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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