Definition [Monomial of max-degree 1]. Given n variables x 1 , . . . ,...
Definition [Monomial of max-degree 1]. Given variables , a multivariate monomial of max-degree 1 is an expression of the form: , where and all exponents are either 0 or 1.
For example is a monomial of max-degree 1, but is not.
Definition [Polynomial of max-degree 1]. A polynomial of max-degree 1 is a sum of multivariate monomials of max-degree 1.
For example: is a Polynomial of max-degree 1.
Definition [System of Polynomial inequalities of max-degree 1]. A system of polynomial inequalities is a finite conjunction of inequalities of the form or or .
I have came across this notion recently, and I am not at all an expert. I have the following question
QUESTION Can a system of polynomial inequalities of max-degree 1 have a solution in the reals R but none in rationals ? Any example?