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How can I write the input code for a comparison

• To: mathgroup at smc.vnet.net
• Subject: [mg119828] How can I write the input code for a comparison
• From: Nan <nzxos at yahoo.com>
• Date: Fri, 24 Jun 2011 07:46:32 -0400 (EDT)

I need to compare
A=(6+4R+B^2 R-5R^2-R^3+R^4+B(R^2+R-2))
with
B=(6+4γ+β^2 γ-5γ^2-γ^3+γ^4+β(γ^2+γ-2)),
where 0 < γ < R < 1,  0 < β < B < 1.

How can I do that by Mathematica? Can I use MinValue or FindMinvalue? That is, if the minimum value of A - B >0, then A>B. How can I write the input command so that I can include the constraint? Please help! Thanks a lot!