We know that x^2-2xy+y^2 is nonnegative if x and y are real variables, since it is equal to (x-y)^2. Furthermore, when we know beforehand that a is positive, x^2-2xy+y^2+a is positive. FindSign gives you the sign of a polynomial of several variables and parameters, all of which are in real domain.
"FindSign.m" is a Mathematica package for determing signs, and "FindSign.exe" is a front-end program for an easy-to-use manipulation.
After starting FindSign.exe, you will see
Type an expression in the "Expression" box. Type variables of which signs are known in the corresponding box of the "Sign-Known Varialbes." Press the "Evaluate" button and you get the answer in the "Output:Sign" box. Pressing the "See Structure" gives you the information of a polynomial as:
It is easy, isn't it?
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Yuji Itaya: itaya@alice.asahi-u.ac.jp