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>