       Re: How can I write the input code for a comparison

• To: mathgroup at smc.vnet.net
• Subject: [mg119861] Re: How can I write the input code for a comparison
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Sun, 26 Jun 2011 06:26:28 -0400 (EDT)
• References: <201106250928.FAA20187@smc.vnet.net>

```m > n is not always true, since:

m = (6 + 4 R + B^2 R - 5 R^2 - R^3 + R^4 + B (R^2 + R - 2));
n = (6 + 4 r + k^2 r - 5 r^2 - r^3 + r^4 +
k (r^2 + r - 2)); condition = {0 < r < R < 1, 0 < k < B < 1};

FindInstance[Flatten@{m < n, condition}, {r, R, k, B}, Reals]

{{r -> 1/64, R -> 283/16384, k -> 1/4, B -> 513/1024}}

Bobby

On Sat, 25 Jun 2011 04:28:00 -0500, Nan <nzxos at yahoo.com> wrote:

> Sorry for the notation misusage problem in my previous post, it should
> be:
>
> I need to compare M with N
> M=(6+4R+B^2 R-5R^2-R^3+R^4+B(R^2+R-2))
> N=(6+4r+k^2 r-5r^2-r^3+r^4+k(r^2+r-2)),
> where 0 < r < R < 1, 0 < k < B < 1.
>
> Notice that M and N have same form of functions but with different
> variables. Actually I need to prove that they have certain relationship,
> say M>N. How can I do that by Mathematica? Can I use MinValue or
> FindMinvalue? That is, if the minimum value of M - N >0, then M > N. How
> can I write the input command so that I can include the constraint?