Re: Problem with element and Maximize

*To*: mathgroup at smc.vnet.net*Subject*: [mg82814] Re: [mg82746] Problem with element and Maximize*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Wed, 31 Oct 2007 06:20:56 -0500 (EST)*References*: <4209462.1193744482571.JavaMail.root@m35>*Reply-to*: drmajorbob at bigfoot.com

Don't round the real-valued solution; it won't always get you the best integer solution. But this should work: data = {{0, 0}, {10, 10}, {20, 0}, {30, 10}}; eq = Fit[data, {1, x, x^2, x^3}, x] proxy = Rationalize[eq, 10^-15] Maximize[{proxy, x \[Element] Integers, x <= 20}, x] eq /. Last@% 1.96128*10^-15 + 3.33333 x - 0.3 x^2 + 0.00666667 x^3 1/509872338168900 + (10 x)/3 - (3 x^2)/10 + x^3/150 {5567805932804389/509872338168900, {x -> 7}} 10.92 Without the upper bound the function has no maximum and, with approximate coefficients, Maximize can't use efficient integer optimization methods. Bobby On Tue, 30 Oct 2007 03:31:51 -0500, Uncle Paul <paul at desinc.com> wrote: > I'm not sure what I am doing wrong. I am trying to get the nearest > integer maximim for the mentioned equation. I could round the X > value, but I would like to operate Mathematica correctly. > > (*generate the equation*) > data = {{0, 0}, {10, 10}, {20, 0}, {30, 10}}; > eq = Fit[data, {1, x, x^2, x^3}, x] > Plot[eq, {x, 0, 30}] > > Maximize[{eq, x \[Element] Integers}, x] (*wrong!*) > > Maximize[{eq}, x] (*correct, but not integer, of course*) > > > Best Regards, > Paul > > -- DrMajorBob at bigfoot.com