
>
> Thanks in advance.
>
--
Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh at metrohm.com>
Internet:<http://www.metrohm.com>
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